PHYSICS EXPERIMENTS EXPLAINED

(For students in Btech 2nd Sem)

How to use this material:

Physics Experiments Explained has been designed for an all reader. I tend to categorize students into 3 categories:

1. Student who wishes to know all theory and concepts behind a practical and to an external invigilator he/she says ‘Bring it on’!

2. Student who wishes to learn only few details of the experiment and does not care what’s deep inside it.

3. Student, who does the practical as instructed, goes and says “Rest is History”.

In order to make this so flexible I have included extra theory in the Additional Reading Section and Students from category 1 can refer to that.

All experiments in general have been designed for cat-2 students, for cat- 3 students please only refer to the procedure and ‘important points of the experiment’.

This first edition is a humble and sincere effort to bring this one of a kind of ‘book’, where I try to bridge the gap between theory and practical. I say no to rote learning and emphasise on concepts. Rest depends upon the user.

Thanks,

Kalim Nama

Table of contents:

1. To calculate Planck’s constant using a Photocell (Digital).

2. To calculate Planck’s constant using a Photovoltaic cell (Analog).

3. To study the charging and discharging of a capacitor.

4.

EXPERIMENT 1: PLANCKS CONSTANT BY PHOTOCELL

OBJECTIVE: To determine the Planck’s constant using a photocell.

APPARATUS : Photocell, DC power supply, Digital Ammeter and Voltmeter, Light Source of variable intensity, Wires.

THOERY :

Formula:

h= (e (V2-V1)*λ1*λ2)/(c (λ1-λ2))

Where,

e=electronic Charge

V1= Stopping Potential*(corresponding to wavelength of filter 1)

V2= Stopping Potential*(corresponding to wavelength of filter 2)

c= Velocity of Light

λ1= wavelength of filter 1

λ2= wavelength of filter 2

What is a Photocell?

A photocell is a technological application of the photoelectric effect. In the photoelectric experiment electrons are emitted by a photosensitive material when light of a suitable wavelength is incident on it. Similarly a photocell consists of bulb (to see the bulb turn the instrument and look closely through the region from where light enters) inside which is an emitter plate (which is again a photosensitive material) and a collector plate/electrode.

Stopping potential: It is amount of voltage that holds back/stops even the most energetic electron emitted from the photosensitive material /junction. (While turning the 20 V knob towards the right, you are actually applying an opposite voltage). It depends only upon the frequency of the incident wavelength and is independent of the intensity of the radiation- for a particular material.

Work function: Work function of a photosensitive material is the minimum amount of energy required to extract the most loosely bound electron present on the surface of the material.

The filters are simple devices that allow light of only a particular wavelength to pass through.

Constants used in the experiment:

e= 1.6 * 10^-19 C

c= 3*10 ^8 m/sec

λ1 - yellow filter = 560 nm

λ2- green filter= 520 nm

λ 3-Red filter= 640 nm

Figure 1

Figure 2

PROCEDURE:

1. Make the connections as per Fig. 1.2. Keep Micro ammeters Range Selector switch towards 20µA side, Voltmeter range selectors

switch towards 2 V side and output switch towards 2 V side. 3. Light Source is arranged and the light is allowed to fall on the tube which is enclosed in a box.

The distance between the photocell and the light source is adjusted such that there is a sufficient flow of current.

4. Now a suitable filter of wavelength λ2 is placed in the path of light (in the slit provided).5. A reading is observed in the micro ammeter. This reading corresponds to zero anode potential

with that particular filter.6. A small –ve potential is applied and is gradually increased in step and each time the reading in

voltmeter and micro ammeter is noted till micro ammeter reading comes to 0.7. This is stopping potential V2 corresponds to filter with λ 2.8. The experiment is repeated with another filter of known wavelength λ1 and λ3 and

corresponding stopping potential V1 and V2 are noted.9. A graph is plotted by taking –ve anode potential on X axis and corresponding reading in micro

ammeter on Y axis.10. By using above values Planck’s constant h is calculated by the formula give. Standard values of

e,c and λ of standard filters are given .

OBSERVATIONS:

S.No Filter Wavelength of light incident upon photocell

Stopping potential (V)

1.2.

Put the above data in the formula given in the beginning of the experiment.

Graph:

We plot a graph V0 as a function of frequency, the slope of the straight line is equal to (h/e)

e V0= h*frequency – work function

Dividing by e:

V0= (h/e) – (W.F)/ e (this equation is of the type y=mx +c)

e.g:

RESULT:

From the above experiment the value of Planck’s constant was found out to be: _____________

EXPERIMENTAL ERROR:

Known value of Planck’s constant (h)= 6.626 * 10 ^-34 J sec

Value from experiment:

Percentage Error= (Original – Observed/ Original )*100=

COMMENTS:

_____________________________________________________________________________________

EXPERIMENT 2: Charging Discharging of a capacitor

OBJECTIVE: To study the charging and discharging of a capacitor.

APPARATUS: wires, circuit board consisting of a voltmeter, ammeter, capacitors, resistors.

THOERY:

The capacitance of a given system is defined as its charge holding capacity at a particular voltage.

e.g. for a system comprising of a two metal sheets , a graph between the charge on the sheets to the voltage/potential drop between the 2 sheets is observed. The ratio of the charge to the potential diff. is found to be constant for that system and is termed as its capacitance.

The capacitance of a system depends only upon its geometry. For a pair of parallel metal sheets it is equal to:

C= (ε*A)/d ------------------------------------------------------------------1

Where,

ε= Coefficient of permittivity

A=Area common to both the plates

d= distance of separation between the 2 plates

RC CIRCUIT:

We know that a simple RC circuit consists of a source of potential difference i.e. a battery, a capacitor and a resistor.

Vc= Q/C

For a capacitor to show some potential difference it is necessary that it holds some static charge or in other words a difference in potential between the plates will only be observed if they have some charge.

Vr=I/R

For a resistor to show potential diff. a current should flow through it.

In a RC circuit at any instant of time,

Vo= Vc +Vr ---------------------------------------------2

Vo is the voltage supplied by the battery. It should be remembered, that a battery is a device which maintains a constant voltage difference throughout the circuit no matter what other components are present, and hence Vo is a constant.

Let’s try to better understand equation 2,

At t=0, Vo= Vr, since at the initial time no charge has been accumulated on the capacitor and the whole pot. drop occurs across the resistor.

As time progresses, Vc begins to grow whereas Vr tends to decrease so as to justify eq. 2.

When the capacitor is fully charged, it blocks any current passing through it. At this point,

Vo=Vc and Vr=0.

Figure 3

In the following figure when you switch on S1 then the capacitor gets charged and when you turn on the switch S2 (S1 off) the capacitor losses its energy through the load. The main purpose of the resistor is to slow down the rate of flow of energy because if a large amount of current flows through the wire, the enormous heat produced can melt the wires. It can be shown that the charging of a capacitor can be represented by the equation:

q=q’ (1-e^ (-t/RC))

Where q is the charge on the plates a time t, and q’ is the final charge on the capacitor i.e. when it is fully charged, similarly the discharge occurs through the relation

q=q’*e^ (-t/RC)

From the above equation it can be seen that RC it the time during which the charge on the capacitor drops to 1/e of the initial value. Since, it has dimensions of time, it is also called the time constant of the circuit.

> When you start with this experiment you will be given a large circuit/network board and a set of wires. Pls. do not get scared!

Let’s first get familiar with the instruments that we have:

We all know that an ammeter measures current through a part of the circuit, a voltmeter the potential difference between any 2 points in the circuit, and an ohmmeter the resistance of a resistor.

A multimeter as the name suggests is a device which is capable of doing all these functions together!

This is how a multimeter looks like:

The central knob has lots of positions and you must choose which one is appropriate for the measurement you want to make. If the meter is switched to 20 V DC, for example, then 20 V is the maximum voltage which can be measured, this is sometimes called 20 V fsd, where fsd is short for full scale deflection.

DC ranges are indicated by on the meter. Sometimes, you will want to measure smaller voltages, and in this case, the 2 V or 200 mV ranges are used.

If you want to calculate AC switch to the section marked by , on your multimeter.

Similarly, you can measure current and resistance, by choosing the appropriate section and range on your multimeter.

While connecting the leads Red is plus and black is taken as negative. Leave the hole which says 10 ADC, and use the other two.

The circuit board is something like this:

Figure 4

PROCEDURE:

PART A:

Study the charging of a capacitor in an RC circuit.

1. Connect the wires acc. To the circuit diagram:

2. We are trying to observe how the voltage rises with respect to time and hence we need to calculate both the voltage and the time in specific intervals.

3. If the input voltage is 20 V , then mark out intervals as V=1/2 Vo , V=1/4 Vo, V=1/8 Vo etc. (V is the output voltage observed on the multimeter). Calculate the time taken (using a stopwatch) to reach these respective voltage values and plot a graph by taking voltage on the y axis and time on the x axis.

4. Perform part 1-3 again by keeping the capacitance same and vary the resistance by connecting the leads to different resistors.

5. Then take different capacitance and so on.

OBSERVATIONS:

A graph like this would be observed.

As mentioned earlier, we marked the points corresponding to V=1/2Vo, V=1/4 Vo ….. and calculated the time in which the respective values were reached.

It was found that the interval between successive steps comes out within the experimental limits. This kind of rise is called exponential rise of V or in other words V0-V falls exponentially. In equal times Vo rises by equal factors. You could take 1/2 or 1/e and in each case the time interval comes out to be equal.

PART B:

To study the discharging of the capacitor.

1. Repeat all the steps as in PART A, but remove the voltage source.

OBSERVATIONS:

RESULT:

COMMENTS:

EXPERIMENT 3:

OBJECTIVE: To calculate Planck’s constant using a Photovoltaic cell (Analog).

APPARATUS: Wires, the instrument given contains an inbuilt Photovoltaic cell, a light source of variable intensity, a load Resistance.

THEORY:

A photovoltaic cell/Solar Cell consists of a light absorbing material which is connected to an external circuit. Charge carriers are generated in the material by the absorption of photons of light and are driven towards the contacts by the built in spatial asymmetry. This light driven charge separation establishes a voltage at open circuit and generates a photocurrent at short circuit (zero resistance). When a cell is connected to a load, the cell produces both current and voltage.

The Solar cell can take place of a battery in a simple electric circuit (Fig. 1.2). In dark (i.e. absence of light), the cell –marked (a) does nothing. When placed in the presence of light, it develops a voltage or e.m.f similar to the battery in circuit (b). The voltage developed when the terminals are isolated- not connected together (infinite load resistance) is called the open source voltage Voc. The current drawn when the terminals are connected together is the short circuit current Isc. For any intermediate value of load resistance R, the cell develops a voltage between 0 and Voc and delivers a current I such that V=IR and I(v) is determined by the current voltage characteristic of the cell under that illumination. Thus both I and V are determined/depends upon the intensity and wavelength of the incident radiation as well as the load

It is being shown here without proof, that the value of h(the Planck’s constant ) can be calculated by the formula:

h= 2.303*λ*K* ∆log 10 Ip

__________________________

C * ∆(1/T)

Where,λ= wavelength of incident lightK= Boltzmann constant= 1.38 * 10-23 J deg KIp=Photocurrent detected in the microammeterC= Speed of Light = 3*108 m/secT= Temperature in Kelvin

Thus, the value of ‘h’ can be calculated by drawing a graph between log 10 Ip and (1/T) which will be a straight line. Putting this value in the equation above we can find h.

The temperature T can be calculated by using the relation:

Rt = (T) 1.2

_______________Rr = (273 + Tr) 1.2

Where,Rt is the Resistance at temperature T.Rr is the temperature at room temperature (Tr= 298K)

PROCEDURE AND OBSERVATIONS:

1. Keep the supply control coarse and fix towards fully counter clockwise position i.e. minimum.2. Place a filter between the lamp house and the photovoltaic cell.3. Gently increase the fine control such that a very low reading in mA meter is achieved say

between 250-260 mA.4. Note the value in millivolt too. Calculate Rr(resistance at room temperature as mV/mA ,in ohms5. Increase the supply , change the range from 3 V to 15 Volts, at a certain voltage the light patch

will be incident upon the photovoltaic cell. Note V & I from supply and I in microamperes from the microammeter. Calculate Rt as V/I from supply. Calculate the value of T by putting in all the other values obtained.

6. Increase the supply again and evaluate the Rt again, then calculate T again in the same way as mentioned in the previous step..

7. Take more observations increasing supply in steps.Tabulate the results:

Table 1:S.No Rr Rt Rt/Rr T(in K) Ip(microampere)123

Table 2:

S.No T (in Kelvin) Log10 (Ip) (I/T)

8. Plot log 10 Ip against (1/T) from the observations in the table. The graph should be a straight line. From the slope of the line deduce –refer to equation.

9. Repeat the set of procedure from 5 to 8 for other filter.

RESULT:

COMMENTS:

Additional Reading:

Energy Levels in a Crystalline Solid

What do you know about an atom of Copper? Well, It has a total of 29 electrons, distributed in its energy levels as 1s2, 2s2, 2p6, 3s2, 3p6, 4s1. The configuration clearly explains to us that the 4s is the valence energy level ( the outermost shell) and can accommodate 1 more electron to its cabin.

However, we are well aware of the fact that in reality an atom is not isolated. If we take a piece of elemental Copper and examine it under a very powerful microscope we will be able to find lots of Copper atoms closely huddled together. So, what happens in this case, does the electronic configuration and the energy levels still remain the same?. The answer is a plain, NO.

Why? When Two (could be more) atoms are brought close to each other they will- speaking loosely sense each others presence. In the language of Quantum Physics their wave function (which is nothing but mathematical solutions of finding an electron in space) start to overlap, beginning with the outermost electrons.

When this happens, we don’t speak of one individual atom but a collective 2 atom system (Imagine breaking two eggs – where the two yellow yolks resemble the 2 central nucleus surrounded by ‘white’ of electrons). The system now contains not 29 but 29*2= 58 e-

Using the Paulis Exclusion Principle here, each e- should have a different set of Quantum Numbers, so each of the 58 e- occupy a diff. quantum state.

In fact , 58 quantum states are available for because each energy level of the isolated atom splits into 2 levels for the two atom system. ( the reason is simple, suppose an electron is in a 3p, l=0 level , and in another Cu atom nearby one e- will also be in a 3p,l=0 level , which is not possible because of Paulis principle , and hence a particular energy level is broken down in 2 parts so that both electrons in the neighboring atoms have diff. quantum states say 3p, l=0 and 3p, l’=0).

If we bring up more atoms, we get a copper lattice. If our lattice contains N atoms, then each level of an isolated copper atom is split into N levels in a solid. Thus, the individual energy levels of the solid form energy bands, with adjacent bands being separated by some energy gap.

The next general question which may arise is that why are there energy bands. If we again think about the interaction between two isolated atoms we can find the answer. When the atoms are brought very close, the outermost electrons are ones which are disturbed the most while the inside ones are very well shielded. Thus, based upon how each one is effected we get energy bands (which are closely spaced energy levels). The energy band which is on the top or farthest way from the nucleus is called the valence band*. Above the valence band (separated by some distance) is the conduction band. But, the question arises how is this conduction band is formed? Recall that the electron in the last shell in a Cu atom was in 4s, but does that mean the vacant orbital 4p does not exists? Of course it does, and this ‘collection’ of different vacant orbitals (from neighboring atoms) is what constitutes the conduction band.

The difference in energy between the top of valence band and bottom of conduction band is known as the Energy Band Gap (Eg). The numerical value of Eg range from 0 ev for metals, 0<Eg<3 for semiconductors and Eg>3 ev for insulators.

What are intrinsic type semiconductors?

In some elements more precisely semiconductors the value of Eg is low and can be provided by the thermal energy at room temperature (Average K.E for a molecule at temp. T= ½*k*T^2 where k=Boltzmann’s constant= ).

Thus some of the electrons get excited and jump from the valence to the conduction band, where they contribute to conduction. At the same time, the electrons from neighboring locations in the valence band try to occupy the vacant position of the electron which has left. Since, this motion keeps on simultaneously gives rise to holes (places where e- is absent), and the motion of holes is opposite that of electrons, we say it is the hole current. .

In Intrinsic Semiconductors:

N(e)= N(h)-N(i), i.e.

The number of electrons=number of holes=the intrinsic carrier concentration.

*In some books for simplification only the valence band and conduction band are mentioned, with the valence band containing all the electrons.