Modern Physics Laboratory Manual Phys 381

Modern Physics Laboratory Manual

Phys 381

Contents:

Experiment No. 1: Alpha-particle scattering

Experiment No. 2: Millikan's experiment

Experiment No. 3: Frank-Hertz experiment

Experiment No. 4: Electron diffraction

Experiment No. 5: The specific charge of the electron

Experiment No. 6: Photoelectric effect

By Salman Aboud

1

Experiment No. 1

Alpha particles scattering

Introduction:

John Dalton explained atom as a hard, dense and smallest indivisible particle of

matter. However, the emission of radioactive rays from radioactive elements proved

that atom is not an indivisible but consists of some fundamental particles called as

subatomic particles.

The next step in the identification of atomic structure was taken by J. J. Thomson.

He discovered the negatively charged particles in cathode rays and calculates the

charge by mass ratio by subjecting the beam of electrons produced in a discharge

gas tube. Robert Millikan determined the charge on electron by using the oil drop

experiment that is equals to 1.6 x 10^-19coulomb.

The careful experiments with discharge tubes containing perforated cathode reveal

the emission of another type of radiations which starts from anode and pass through

the holes of the cathode. These radiations called as canal rays or positive rays contain

positively charged particles which attracted towards negatively charged cathode.

These positively charged particles termed as protons. To explain the distribution of

electrons and protons in an atom, J.J. Thomson purposed the Plum-Pudding model.

The next step in the development of atomic model was given by Ernest Rutherford

in 1911. Rutherford used a "Gold foil experiment" for explaining the atomic model

given by J. J. Thomson. A decade earlier, Rutherford only identified one of type of

radiation given off by radioactive elements like polonium, uranium etc and named

them as alpha particles.

one

Highlight

2

The Objectives:

1- To record the direct counting rate of Alpha particles scattered by a gold foil and

aluminum foil as function of the angle.

2- To classify the relation between the number of counts and the angles.

3- To demonstrate a new model of the atom based on the data gained from the

experiment.

The theory:

According to Dalton’s atomic theory the atom was indivisible and indestructible.

But the discovery of two fundamental particles (electrons and protons) inside the

atom, led to the failure of this aspect of Dalton’s atomic theory. It was then

considered necessary to know how electrons and protons are arranged within an

atom. For explaining this, many scientists proposed various atomic models. J.J.

Thomson was the first one to propose a model for the structure of an atom.

Thomson proposed that:

(i) An atom consists of a positively charged sphere and the electrons are embedded

in it

(ii) The negative and positive charges are equal in magnitude. So, the atom as a

whole, is electrically neutral.

Although Thomson’s model explained that atoms are electrically neutral, the results

of experiments carried out by other scientists could not be explained by this model.

Based on Thomson’s model, Rutherford expected that the positively charged alpha

particles should pass throughout the uniform sphere of positively charged matter

with little or no deflection.

Rutherford model of an atom:

Ernest Rutherford was interested in knowing how the electrons are arranged within

an atom. Rutherford designed an experiment for this. In this experiment, fast moving

alpha (α)-particles were made to fall on a thin gold foil.

• He selected a gold foil because he wanted as thin a layer as possible. This gold foil

was about 1000 atoms thick.

3

• Alpha-particles are doubly-charged helium ions. Since they have a mass of 4 u,

the fast-moving α-particles have a considerable amount of energy.

It was expected that α -particles would be deflected by the sub-atomic particles in

the gold atoms. Since the α-particles were much heavier than the protons, he did not

expect to see large deflections. But, the α -particle scattering experiment gave totally

unexpected results. A brilliant demonstration of how the two different models of

atoms would look if they were performed in the same manner of alpha particle

experiment in Figure 1.

Figure 1: a comparison between the two models and how Rutherford's experiment would be seen

if it's carried upon each model.

The principles of the experiment that will be performed is that If α-particles are

allowed to strike a thin gold foil, they are deflected from their path (“scattering“),

each by an angle θ. The majority of α-particles is scattered by angles less than 1°. A

few particles, however, show substantially larger scattering angles θ, in the extreme

case up to 180° (“back scattering“). These initially qualitative observations can only

be explained by assuming that the gold atoms have a very small nucleus, containing

practically the whole atomic mass, and being positively charged. On the basis of this

4

idea Rutherford calculated the angular distribution of the scattering rate N(θ). The

scattering rate is the number of particles which are scattered during the time unit in

a determined interval dθ around an average angle θ. The result of this calculation is

“Rutherford’s scattering formula “:

The experimental setup:

The apparatus of the experiment as performed by Rutherford is different from the

one that we will perform the experiment with. Therefore, the old setup was the

same as Figure 1 and the new setup is demonstrated in Figure 3 and completed in

Figure 4.

5

Figure 2: the old setup

Figure 3: The scattering chamber

Figure 4: The complete set-up

The description of numbers: (1) Preparation (alpha source Americium- 241) (2)

Holder: hold the foil and slit in place (3) Slit: defines the beam width and divergence

of the alpha particles (4) Gold foil and aluminum foil about 2 micrometer thick (5)

swivel arm adjustment for incidence angle (6) detector (7) vacuum chamber

6

(scattering chamber): the vacuum chamber where the scattering takes place.(8)

Discriminator or preamplifier: to match the signal between the detector and the

counter (converts the current signal from the detector to a voltage pulse (9) counter:

count the number of voltage pulses. (10) Vacuum pump: pumps the scattering

chamber to prevent collisions of the alpha particles with gas atoms in the chamber.

(11) Power supply Supplies power.

The procedure:

The procedure mainly has three parts, the first one is recording the scattering rate as

function of the angel: In this case we don't need to care about the proportionality

factors in equation (I) which are kept constant in our experiment. The relevant shape

of this angular distribution curve is described by the function:

𝑵(𝜽) = 𝒔𝒊𝒏−𝟒 (𝜽

𝟐)

The scattering rates confirms the relation:

𝒏(𝜽) ≈ 𝒁𝟐

For each scattering angle calculate the counting rate, record your results in the

table.

The second part of the procedure is preparing the electrical counting components:

Connect the scattering chamber, discriminator preamplifier and counter S. Set

discriminator to zero (turn potentiometer fully anticlockwise).

And last but not least, the last step is how to record the scattering rate as function of

the angle:

Prepare the counter S for pulse counting by pressing the push button MODE to

activate NA,E.

7

Select gate time t(θ) = 100 s by pressing the toggle button GATE three times Note:

t(θ) = 100 s is useful for small angles, i.e. angle up to +/ 15°. By pressing GATE +

MODE, longer gate times are can be adjusted, i.e. up to 9999 s (MODE upwards,

GATE downwards).

Data and Analysis:

We notice that after taking the measurements of the counts, the values of f(Ɵ)

decrease rapidly with increasing scattering angle Ɵ. Hence, the graphical

representation of f(Ɵ) is plotted in a logarithmic scale over Ɵ. A singularity spot

becomes visible at Ɵ = 0°. Therefore, we will compare measuring results with the

theoretical slope only outside of this region, i.e. for values Ɵ ˃ 5°.

As for higher scattering angles θ the counting rates become very small, the gate times

t(θ ) for determining the counting rate N(θ) have to be increased with increasing

angle θ to obtain an acceptable accuracy.

Upon the basis of the same results mentioned, the results which Rutherford gained

is that he observed that the majority of alpha particles (97%) penetrated the foil either

undeflected or with only a slight deflection (2-3% were deflected). In some

instances, an alpha particle actually bounced back in the direction from which it had

come (Less than 1% bounced back). This was a most surprising finding, for in

Thomson’s model the positive charge of the atom was so diffuse or spread out, that

the positive alpha particles were expected to pass through the foil with very little

deflection. Upon making this discovery Rutherford explained it was almost as

incredible as if you fired a 15-inch shell at a piece of tissue paper, and it came back

and hit you.

The measured values of which we performed are recorded in Table 1.

8

Table 1: Measured values (with gold foil)

9

Now, we demonstrate the results in a graph that could assert the relation between the

scattering angles and the function:

Figure 5: Results (filled circles) with a shifted fitting curve according for the equation

N(𝜽) = 𝒔𝒊𝒏−𝟒 (𝜽

𝟐)

And for further confirmation of the relation between the pulse counts and the

scattering angels, we performed the same procedure for different values of voltage

of the preamplifier.

10

• The first trial must be performed with -0.2 V in the preamplifier and the gained

results must be written in the following Table 2:

Angles (𝜽)

Average pulse counts n (𝜽)

Table 2: Measured values with -0.2 V (gold foil)

• After you measured the values, you must plug the angles versus pulse counts

values in a graph to demonstrate the relation between them.

• The second trial must be performed with -0.4 V in the preamplifier the gained

results must be written in the following Table 3:

Angles (𝜽)


Table 3: Measured values with -0.4V (gold foil)

11



• The third trial performed with -0.3 V in the preamplifier and we gained the

following data in Table 3:

Angles (𝜽)


Table 4: Measured values with -0.3V (gold foil)



12

Now, it's confirmed that the values of f(Ɵ) in gold foil decrease rapidly with

increasing scattering angle Ɵ. And as for higher scattering angles θ the counting

rates become very small, the gate times t(θ ) for determining the counting rate N(θ)

have to be increased with increasing angle θ to obtain an acceptable accuracy. It's so

important to know that the gate times for the three graphs above is 100s.

What if we compare the scattering rates between the gold foil as we performed

previously and Aluminum foil? at the same angle and preamplifier voltage (-0.3V).

Shall we get a lower counting rate than the gold foil? Or higher? supposing that we

know the nuclear charge number of Aluminum (Z=13) and Gold (Z=79) . We first

measured the values of the pulse counting (gold foil) in -0.3V, the data are in Table

4. Then, we measured the value of pulse counting (aluminum foil) in -0.3V for only

one angle in Table 5, afterwards, we plot the aluminum foil single angle counting

rate and the gold foil same angle in a graph in order to assert the relationship between

the two parameters.

Table 5: Measured values with

-0.3V

The foil material

Angles (𝜽)

Average pulse

counts n (𝜽)

Gold 5

Aluminum 5

13

Discussion

Rutherford proposed and concluded from this experiment the following:

Most of the space inside the atom is empty because most of the α-particles passed

through the gold foil without getting deflected. Very few particles were deflected

from their path, indicating that the positive charge of the atom occupies very little

space. A very small fraction of α-particles were deflected by very large angles,

indicating that all the positive charge and mass of the gold atom were concentrated

in a very small volume within the atom.

From the data he also calculated that the radius of the nucleus is about 105 times less

than the radius of the atom. Based on his experiment, Rutherford put forward the

nuclear model of an atom, which had the following features:

There is a positively charged center in an atom called the nucleus. Nearly all the

mass of an atom resides in the nucleus.

Apparently, there's a clear relationship between the counts number function

(counting rate) and the detector angles, and it's inverse proportional.

We found also that the scattering rate counts difference between the aluminum foil

and the gold foil is about ten times, which implies that the composition of the

material plays a massive rule in determining the number of counts.

Furthermore, while we were conducting and gathering the readings of aluminum foil

counting rates, we got some contradicting values, and that occurred because of some

wrinkles which impeded the alpha particles and deflected them and eventually, made

error readings in the digital counter.

1

Experiment No. 2

Millikan's Experiment

Introduction

In the early 20th century, it is known that the molecules are composed of the atoms

and their constituent particles are proton, neutron and electron, although it was not

widely accepted phenomenon. As the scientist community was not united on the

existence of atoms and their constituent particle hence the associated parameters of

these particles were unknown at that time. Several scientists conducted various

experiment to establish the very existence of the particle by find the various

parameters associated with these particles, like mass, charge, etc.

The initial experiment for finding the charge was conducted by Thomson, while he

was working on the Roentgen’s x-rays experiment. He performed an experiment on

the x-rays to find the discrepancy in the behavior of the cathode rays under varying

electric and magnetic fields.

Although he was not able to establish the mass or the charge of the elementary

particle, but he was able to find the ratio of charge to mass (e/m). This ratio helps,

to a large extent, Professor Millikan to find the charge of the electron in his path

breaking experiment. His experiment was termed as Millikan’s Oil Drop

Experiment.

After Thomson’s and Rutherford’s experiments, it was confirmed that protons are

positively charged particles whereas electrons are negatively charged particles. The

overall charge on an atom must be zero. Next task must be the determination of

charges which must be same on electrons and protons to get a neutral atom. In 1911

American physicist Robert Millikan performed an experiment to determine the

charge of electrons. He calculated the terminal velocity of the drop to find the charge

on a drop.

one

Highlight

one

Highlight

one

Highlight

2

The objectives:

1- To calculate the time that the oil droplet takes to reach a determined distance.

2- To calculate the charge of the electron.

3- To demonstrate the relation that occurs as integral multiples of an elementary

charge e.

The theory:

The experiment entailed observing tiny electrically charged droplets of oil located

between two parallel metal surfaces, forming the plates of a capacitor. The plates

were oriented horizontally, with one plate above the other. A mist of atomized oil

drops was introduced through a small hole in the top plate. First, with zero applied

electric field, the velocity of a falling droplet was measured. At terminal velocity,

the drag force equals the gravitational force. As both forces depend on the radius in

different ways, the radius of the droplet, and therefore the mass and gravitational

force, could be determined (using the known density of the oil). Then, a voltage,

inducing an electric field, was applied between the plates and adjusted until the drops

were suspended in mechanical equilibrium, indicating that the electrical force and

the gravitational force were in balance. Using the known electric field, Millikan and

Fletcher could determine the charge on the oil droplet. By repeating the experiment

for many droplets, they confirmed that the charges were all small integer multiples

of a certain base value, which was found to be 1.5924(17) × 10−19 C, about 0.6%

difference from the currently accepted value of 1.602176487(40) × 10−19 C.They

proposed that this was the magnitude of the negative charge of a single electron.

Initially, the oil drops are allowed to fall between the plates with the electric field

turned off. They very quickly reach a terminal velocity because of friction with the

air in the chamber. The field is then turned on and, if it is large enough, some of the

drops (the charged ones) will start to rise. (This is because the upwards electric force

3

FE is greater for them than the downwards gravitational force Fg, (in the same way

bits of paper can be picked by a charged rubber rod). A likely looking drop is selected

and kept in the middle of the field of view by alternately switching off the voltage

until all the other drops have fallen. The experiment is then continued with this one

drop.

The drop is allowed to fall and its terminal velocity v1 in the absence of an electric

field is calculated. The drag force acting on the drop can then be worked out using

Stokes' law:

𝐅𝐝 = 𝟔𝝅𝒓𝜼𝒗𝟏

where 𝑣1 is the terminal velocity (i.e. velocity in the absence of an electric field) of

the falling drop, η is the viscosity of the air, and r is the radius of the drop.

The weight w is the volume D multiplied by the density ρ and the acceleration due

to gravity g. However, what is needed is the apparent weight. The apparent weight

in air is the true weight minus the upthrust (which equals the weight of air

displaced by the oil drop). For a perfectly spherical droplet the apparent weight can

be written as:

𝑾 =𝟒𝝅

𝟑𝒓𝟑(𝛒 − 𝛒𝐚𝐢𝐫)𝒈

At terminal velocity the oil drop is not accelerating. Therefore, the total force

acting on it must be zero and the two forces F and W must cancel one another out

(that is, F = w). This implies:

𝒓𝟐 =𝟗𝜼𝒗𝟏

𝟐𝒈(𝛒 − 𝛒𝐚𝐢𝐫)

Once r is calculated, W can easily be worked out.

Now the field is turned back on, and the electric force on the drop is

𝑭𝑬 = 𝒒𝑬

4

where q is the charge on the oil drop and E is the electric field between the plates.

For parallel plates.

E is calculated as follows:

𝑬 =𝑽

𝑫

where V is the potential difference and d is the distance between the plates.

One conceivable way to work out q would be to adjust V until the oil drop

remained steady. Then we equate the both equal forces (F and W) and after that we

substitute the value of W in the equation to get the charge:

𝒒𝑬 = 𝑾 → 𝒒 =𝑫 ∙ 𝑾

𝑽

The constants values:

(𝛒 − 𝛒𝐚𝐢𝐫) = 𝟖𝟔𝟗. 𝟕𝟕𝟓 𝑲𝒈. 𝒎−𝟑

𝜼 = 𝟏𝟖. 𝟔 × 𝟏𝟎−𝟔 𝒑𝒂. 𝒔

𝑫 = 𝟔 𝒎𝒎

5

The experimental apparatus:

The Millikan apparatus (Fig.1) is used to verify the quantization of the electrical

charge and to determine the elementary charge by observing the motion of

individually charged oil droplets in a homogenous electrical field.

Figure 1: (1) Base plate (2) Measuring microscope with micrometer eyepiece (3) Plate capacitor

(4) Illumination device (5) Oil atomizer (6) Rubber ball.

Figure 2: 1 Base plate with holder for oil atomizer,

pins for plate capacitor (1)

2 Measuring microscope, Knurled knobs (2a),

micrometer eyepiece (2b)

3 Plate, capacitor Viewing window (3a), acrylic glass

cover (3b),connecting sockets (3c), oil filling openings

(3d)

4 Illumination device with adjusting screws,

condenser (4a), fastening screw (4b), connecting

sockets (4c)

5 Oil atomizer, Spray nozzle (5a), capillary tube (5b)

6

The procedure:

We shall first connect the Millikan supply unit and then carry on preforming the

experiment:

-Connect the plate capacitor with the connector for plate capacitors on the Millikan

supply unit (if need be, use the adapters for the safety plug at the sockets of the plate

capacitor).

- Connect the illumination device to the connector for illumination devices on the

Millikan supply unit and turn on the illumination device.

-Turn the lens holder of the micrometer eyepiece until you can clearly see the

micrometer scale.

- If necessary, turn the eyepiece to orient the micrometer scale vertically. For this

purpose, you should slightly loosen the fastening screw.

- Use the knurled knob to push the measuring microscope close to the plastic cover.

The illuminated capacitor plates can be seen at the top and bottom in the circular-

viewing field. The beginning and end of the micrometer scale are at a small distance

to the capacitor plates.

To eliminate disturbing light reflex or to correct the observation space, if you are not

satisfied with the illumination:

- Loosen the fastening screw of the capacitor and move the capacitor.

- You can also adjust the lamp with the help of the adjusting screw (recessed head

screw).

- Use the rubber ball to spray oil between the capacitor plates so that oil droplets can

be seen in the entire observation field.

7

- By moving the measuring microscope with the help of the knurled knobs (2a),

create a plane, in which a selected oil droplet is clearly seen as light point.

Now, after we set up the apparatus, we exceed to perform the experiment in one of

these methods,

• Floating method

In this version of the experiment, the voltage V at the plate capacitor is adjusted such

that a particular oil droplet floats, i.e. the rising velocity is v2=0. The falling velocity

v1 is measured after switching off the voltage V at the capacitor. Because of v2=0,

the above formulas are slightly simplified.

However, v2=0 cannot be adjusted very precisely for fundamental reasons.

Therefore, the floating

method leads to larger measurement errors and broader scattering in the frequency

distribution than in the case of the following method.

• Falling/rising method

In the second version, the two velocities v1 and v2 the voltage V are measured. This

method makes possible more precise measured values than the floating method

because the velocity v2 is really measured.

Carrying out the experiment

a) Floating method

1) Orient the eyepiece micrometer vertically and turn the lens holder of the

eyepiece until you can clearly see the micrometer scale.

2) First set the switches U and t in the down position

3) Switch the voltage at the capacitor on with the switch U and adjust it with the

rotary potentiometer so (400-600 V) that a selected oil droplet rises with a

velocity of approximately 1-2 scale graduation marks per second (i.e. it is seen

falling when observed through the eyepiece). Then reduce the voltage until the

oil droplet floats.

8

4) Switch the voltage at the capacitor off with the switch U.

5) As soon as the oil droplet is located at the height of a selected scale graduation

mark, start the time measurement with the switch t.

6) As soon as the oil droplet has fallen by another 20 scale graduation marks

(corresponds to 1 mm), stop the time measurement with the switch t and switch

the voltage at the capacitor on again with the switch U.

7) Enter the measured values of the falling time t1 and the voltage U in the table.

The calculated charge q is entered in the histogram automatically.

8) Repeat the measurement for other oil droplets.

b) Falling/rising method

) Orient the eyepiece micrometer vertically and turn the lens holder of the

eyepiece until you can clearly see the micrometer scale.

) First set the switches U and t in the down position.

) Switch the voltage at the capacitor on with the switch U and adjust it with the

rotary potentiometer so (400-600 V) that a selected oil droplet rises with a

velocity of approximately 1-2 scale graduation marks per second (i.e. it is seen

falling when observed through the eyepiece).

) Switch the voltage at the capacitor off with the switch U.

) As soon as the oil droplet is located at the height of a selected scale graduation

mark, start the time measurement with the switch t.

) As soon as the oil droplet has fallen (i.e. risen as observed in the eyepiece) by

another 20 scale graduation marks (corresponds to 1 mm), switch the voltage at

the capacitor on again with the switch U. Thereby the time measurement t2 is

started automatically.

) As soon as the oil droplet is at the height of the first scale graduation mark

again, stop the time measurement with the switch t.

9

) Enter the measured values of the falling time t1, the rising time t2 and the

voltage U in the table. The calculated charge q is entered in the histogram

automatically.

) Repeat the measurement for other oil droplets.

Data and Analysis:

• After you carry the same procedure for the first method, you must be able to

write the gathered data in the following Table 1.

Trial number

D (mm)

Time (s)

V (V)

Velocity (m/s)

1

2

3

4

5

6

7

8

Table 1: The gathered data from the first method

• After you measure the preceding data, you shall find r, W and q for each trial by

the same equations mentioned in the theory part. The calculated results must be

written in Table 2,

10

Table 2: The calculated results

Discussion

Upon the results which we gathered, there's an obvious error percentage appears

when we divide q over the accepted value of the charge of the electron. And this

occurred because of subtle circumstances, however, the ratio between the charge and

the electron charge remains.

The main finding in this experiment is that we shall prove that q only occurs as

integral multiples of an elementary charge e, and thus, the value of the charge is

quantized, since we achieved this aim by calculating the ratio q/e , so as a conclusion

we can say that the charge of the electron is quantized .

Although the Millikan’s experiment is widely known to find the charge of the

electron (or fundamental) particle, he also calculated the mass of the electron using

the calculated charge and the charge to the mass ratio which was given by the

Thomson using the cathode ray tube. The mass of the electron was calculated to be

9.1 x 10-28g. So, with the single experiment Millikan was able to find both the mass

as well as charge of the electron.

Trial number r (m) W (

𝑲𝒈.𝒎

𝒔𝟐)

q (C) q/e

1

2

3

4

5

6

7

8

Average

1

Experiment No. 3

Frank-Hertz Experiment

Introduction

The Bohr model of the hydrogen atom was successful in that it correctly explained

the spectrum of radiation from these atoms to high accuracy. The model indicated

the presence of discrete electronic energy levels in atoms, which could be computed

on the hypothesis that the angular momentum of the orbiting electrons was

quantized. A combination of the concept of quantized energy levels with the idea

that quanta of radiation can only be emitted (with frequency given by the Einstein

relation) when an atom changes its energy to a more tightly bound state, completed

the explanation of the spectrum of atomic hydrogen. There are, however, other ways

to get more direct evidence of the existence of discrete energy levels in atomic

systems.

In this experiment we shall examine the effect of bombarding atoms of argon with

electrons. Since atoms are believed to have discrete energy levels one would expect

that in collisions with electrons, the transfer of energy to the atom should occur in

discrete amounts. One possible mechanism would be inelastic scattering in which a

discrete amount of the incident electron energy is absorbed by the whole atom which

is thus raised to an excited state. The kinematics of such a collision allow that almost

all the energy of the incident electron can be absorbed by the atomic system,

provided the atom does not become ionized.

Franck and Hertz first attempted to verify these ideas in 1914. Namely that the

atomic systems have discrete energy levels which can be excited by collisions with

bombarding electrons and that the energy differences in the levels correspond with

the spectroscopic results.

The objectives:

1- To experimentally demonstrate the concept of quantization of energy levels

according to Bohr’s model of atom.

2- To determine the minimum excitation energy of argon.

one

Highlight

2

The theory:

James Franck and Gustav Hertz conducted an experiment in 1914, which

demonstrated the existence of excited states in argon atoms. It confirms the

prediction of quantum theory that electrons occupy only discrete, quantized energy

states. This experiment supports Bohr model of atom. For this great invention they

have been awarded Nobel Prize in Physics in the year 1925.

Apparatus used for the experiment consist of a tube containing low pressure gas,

fitted with three electrodes: cathode for electron emission, a mesh grid for the

acceleration of electrons and a collecting plate.

With the help of thermionic emission, electrons are emitted by a heated cathode, and

then accelerated toward a grid which is at a positive potential, relative to the cathode.

The collecting plate is at a lower potential and is negative with respect to mesh grid.

If electrons have sufficient energy on reaching the grid, some will pass through the

grid, and reach collecting plate, and it will be measured as current by the ammeter.

Electrons which do not have sufficient energy on reaching the grid will be slowed

down and will fall back to the grid. The experimental results confirm the existence

of discrete energy levels.

As long as the electron collision is elastic, the electrons will not lose energy on

colliding with gas molecules in tube. As the accelerating potential increases, the

current also increases. But as the accelerating potential reaches a particular value,

(4.9eV for argon, 19eV for neon), each electron possesses that much of potential and

now the collision become inelastic. As a result, the energy level of electron bound

to the atom is raised. Now the electron almost loses its energy and measured current

drops.

The Frank-Hertz tube in this instrument is a tetrode filled with the vapour of the

experimental substance. Fig.1 indicates the basic scheme of experiment.

The electrons emitted by filament can be accelerated by the potential VG2K between

the cathode and the grid G2. The grid G1 helps in minimizing space charge effects.

The grids are wire mesh and allow the electrons to pass through. The plate A is

maintained at a potential slightly negative with respect to the grid G2. This helps in

making the dips in the plate current more prominent. In this experiment, the electron

current is measured as a function of the voltage VG2K. As the voltage increases, the

3

electron energy goes up and so the electron can overcome the retarding potential

VG2A to reach the plate A. This gives rise to a current in the ammeter, which

initially increases. As the voltage further increases, the electron energy reaches the

threshold value to excite the atom in its first allowed excited state. In doing so, the

electrons lose energy and therefore the number of electrons reaching the plate

decreases. This decrease is proportional to the number of inelastic collisions that

have occurred. When the VG2K is increased further and reaches a value twice that

of the first excitation potential, it is possible for an electron to excite an atom halfway

between the grids, lose all its energy, and then gain a new enough energy to excite a

second dip in the current. The advantage of this type of configuration of the potential

is that the current dips are much more pronounced, and it is easy to obtain fivefold

or even larger multiplicity in the excitation of the first level.

Figure 1: A circuit diagram for the Franck-Hertz experiment.

4


Frank-Hertz Experiment Set-up, in Fig.2, consists of the following:

• Argon filled tetrode

• Filament Power Supply: 2.6-3.4V continuously variable

• Grids Power Supplies

VG1K: 1.3-5V continuously variable

VG2A: 1.3 - 12V continuously variable

VG2K: 0 - 95V continuously variable

• Sawtooth waveform for CRO display

• Multirange Digital Ammeter (Range multipliers: 10^-7, 10^-8, 10^-9)

Figure 2: Franck-Hertz experiment setup model no. FH 3001.

5

The procedure:

❖ Manual Mode

1- Ensure that the Electrical power is 220V ± 10%, 50 Hz.

2- Before the power is switched ‘ON’ make sure all the control knobs are at

their minimum position and Current Multiplier knob at 10-7 position.

3- Switch on the Manual-Auto Switch to Manual, and check that the Scanning

Voltage Knob is at its minimum position.

4- Turn the Voltage Display selector to VG1K and adjust the VG1K Knob until

voltmeter reads 1.5 V.

5- Turn the voltage Display selector to VG2A and adjust the VG2A Knob until

the voltmeter read 7.5 V.

6- Before proceeding to the next step check that the initial parameters are

Filament Voltage: 2.6V (minimum position) VG1K: 1.5 V, VG2A: 7.5V,

VG2K: 0V, Current Amplifier: 10^-7

7- These are suggested values for the experiment. The experiment can be done

with other values also.

8- Rotate VG2K knob and observe the variation of plate current with the

increase of VG2K. The current reading should show maxima and minima

periodically. The magnitude of maxima could be adjusted suitably by

adjusting the filament voltage and the value of current multiplier.

9- Now take the systematic readings, VG2K vs Plate Current. For better

resolution and observation of the maxima / minima VG2K is varied from 0-

80 V in the increments of 0.1 V or 0.01 V. Increments of 0.1 will be used for

the data set away from the peak or the dip. The interval 0.01V may be chosen

to finer the observation near maxima or minima.

6

10- Plot the graph with output current on Y- axis and Accelerating Voltage

VG2K at X-axis.

❖ Auto Mode

1- Turn the Manual-Auto switch to ‘Auto’, connect the instruments Y, G, X

sockets to Y, G, X of Oscilloscope. Put the Scanning Range switch of

Oscilloscope to X-Y mode/external ‘X’.

2- Switch on the power oscilloscope, adjust the Y and X shift to make the scan

base line on the bottom of screen. Rotate the Scanning Knob of the

instrument and observe the wave form on the Oscilloscope Screen. Adjust

the Y-gain and X-gain of oscilloscope to make wave form clear and Y

amplitude moderate.

3- Rotate the scanning potentiometer clockwise to end. Then the maximum

scan voltage is 85V.

4- Measure the horizontal distance between the peaks. The distance of two

consecutive peaks (no of grids) and multiply it by V/ grid factor (X-gain) of

oscilloscope. This would give the value of argon atom’s first excitation

potential in eV.

7

Data and Analysis:

❖ Automatic Mode: Taking the measurement of the accelerating voltage versus

current

Least count of Voltmeter = 0.1 V

Least count of Ammeter=10^-9 A

VG1K: 1.5 V

VG2A: 7.5 V

1

2

3

4

5

6

7

8

9

10

11

Table.1: Measurements of the voltages and currents

8

• After you take the measurements of the voltages and currents of some selected

points in the display screen of the oscilloscope. therefore, you fill the following

Table.2 based on the results you gained.

Table.2: the maximum values of voltage with the difference of the preceding value

• Now, you must plug the points in a graph of the current vs accelerating voltage

VG2K from Table.1.

Discussion

As seen from the curve between the current and VG2K in graph Fig.3, the electrons

can excite the argon atoms only if they are accelerated by a specific value of the

voltage or its integer multiples. This verifies the discrete atomic energy levels of the

argon atoms. A significant decrease in electron (collector) current is noticed every

time the potential on grid 2 is increased by approximately (11± 2) eV, thereby

indicating that the energy is transformed from the beam in quanta of (11 ± 2) eV

only.

The average value of spacing between the peaks is 11 eV compared to the first

excited state of the argon atom 11.83 eV observed from the spectroscopy evidences.

We also noticed that when we increase the Filament Power Supply, we get a

magnified waveform.

1

Experiment No. 4

Electron diffraction

Introduction

In classical mechanics we describe motion by assigning momenta to point particles.

In quantum mechanics we learn that the motion of particles is also described by

waves, with the crucial parameters of the two viewpoints related through the de

Broglie relation:

where p is the momentum, λ is the wavelength, and h is Planck’s constant

To observe wave-like behavior, we require some kind of grating where the “distance

between slits” is of order the wavelength. At typical laboratory energies, the

electron’s de Broglie wavelength is of order one Angstrom (10^–8 cm), about the

same size as the interatomic spacings in common crystals. The regular atomic arrays

in crystals are thus perfectly scaled gratings for creating a “matter wave” diffraction

pattern, measuring their wavelength, and verifying Eq. 1. As an added bonus, with

the principle verified, the diffraction patterns then become powerful tools for the

study of crystal structure.

In this experiment, you will use a cathode ray tube with a graphite crystal target that

shows the diffraction pattern on the screen. You will verify the de Broglie relation,

and analyze crystal structures, including measurement of the inter-atomic distance

in the crystal.

mv

h=

2

The objectives:

1- To determine the wavelengths of the electrons

2- To verify de Broglie’s equation

3- To calculate the lattice plane spacing of graphite

The theory:

Louis de Broglie suggested in 1924 that particles could have wave properties in

addition to their familiar particle properties. He hypothesized that the wavelength of

the particle is inversely proportional to its momentum:

(1)

𝜆: wavelength

h: Planck’s constant

p: momentum

His conjecture was confirmed by the experiments of Clinton Davisson and Lester

Germer on the diffraction of electrons at crystalline Nickel structures in 1927. In the

present experiment the wave character of electrons is demonstrated by their

diffraction at a polycrystalline graphite lattice (Debye-Scherrer diffraction). In

contrast to the experiment of Davisson and Germer where electron diffraction is

observed in reflection this setup uses a transmission diffraction type similar to the

one used by G.P. Thomson in 1928. From the electrons emitted by the hot cathode a

small beam is singled out through a pin diagram. After passing through a focusing

electron-optical system the electrons are incident as sharply limited monochromatic

beam on a polycrystalline graphite foil. The atoms of the graphite can be regarded

mv

h=

3

as a space lattice which acts as a diffracting grating for the electrons. On the

fluorescent screen appears a diffraction pattern of two concentric rings which are

centred around the indiffracted electron beam (Fig. 1).

Fig. 1: Schematic representation of the observed ring pattern due to the diffraction of electrons

on graphite. Two rings with diameters D1 and D2 are observed corresponding to the lattice plane

spacings d1 and d2 (Fig. 3)

The diameter of the concentric rings changes with the wavelength l and thus with

the accelerating voltage U as can be seen by the following considerations:

(2)

and substituted into the de Broglie relation, to obtain

2

2mveVA =

4

(3)

In 1913, H. W. and W. L. Bragg realized that the regular arrangement of atoms in a

single crystal can be understood as an array of lattice elements on parallel lattice

planes. When we expose such a crystal lattice to monochromatic x-rays or mono-

energetic electrons, and, additionally assuming that those have a wave nature, then

each element in a lattice plane acts as a “scattering point”, at which a spherical

wavelet forms. According to Huygens’ principle, these spherical wavelets are

superposed to create a “reflected” wave front. In this model, the wavelength l

remains unchanged with respect to the “incident” wave front, and the radiation

directions which are perpendicular to the two wave fronts fulfil the condition “angle

of incidence = angle of reflection”. Constructive interference arises in the

neighbouring rays reflected at the individual lattice planes when their path

differences D = D1 + D2 = 2×d×sinJ are integer multiples of the wavelength (Fig.

2):

2𝑑 𝑆𝑖𝑛 𝜃 = 𝑛𝜆 (4)

d: lattice plane spacing

𝜃: diffraction angle

)(3.122

21

AngstromsVemV

h

mv

hA

A

−

===

5

Fig. 2: Schematic representation of the

Bragg condition.

This is the so called ‘Bragg condition’ and the corresponding diffraction angle J is

known as the glancing angle. In this experiment a polycrystalline material is used as

diffraction object. This corresponds to a large number of small single crystallites

which are irregularly arranged in space. As a result, there are always some crystals

where the Bragg condition is satisfied for a given direction of incidence and

wavelength. The reflections produced by these crystallites lie on cones whose

common axis is given by the direction of incidence. Concentric circles thus appear

on a screen located perpendicularly to this axis. The lattice planes which are

important for the electron diffraction pattern obtained with this setup possess the

lattice plane spacings (Fig. 3):

d1 = 2.13× 10−10m

d2 = 1.23× 10−10m

6

Fig. 3 Lattice plane spacings in graphite: d1 = 2.13× 10−10m ,d2 = 1.23× 10−10𝑚

Fig.4:Schematic sketch for determining the diffraction angle. L = 13.5 cm

(distance between graphite foil and screen), D: diameter of a diffraction ring

observed on the screen, 𝜃: diffraction angle. For meaning of F1, F2, C, X and A

see Fig. 5.

7

From Fig. 4 we can deduce that the condition for diffraction for small angles is:

d= where the small angle can be calculated from the geometrical

relationship of figure 2 as LD

2=

and so from equation (3):

𝑑𝐷

2𝐿= 𝜆 (5)

where: D = ring diameter (m)

d = interatomic spacings (Å)

L = pathlength from the carbon target to the luminescent screen (m)

D and VA are the only variables.

Due to equation (3) the wavelength l is determined by the accelerating voltage U.

Combining the equation (3) and equation (8) shows that the diameters D1 and D2 of

the concentric rings change with the accelerating voltage U:

𝐷 = 𝑘1

√𝑈 (6)

With

𝑘 =2 ∙ 𝐿 ∙ ℎ

𝑑√2𝑚𝑒 (7)

Measuring Diameters D1 and D2 as function of the accelerating voltage U allows us

to determine the lattice plane spacings d1 and d2.

8


Set-up:

The apparatus is shown in Fig. 4. Electrons emitted by thermionic emission from a heated

filament (4) inside the cathode are accelerated towards the graphite target (9) of the anode by

a potential difference, between the cathode and anode. A focusing electrode (8) is located

in front of the target to focus the electron beam in order to provide a sharp interference pattern

on the screen (11).

Figure 4: Overview of the electron diffraction tube.(1)4-mm socket for filament heating supply,

(2) 2-mm socket for cathode connection, (3) internal resistor, (4) filament. (5) cathode, (6)

anode, (7) 4-mm plug for anode connection (HV), (8) focusing electrode, (9) polycrystalline

graphite grating, (10) Boss, (11) fluorescent screen.

9

The procedure:

1- Apply an accelerating voltage U ≤ 5 kV and observe the

diffraction pattern.

Hint: The direction of the electron beam can be influenced by means of a magnet

which can be clamped on the neck of tube near the electron focusing system. To

illuminate another spot of the sample an adjustment of the magnet might be

necessary if at least two diffraction rings cannot be seen perfectly in the diffraction

pattern.

2- Vary the accelerating voltage U between 3 kV and 5 kV in step of 0.5 kV and

measure the diameter D1 and D2 of the diffraction rings on the screen (Fig. 1).

3- Measure the distance between the graphite foil and the screen.

Data and Analysis:

• Measured example

Table 1: Measured diameters D1 and D2 (average of 5 measurements) of the

concentric diffraction rings as function of the accelerating voltage U.

Distance between graphite foil and screen: L = 13.5 cm

• Determination of wavelength of the electrons

10

From the measured values for D1 and D2 and the lattice plane spacings d1 and d2

the wavelength can be determined using equation (6). The result for D1 and D2 is

summarized in Table 2 and Table 3, respectively.

We use the equation (5), with knowing that: d1 = 2.13× 10−10m,

d2 = 1.23× 10−10m.

Table 2: Measured diameter D1 of the concentric diffraction rings as function of

the accelerating voltage U. The wavelengths 1 and 1,theory are determined by

equation (5); and equation (3), respectively.

Table 3: Measured diameter D2 of the concentric diffraction rings as function of

the accelerating voltage U. The wavelengths 2 and 2,theory are determined by

equation (5); and equation (3), respectively.

11

• Measuring values

Now, you must measure the first diameter of the concentric diffraction rings with

the accelerating voltage U values, then you will be able to calculate the wavelength

and the theory wavelength by using equation (5); and equation (3), respectively.

Table 4: Measured diameter D1 of the concentric diffraction rings as function of the accelerating

voltage U. The wavelengths 1 and 1, theory are determined by equation (5); and equation (3),

respectively.

After that, you must measure the second diameter of the concentric diffraction rings

with the accelerating voltage U values, then you will be able to calculate the

wavelength and the theory wavelength by using equation (5); and equation (3),

respectively.

𝑼

𝒌𝑽

𝑫𝟏

𝒄𝒎

𝝀𝟏

𝒑𝒎, 𝒕𝒉𝒆𝒐𝒓𝒚

𝝀𝟏

𝒑𝒎

𝑼

𝒌𝑽

𝑫𝟐

𝒄𝒎

𝝀𝟐

𝒑𝒎, 𝒕𝒉𝒆𝒐𝒓𝒚

𝝀𝟐

𝒑𝒎

Table 5: Measured diameter D2 of the concentric diffraction rings as function of the

accelerating voltage U. The wavelengths 2 and 2, theory are determined by equation (5); and

equation (3), respectively.

12

• Determination of lattice plane spacings of graphite

In Fig. 6 the ring diameters D1 and D2 are plotted versus 1/ √𝑈 . The slopes k1

and k2 are determined by linear fits through the origin according equation (6) to

the experimental data:

k1 = 1,578×m √𝑉

k2 = 2.729×m√𝑉

Fig. 6: Ring diameters D1 and D2 as function of 1/ √𝑈. The solid lines correspond

to the linear fits with the slopes k1 = 1.578 m V and k2 = 2.729 m V , respectively.

Resolving equation (7) for the lattice plane spacing d:

𝑑 =2 ∙ 𝐿 ∙ ℎ

𝑘√2𝑚𝑒 (9)

gives

d1 = 2.10× 10−10m

d2 = 1.21× 10−10m

which is within the error limits in accordance of the parameters depicted in Fig. 3.

13

• Determine the lattice plane spacings of graphite by knowing the wavelengths.

We use equation (5) but in the form which d1 and d2 are unknown with

L = 13.5 𝑐𝑚:

𝑑 =2𝐿𝜆

𝐷

And so, you can calculate d1 and d2 in the following tables:

Table 6: Measured diameter D1 of the concentric diffraction rings with the theoretical values of

the wavelengths to calculate d1 and compare it with its correct value d1 = 2.13× 10−10m.

Table 7: Measured diameter D2 of the concentric diffraction rings with the theoretical values of

the wavelengths to calculate d1 and compare it with its correct value d2 = 1.23× 10−10m.

𝝀𝟏

𝒑𝒎𝒕𝒉𝒆𝒐𝒓𝒚

𝑫𝟏

𝒄𝒎

𝒅𝟏

× 𝟏𝟎−𝟏𝟎

𝝀𝟐

𝒑𝒎𝒕𝒉𝒆𝒐𝒓𝒚

𝑫𝟐

𝒄𝒎

𝒅𝟐

× 𝟏𝟎−𝟏𝟎

14

And by the same manner, we can get the value of h by using the practical

wavelengths values.

Discussion

- Verification of the de Broglie’s equation

The de Broglie relation (equation (1)) can be verified using

e = 1.6021 × 10-19 C

m = 9.1091 × 10-31 kg

h = 6.6256 × 10-34 J×s

in equation (3). The results for the wavelengths determined by equation (3) are

and . They are listed for the diameters D1 and D2 in

Table 2 and Table 3, respectively. The values and determined from the diffraction

pattern agree quite well with the theoretical values and due to the

de Broglie relation.

1

Experiment No. 4

The specific charge of the electron

Introduction

We can’t build a balance scale small enough and even if we could, the electron

wouldn’t stand still long enough to make a measurement. But we can infer what the

mass m of an electron is by making other measurements. In particular we can find

the specific charge (the mass-normalized charge) of this fundamental particle. Since

we can find the charge e on an electron from other experiments (like Millikan’s oil

drop experiment), an experimental e/m ratio can also give the electron’s weight (that

is, its mass).

The charge-to-mass ratio of an electron has been determined using many methods

requiring different combinations of applied electric fields and magnetic fields. In

1897, J. J. Thomson determined the ratio of charge to mass of particles in cathode

rays, using different residual gases in the discharge tubes. He discovered that e/m

for each particle was the same regardless of which gas he used. Thompson concluded

that these different atoms all contained the same particle. Today, this particle is

known as the electron.

We will determine the charge-to-mass ratio by Lenard’s method of measuring a

beam of electrons (the cathode ray) bent into a circular path by a known magnetic

field. The value of e/m can be determined from the radius of curvature of the path

of the electrons.

2

The objectives:

1- Study of the deflection of electrons in a magnetic field into a circular orbit.

2- Determination of the magnetic field B as a function of the acceleration potential

U of the electrons at a constant radius r and once again with keeping the current

constant.

3- Determination of the specific charge of the electron

The theory:

J. J. Thomson first determined the specific charge (charge to mass ratio e/m) of the

electron in 1887. In his experiment, J. J. Thomson had found a charged particle that

had a specific charge two thousand times that of the hydrogen ion, the lightest

particle known at that time. Once the charge on the particles was measured he could

conclude with certainty that these particles were two thousand times lighter than

hydrogen. This explained how these particles could pass between atoms and make

their way out of thin sheets of gold. Measurement of the specific charge of cathode

rays for different metals made him conclude that the particles that constituted

cathode rays form a part of all the atoms in the universe. For his work J. J. Thomson

received the Nobel Prize in Physics in 1906,

“in recognition of the great merits of his

theoretical and experimental investigations

on the conduction of electricity by gases”.

The direct measurement of mass of the

electron is difficult by experiments. It is

easier to determine the specific charge of the

electron e/m from which the mass m can be

calculated if the elementary charge e is

3

known. Charged particle in a magnetic field accelerated by a potential an

electron moving at velocity v perpendicularly to a homogenous magnetic field B, is

subject to the Lorentz force F:

which is perpendicular to the velocity and to the magnetic field. The electron takes

a circular orbit with its axis parallel to the direction of magnetic field. The Lorentz

force is balanced by the centripetal force which forces the electron into an orbit r

(see Fig. 1). Hence

where me is the mass of electron. Thus, the specific charge of electron (e/me) is

given by:

B. Electrons accelerated by a potential U

In the experiment, the electrons are accelerated in a beam tube by applying a

potential U. The resulting kinetic energy is given by:

Combining equation (3) and (4), the specific charge of the electron thus is

C. The magnetic field generated in a pair of Helmholtz coils

The magnetic field generated by a pair of Helmholtz coils is twice the field

generated by a single coil. If R is the radius of each coil and I is the current flowing

through each of them having

N turns, then the magnetic

4

field due to both the coils at a distance x = R/2 is given as

Where

Thus, from equations 5 and

6, the final expression for e/m is given as

𝑒

𝑚𝑒=

2 ∙ 𝑈

𝐵2𝑟2 =

2 ∙ 𝑈

𝐼2 ∙ 𝑘2 ∙ 𝑟2 (7)

With knowing that 𝑅 = 0.14 𝑚 𝑎𝑛𝑑 𝑁 = 160. So k value is 𝑘 =

0. 78 × 10−3 𝑇

𝐴 calculated by using


• Apparatus:

The set up contains the following parts:

1. Narrow electron beam tube

2. Pair of Helmholtz coils of radii 0.14m each (No. of turns in each coil = 160,

current limit 1.8A)

3. Power supply (0 – 250V)

• Experimental set up:

When we run the power supply, the electrons are accelerated in a beam tube by

applying a potential U which makes them move in a straight line until we apply the

magnetic field generated by a pair of Helmholtz coils. The magnetic field is twice

5

the field generated by a single coil. And consequently, the beam of electrons will

make a circular trajectory like Figure 5. We shall measure the radii of the trajectory

of the beam of electrons by using the measuring device illustrated in Figure 2.

Figure 2: Experiment setup for determining the specific electron charge

(a) Helmholtz coils (b) Fine beam tubes (c) Measuring device

6

Figure 3: The electric connection of the set up

The procedure:

• Carrying out the experiment

- Move the left slide of the measuring device so that its inner edge, mirror image and

escape aperture of the electron beam come to lay on one line of sight.

- Set the right slide for both inside edges to have a distance of 8 cm.

7

- Sight the inside edge of the right slide, align it with its mirror image and adjust the

coil current I until the electron

beam runs tangentially along the

slide edge covering the mirror

image (see Fig. 4).

- Reduce the acceleration potential

U in steps of 10 V to 200 V and

choose the coil current I so that the

orbit of the electron beam has a

diameter of 8 cm.

- Record acceleration potential U

and coil current I.

- Power up the tube power supply

and set acceleration potential U =

300 V. Thermionic emission starts

after warming up for a few minutes.

- Optimize focusing of the electron beam by varying the voltage at the Wehnelt-

cylinder from 0...10 V until it leads to a narrow, well defined beam with clear edge

definition.

- Connect the DC power supply of the Helmholtz coils and look for current I, at

which the electron beam is deflected into a closed orbit. If the electron beam after

leaving the anode is deflected to the wrong (left) side:

- disconnect both power supplies.

- exchange the connections at the DC power supply in order to change the

polarization of the magnetic field. If the electrons do not move on a closed orbit but

on a helical curve line:

- Loosen the mounting bolts of both holding brackets (read the information manual

for the fine beam tube).

- Carefully rotate the fine beam tube around its longitudinal axis, until the electron

beam runs on a closed circular orbit.

Figure 4: Measurement of the orbit

diameter with the measuring device

8

- Fasten mounting bolts.

After setting up the experiment, we shall get a trajectory of electrons beam as

illustrated in Fig.5. And this is because of the exerted magnetic and electric fields.

Figure 5: Circular trajectory of electron beam

9

Data and Analysis:

- Determination of the magnetic field B as a function of the acceleration potential


constant. And we consider that 𝑘 = 0. 78 × 10−3 𝑇/𝐴

- Determination of the magnetic field B as a function of the acceleration potential


constant. And we consider that 𝑘 = 0. 78 × 10−3 𝑇/𝐴

- Firstly, determining B as a function of the acceleration potential U of the

electrons at a constant radius r:

r= 4.25 cm

U(V) I (A) (𝑰 ∙ 𝒓 ∙ 𝒌)𝟐

𝟐 (𝒏

𝑲𝒈 ∙ 𝒎𝟐

𝒔𝟐)

Table 3: The coil current I as a function of the acceleration potential U of the

electrons at a constant radius r

10

- Secondly, determining B as a function of the acceleration potential U of the

electrons at the current constant:

I=1 A

U(v) r (cm) (𝑰 ∙ 𝒓 ∙ 𝒌)𝟐

𝟐(𝒏

𝑲𝒈 ∙ 𝒎𝟐

𝒔𝟐)

Table 4: The magnetic field B as a function of the acceleration potential U of the

electrons at the coil current I constant

- Now you plot (𝑰∙𝒓∙𝒌)𝟐

𝟐 in x-axis & U in the y-axis in both tables and find the

slopes by straight lines fitting and then determine e/me directly from the slope

values.

11

Discussion

Determination of the specific charge of the electron is done by making graphs as

follows:

Plot (𝑰∙𝒓∙𝒌)𝟐

𝟐 in x-axis & U in the y-axis in both tables and find the slopes by

straight lines fitting and then determine e/me.

The slope will give us 𝑆𝑙𝑜𝑝𝑒 = U

(𝑰∙𝒓∙𝒌)𝟐

𝟐

= 𝑒

𝑚𝑒

The documented and accepted value of 𝑒

𝑚𝑒 is

𝑒

𝑚𝑒= 1.76 × 1011 𝐶

𝐾𝑔.

And constructively, you can calculate the percentages of error for the first and the

second values of the ratio.

1

Experiment No. 6

The photoelectric effect

Introduction

The photoelectric effect is the emission of electrons from the surface of a metal when

electromagnetic radiation (such as visible or ultraviolet light) of the right frequency

shines on the metal. At the time of its discovery, the classical wave model for light

predicted that the energy of the emitted electrons would increase as the intensity

(brightness) of the light increased.

Instead, it was discovered that the energy of the emitted electrons was directly

proportional to the frequency of the incident light, and that no electrons would be

emitted if the light source was not above a certain threshold frequency. Lower energy

electrons were emitted when light with relatively low frequency was incident on the

metal, and higher energy electrons were emitted when light with relatively high

frequency was incident on the metal.

The objectives:

1- Measuring and Calculating Planck’s Constant, h.

2- Measuring Current-Voltage Characteristics of Spectral Lines - Constant

Frequency, Different Intensity.

3- The relationship between the frequency of light and the intensity.

2

The theory:

Many people contributed to the discovery and explanation of the photoelectric effect.

In 1865James Clerk Maxwell predicted the existence of electromagnetic waves and

concluded that light itself was just such a wave. Experimentalists attempted to

generate and detect electromagnetic radiation and the first clearly successful attempt

was made in 1886 by Heinrich Hertz. In the midst of his experimentation, he

discovered that the spark produced by an electromagnetic receiver was more

vigorous if it was exposed to ultraviolet light. In 1888 Wilhelm Hallwachs

demonstrated that a negatively charged gold leaf electroscope would discharge more

rapidly than normal if a clean zinc disk connected to the electroscope was exposed

to ultraviolet light. In 1899, J.J. Thomson determined that the ultraviolet light caused

electrons to be emitted from the metal.

In 1902, Phillip Lenard, an assistant to Heinrich Hertz, used a high intensity carbon

arc light to illuminate an emitter plate. Using a collector plate and a sensitive

ammeter, he was able to measure the small current produced when the emitter plate

was exposed to light. In order to measure the energy of the emitted electrons, Lenard

charged the collector plate negatively so that the electrons from the emitter plate

would be repelled. He found that there was a minimum “stopping” potential that kept

all electrons from reaching the collector. He was surprised to discover that the

“stopping” potential, V, - and therefore the energy of the emitted electrons - did not

depend on the intensity of the light. He found that the maximum energy of the

emitted electrons did depend on the color, or frequency, of the light.

In 1901 Max Planck published his theory of radiation. In it he stated that an

oscillator, or any similar physical system, has a discrete set of possible energy values

or levels; energies between these values never occur. Planck went on to state that the

emission and absorption of radiation is associated with transitions or jumps between

3

two energy levels. The energy lost or gained by the oscillator is emitted or absorbed

as a quantum of radiant energy, the magnitude of which is expressed by the equation:

E = hf where E equals the radiant energy, f is the frequency of the radiation, and h

is a fundamental constant of nature. (The constant, h, became known as Planck's

constant.) In 1905 Albert Einstein gave a simple explanation of Lenard’s discoveries

using Planck’s theory. The new ‘quantum’-based model predicted that higher

frequency light would produce higher energy emitted electrons (photoelectrons),

independent of intensity, while increased intensity would only increase the number

of electrons emitted (or photoelectric current). Einstein assumed that the light

shining on the emitter material could be thought of as ‘quanta’ of energy (called

photons) with the amount of energy equal to hf with f as the frequency. In the

photoelectric effect, one ‘quantum’ of energy is absorbed by one electron. If the

electron is below the surface of the emitter material, some of the absorbed energy is

lost as the electron moves towards the surface. This is usually called the ‘work

function’ (Wo). If the ‘quantum’ is more than the ‘work function’, then the electron

is emitted with a certain amount of kinetic energy. Einstein applied Planck's theory

and explained the photoelectric effect in terms of the quantum model using his

famous equation for which he received the Nobel prize in 1921:

𝐸 = ℎ𝑓 = 𝐾𝐸𝑚𝑎𝑥 + 𝑊0

where KE max is the maximum kinetic energy of the emitted photoelectron. In terms

of kinetic energy, 𝐾𝐸𝑚𝑎𝑥 = ℎ𝑓 − 𝑊0

If the collector plate is charged negatively to the ‘stopping’ potential so that electrons

from the emitter don’t reach the collector and the photocurrent is zero, the highest

kinetic energy electrons will have energy eV where e is the charge on the electron

and V is the ‘stopping’ potential.

4

𝑒𝑉 = ℎ𝑓 − 𝑊0 → 𝑉 =ℎ

𝑒 𝑓 −

𝑊0

𝑒

Einstein’s theory predicts that if the frequency of the incident light is varied, and the

‘stopping’ potential, V, is plotted as a function of frequency, the slope of the line is

h/e (see Figure 1).

Figure 1: Stopping voltage versus frequency (v)

• Principle of the Experiment:

In Figure.2, when incident light shines on the cathode (K),

photoelectrons can be emitted and transferred to the anode (A).

This constitutes a photocurrent. By changing the voltage

between the anode and cathode, and measuring the photocurrent,

you can determine the characteristic current-voltage curves of

the photoelectric tube.

Figure 2

The basic facts of the photoelectric effect experiments are as follows:

5

• For a given frequency (color) of light, if the voltage between the cathode and anode,

VAK, is equal to the stopping potential, V, the photocurrent is zero.

• When the voltage between the cathode and anode is greater than the stopping

voltage, the photocurrent will increase quickly and eventually reach saturation. The

saturated current is proportional to the intensity of the incident light. See Figure 3.

• Light of different frequencies (colors) have different stopping potentials. See

Figure 4

• The slope of a plot of stopping potential versus frequency is the value of the ratio,

h/e. See Figure 1.

• The photoelectric effect is almost instantaneous. Once the light shines on the

cathode, photoelectrons will be emitted in less than a nanosecond.

Figure 3: Current. vs Intensity Figure 4: Current. vs Frequency

6


The Photoelectric Effect apparatus contains optical set, Mercury Light Source

Enclosure, Photodiode Enclosure and power supply. They are all illustrated in

Figure 4 and 5 respectively.

Figure 4: The Photoelectric Effect complete apparatus

The h/e Photoelectric Effect Apparatus as shown in Figure 5, has four knobs, three

buttons and two digital displays on its front panel, and four ports (labeled A, K,

‘down arrow’, and POWER SUPPLY) on its back panel. The apparatus measures

the photocurrent through the photodiode tube and the voltage across the

photodiode tube.

7

Figure 5: Photoelectric Effect Apparatus

• Current Range switch: Sets the current range for the instrument’s current amplifier

(10-8 to 10-13 A).

• Ammeter: Displays the photocurrent through the photodiode tube.

• Voltmeter: Displays potential across the photodiode tube.

• Voltage Range switch: Sets the voltage range as -2 to +30 V for plotting current-

voltage characteristics and -2 to 0 V for measuring the stopping potential.

• Power switch: Turns the power to the instrument ON or OFF.

• Voltage Adjust: Sets the potential across the photodiode tube for both voltage

ranges.

• Current Calibration: Sets the current through the instrument to zero.

• Phototube Signal switch: Sets the signal from the photodiode tube to

CALIBRATION or MEASURE.

8

The procedure:

Preparation before measurement:

1. Cover the window of the Mercury Light Source enclosure with the Mercury Lamp

Cap from

the Optical Filters box. Cover the window of the Photodiode enclosure with the

Photodiode Cap from the Optical Filters box.

2. On the h/e Power Supply, turn on POWER and MERCURY LAMP. On the

Photoelectric Effect Apparatus, push in the POWER button to the ON position.

3. Allow the light source and the apparatus to warm up for 20 minutes.

4. On the apparatus, set the VOLTAGE Range switch to –2 — 0 V. Turn the

CURRENT RANGES switch to 10-13.

5. To set the current amplifier to zero, first disconnect the ‘A’, ‘K’, and ‘down arrow’

(GROUND) cables from the back panel of the apparatus.

6. Press the PHOTOTUBE SIGNAL button in to CALIBRATION.

7. Adjust the CURRENT CALIBRATION knob until the current is zero.

8. Press the PHOTOTUBE SIGNAL button to MEASURE.

9. Reconnect the ‘A’, ‘K’, and ‘down arrow’ (GROUND) cables to the back of the

apparatus.

For Measuring and Calculating Planck’s Constant, h:

1. Uncover the window of the Photodiode enclosure. Place the 4 mm

diameter aperture and the 365 nm filter onto the window of the enclosure.

2. Uncover the window of the Mercury Light Source. Spectral lines of 365 nm

wavelength will shine on the cathode in the phototube.

3. Adjust the VOLTAGE ADJUST knob until the current on the ammeter is zero.

4. Record the magnitude of the stopping potential for the 365 nm wavelength in

Table 1.

9

5. Cover the window of the Mercury Light Source.

6. Replace the 365 nm filter with the 405 nm filter.

7. Uncover the window of the Mercury Light Source. Spectral lines of 405 nm

wavelength will shine on the cathode in the phototube.

8. Adjust the VOLTAGE ADJUST knob until the current on the ammeter is zero.

9. Record the magnitude of the stopping potential for the 405 nm wavelength in

Table 1.

10. Cover the window of the Mercury Light Source.

11. Repeat the measurement procedure for the other filters. Record the magnitude of

the stopping potential for each wavelength in Table 1

12. Repeat the data measurement and analysis procedure for the other two apertures

in the OPTICAL FILTERS box.

For Measuring Current-Voltage Characteristics of Spectral Lines -

Constant Frequency, Different Intensity.

2 mm Aperture

1. Uncover the window of the Photodiode enclosure. Place the 2 mm diameter

aperture and the 436 nm filter in the window of the enclosure.

2. Uncover the window of the Mercury Light Source enclosure. A spectral line of

436 nm will shine on the cathode in the Photodiode enclosure.

3. Adjust the –2—+30 V VOLTAGE ADJUST knob so that the current display is

zero. Record the voltage and current in Table 4.

4. Increase the voltage by a small amount (for example, 1 V). Record the new voltage

and current in Table 4.

5. Continue to increase the voltage by the same small increment. Record the new

voltage and current each time in Table 4. Stop when you reach the end of the

VOLTAGE range.

10

4 mm Aperture

1. Cover the window of the Mercury Light Source enclosure.

2. On the Photodiode enclosure, replace the 2 mm diameter aperture with the 4 mm

diameter aperture. Put the 436 nm filter back onto the window.





5. Increase the voltage by a small amount (e.g., 1 V) and record the new voltage and

current in Table 4. Continue to increase the voltage by the same small increment and

record the new voltage and current each time in Table 4. Stop when you reach the

end of the VOLTAGE range

8 mm Aperture

1. Cover the window of the Mercury Light Source enclosure.

2. On the Photodiode enclosure, replace the 4 mm diameter aperture with the 8 mm

diameter aperture. Put the 436 nm filter back onto the window.





5. Increase the voltage by a small amount (e.g., 1 V) and record the new voltage and

current in Table 4. Continue to increase the voltage by the same small increment and

record the new voltage and current each time in Table 4. Stop when you reach the

end of the VOLTAGE range.

11

Data and Analysis:

For the first part of the experiment, you will measure the stopping voltages of three

different apertures. The results must be written respectively in Tables 1,2 and 3.

Then, you will performe the second part of the experiment and you will measure the

currents and the voltages of the same spectral line with different apertures. The

results must be written in Table 4.

Item 1 2 3 4 5

Wavelength,𝜆(nm) 365.0 404.7 435.8 546.1 577.0

Frequency, f=c/ 𝜆,

(x 10^14 Hz)

8.214 7.408 6.879 5.490 5.196

Stopping

Potential, V (V)

Table 1: Stopping Potential of Spectral Lines, 4 mm diameter Aperture

Now, Repeat the data measurement and analysis procedure for the other two

apertures in the OPTICAL FILTERS box

Item 1 2 3 4 5

Wavelength,𝜆(nm) 365.0 404.7 435.8 546.1 577.0


(x 10^14 Hz)

8.214 7.408 6.879 5.490 5.196

Stopping

Potential, V (V)


12

Item 1 2 3 4 5

Wavelength,𝜆(nm) 365.0 404.7 435.8 546.1 577.0


(x 10^14 Hz)

8.214 7.408 6.879 5.490 5.196

Stopping

Potential, V (V)


• Calculating

1. Plot a graph of Stopping Potential (V) versus Frequency (x 10^14 Hz) for all the

Tables.

2. Record the calculated slope and use it to calculate the value of Planck’s constant,

h.

4. Estimate the error in the slope and round your result to the appropriate value.

Compare your calculated value of h to the accepted value, h0, 6.626 x 10-34 J s.

𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = |ℎ − ℎ0

ℎ0| × 100

• Record your percent differences.

• Measurement of - Constant Frequency, Different Intensities:

𝜆 = 435.8 nm

2 mm dia.

V (V)

I (x 10-11 A)

𝜆 = 435.8 nm

4 mm dia.

V (V)

I (x 10-11 A)

𝜆 = 435.8 nm

8 mm dia.

V (V)

I (x 10-11 A)

Table 4: Current and Voltage of Spectral Lines

13

Analysis

1. Plot the graphs of Current (y-axis) versus Voltage (x-axis) for the one spectral

line, 436 nm, at the three different intensities.

Discussion:

In the first part of the experiment (Measuring and Calculating Planck’s Constant, h),

we used different filters that has discrete and specific wavelengths, and that gave us

different frequencies and eventually different stopping voltage values. So now we

can say that light intensity is totally unaffected with stopping voltage. However, it

only changes when we change the aperture of the Photodiode. Intensity in

photoelectric effect deals with the number of photons attacking electrons to produce

current. It does not affect the kinetic energy of electrons. Hence stopping potential

of anode remains unchanged.

In the second part of the experiment, we see that there's kind of connection between

the three curves illustrated in Figures 9, 10 and 11. They have the same mathematical

cubic function. And they differ and contrast with each other by the values of currents

which is an expected consequence of the different apertures used.

Modern Physics Laboratory Manual Phys 381

Documents

Transcript of Modern Physics Laboratory Manual Phys 381