FHV

Gruppe 8 (Monday) Simone Lingitz; Sebastian Jakob

-1-

The Franck-Hertz Experiment (FHV) Group 8


-2-

1 Introduction

The Franck-Hertz Experiment is one of the basic experiments to determine the atoms structure. It shows, that electrons only can move around the atomic nucleus on certain orbits and gives a magnitude for the binding energies of the outermost electrons. The experiment uses the circumstance that bound electrons can be excited by inelastic collisions into a higher unoccupied orbit. Only certain orbits can be occupied by the electrons, further information hereof can be won from the Bohr model of the atom. When an electron moves from a higher energetic state to a lower one, a spectral line of a certain frequency (depending on the freed energy) is emitted. Bohrs theory can directly be proven by the Franck-Hertz Experiment. 2 Basics of the experiment

In a tube filled with mercury vapour (later in the experiment neon) are two electrodes (cathode, anode). The cathode is heated, so there is electron emission, the anode is a grid, and so electrons can pass it. There is also a collector installed, so the electrons, that have passed the anode can be registered. Between collector and grid there is a small voltage, reversed to the accelerating voltage. The emitted electrons of the cathode are accelerated by a voltage between the two electrodes. On their way they collide with the gas atoms, but lose only a small part of their energy, so they still can overcome the reverse voltage and make their way to the collector. By rising the accelerating voltage, the electrons gain more energy. If now a certain state of energy is reached, a collision of electron and atom causes a bound electron of the atom to rise from its current energy state to the next one possible gaining the energy that the colliding electron loses. The remaining energy of the electron now is too low to reach the collector. If the acceleration voltage is again increased the energy of the electrons doesnt fit the atoms electrons energy demand and a collision will not set the orbital electron to a higher state of energy, the electron again reaches the collector. This behaviour can be seen for any rising voltage. As the current into the collector is measured as a function of the accelerating voltage, the graph of this function is rising until the energy to excite an electron is reached, then is strongly decreasing, to rise again, after this energy-level is passed. So the graphs maximal values show the amount of energy that is needed to excite an electron to the next higher energetic state. 3 Experiment

3.1 Experimental assembly

Common to both experimental assemblies are the following components and their wiring: The Amplifier for the collector is connected to the tube and ground, its signal is sent to the oscilloscope as the vertical component. Anode and cathode are connected to a voltage source (rage 0 to 45 Volts), which is also connected to the ground (same potential). The voltage between the two electrodes is connected to the oscilloscopes input (horizontal). The cathode is heated by an adjustable voltage source so the cathode emits electrons. All mentioned components (except those of the tube) are summed up in one device. In the mercury-experiment the tube is heated by an oven to reach the right working temperature. In the neon-experiment only the tube is changed.


-3-

3.2 Mercury measurements The following measurement values were won by moving in x-direction on the oscilloscope and noting down when the curve reached a maximum or minimum value:

UB [V] Mesurement IMaxima 11,8 16,3 21,6 25,6Distance 4,5 5,3 4,0Minima 14,1 19,2 24,0 28,3Distance 5,1 4,8 4,3

From this values a mean value of voltage difference (Distance) can be archived:

1

Mesurement I

1

1 (4,5 5,3 4,0 5,1 4,8 4,3) 4,76

n

xx

m Un

m V V

==

= + + + + + =

The statistical error has to be calculated by:

1tu sn

=

For this we need the standard deviation VmUn

sn

xx 38,0)(1

11

2 == = ; 11,16 == tn So in the end we get a value for the statistical error:

Vu 17,01 = The systematic error is Vu 5,02 = From u1 and u2 the total error can be calculated as Vuuu 67,021 =+= .

The wavelength can be found by using the following law:

nmEchchE

eVE

3826467,07,4

10.9979,2.10.136,4..

)67,07,4(

815

====

=

The result from our measurement is 4,7 0,67V for the voltage and 263,8 38nm for the wavelength. This means, that the theoretical values of 4,9V and 253,7nm are within the precision range of our experiment.


-4-

3.3 Neon measurements These values were measured in the same way as in 3.2.

UB [V] Mesurement IIMaxima 19,0 36,0 55,0 78,0Distance 17,0 19,0 23,0Minima 0,0 25,0 42,0 63,0Distance 25,0 17,0 21,0

The mean value of measurement II:

1

Measuerement II

1

1 (17 19 23 25 17 21) 20,36

n

xx

m Un

m V V

==

= + + + + + =

This formula was used for the statistical error:

1tu sn

= For its calculation the standard deviation is needed:

VmUn

sn

xx 3,3)(1

11

2 == = ; 11,16 == tn Now we get the errors value:

Vu 5,11 = Together with the systematic error

Vu 0,12 = The total error comes to Vuuu 5,221 =+= . Energy and Wavelength are connected via this formula:

nmEchchE

eVE

5,7615,23,20

10.9979,2.10.136,4..

)5,23,20(

815

====

=

This wavelength does not exist, as the ~19V transition consists of a ~2V and ~17V transition. So instead of one, two different wavelengths are emitted. At the end of the neon experiment, the wavelength of the emitted light should be measured. As the intensity of the neon tubes light emission was too low, there were no spectral lines recognized. Several attempts to find the spectral lines were made but only once there was something to see, it was the complete red to yellow passage of the spectrum between the wavelength of 500nm and 650nm nm.


-5-

4 Questions 4.1 Explain the terms collision and inelastic collision?

If the collision is inelastic, kinetic energy of the collision partners is lost. This lost energy is converted to another form of energy, like deformation (heat) or excitation energy. If the collision is elastic, the amount of kinetic energy before and after the collision is the same and always constant.

4.2 Why is an electron at energies below 4,9eV only able to perform elastic collisions?

Electrons are only able to move on discrete orbits around the atomic nucleus. The difference of energy of two orbits is 4,9eV (mercury). An electron can give its energy to the atom and so the atoms electron is able to lift to a higher orbit. This is an inelastic collision. Below 4,9eV the electrons are only able to perform elastic collisions because they have not yet the discrete energy that is necessary for an atoms electron to reach a higher orbit.

4.3 Why is the energy an electron can transfer to an atom low in elastic collisions?

The amount of transferred energy in a collision depends of the two collision partners mass, respectively their mass ratio (impulse!). If this ratio is 1:1, all energy can be transferred. This is the case in straight collisions. If the ratio between the two partners is very large, as in the case of an atoms and an electrons mass, the energy transferred is very small.

'' AAeeee vmvmvm += (Impulse) ( ) ( )222 '

21'

21

21

AAeeee vmvmvm += (Energy) From this two formula results, that the speed of the electron after the collision is almost the same (another direction), if the mass of the collision partner is much more higher than the mass of the electron. And so almost no energy is transferred.

eeA

Ae

Ae

Aee vvm

mvmmmmv =+

=' 4.4 How does an atom excited by an inelastic collision dispose itself of the acquired energy?

An exited electron drops back to a lower energetic level. The difference of energy is emitted in form of light quanta that can see as spectral lines (discrete wavelength).

4.5 What is the difference between the excitation of an atom by electrons and by light quanta?

The difference between both is the amount of its energy that can be transferred. A light quanta can only be absorbed, this means it can only lose (transfer) its complete energy. For this reason only light quanta of a certain wavelength (=energy) can excite an orbital electron, so it moves to a higher orbit. In an atom-electron collision any part of the free electrons energy can be transferred to the atom; if this energy reaches the amount that is needed to move an orbital electron to a higher orbit, the orbital electron makes the jump into a higher orbit (inelastic collision). If the energy is not reached, the collision only remains an elastic collision, without an orbital electron to jump.


-6-

4.6 Why is it necessary to apply a deceleration voltage between collector electrode and anode grid? The deceleration voltage is kind of barrier for very slow electrons, so only electrons above a certain energetic can pass it. Without this speed filter it would be impossible to distinguish between electrons that have collided with atoms and the ones that have not. So only the electrons that are suitable for the experiment are registered, which makes it possible to determine the maximum and minimum values of the graph and so the levels of energy that excite orbital electrons.

4.7 Compare the functionally of a FranckHertz tube with that of a fluorescent lamp and try

to understand this lamp with the help of the schematic sketch. Why are those lamps called fluorescent lamps? In both cases the recognized light comes from excited electrons, falling back to a lower energetic orbit. The differences between Franck-Hertz tube and fluorescent lamp are that the lamp is working with ions and produces the needed heat to keep the process running itself (but it has to be started by a starter to reach the operating temperature of the electrodes and ionisation voltage), while the tube needs to be heated. When the lamp is running the electrodes emit the electrons for the lighting process; there is also no deceleration voltage needed in the lamp, as its purpose is not the measurement of any atomic behaviour.

4.8 What is the difference to an x-ray tube?

X-rays are created, when high-speed electrons (accelerated by high voltage) are fast decelerated by a metal anode. There are no excited electrons involved in the creating process. In opposite to the Franck-Hertz Tube (mercury!), the x-ray tube is evacuated, because any collisions with atoms (goal in the Frank-Hertz Experiment) lower the electrons energy and so the efficiency of the x-ray tube.

FHV

Documents

Transcript of FHV