The Ramsauer-Townsend Effect

Transcription

1 The Ramsauer-Townsend Effect Evan Sheridan, Tom Power, Chris Kervick Feburary 18th 2013 Abstract The Quantum Mechanical phenomena known as the Ramsauer-Townsend effect is investigated using xenon gas, liquid nitrogen, EM91 thyratron vacuum tube, 10 V and 4 V DC power supplies and multimeters. The energy at which the probability of scattering is minimum was found to be 0.7 ± 0.1eV. The range of values for the mean free path of the electron was given by 3.43x10 3 m λ m. The contact potential was found to be ± 0.004V. Finally, the mean kinetic energy of the electrons was calculated as 1.5 ± 0.02eV. 1

2 Aims To observe the Ramsauer-Townsend effect. To find the energy at which the probability of scattering of electrons by the xenon gas is minimum. To find the maximum and minimum values of the mean free path of the electron. To determine the contact potential and mean thermionic emission energy. Backround and Theory The Ramsauer-Townsend Effect is a quantum mechanical effect that occurs when a beam of electrons is passed through a noble gas. It is observed that for specific energies of the electron current that the electron beam will pass through the gas unscathed. Classically, this makes no sense because there shouldn t be a specific energy at which the probability that electrons will be scattered will achieve a minimum. This is because the classical model treats the phenomena as collisions. In order to describe the effect one must use the tools of quantum mechanics. Instead of treating the electrons and the nucleus of the atoms as point like objects we consider that the electron can behave as a wave and the atom creates a potential barrier. We see that when the wavelength of the electrons is such that λ = 2d n then destructive interference occurs due to the reflected beams from A and B(A is the left potential step and B the right potential step) and we get unity transmission. d is the width of the potential well that we use to describe the potential due to the atom that interacts with the electrons. The phenomena that particles can be reflected from a potential step is not intuitive but a consequence of the 1-dimensional time independent Schrodinger equation. In our case we use xenon and in order to calculate the probability of the scattering we define f(v ) = I P (V ) I S (V ) where the denotes the respective currents when no xenon is present (when we cool it with the liquid nitrogen). I P is the current induced on the plate due to unscattered electrons. I S is the induced current on the shield due to scattered electrons. If we denote P S by the probability of scattering the we have: I P = f(v )I S (1 P S ) with some considerations it can be shown that: = P S = 1 I P I S I S I P P S = 1 e l λ taking logarithms an expression for the mean free path of the electron is given by: λ = l log(p S ) Now in order to predict certain properties of the electrons that are emitted from the cathode we must find the kinetic energy of the electrons. This energy is given by: E kin = ev tot 1

3 where V tot = V + V C + V such that V is the acceleration potential, V C is the contact potential between the two metals in the chamber and V is the mean thermionic energy of the electrons. It can be shown that : I(V r ) = I 0 e 3Vr 2 V log(i(v r ) = log(i 0 ) 3V r 2 V Thus plotting a log plot of Log(I) vs Voltage we can determine V C momentum and wavelength of the accelerated electrons. and V and thus find the The Experiment The circuit is given by: Set up the circuit as shown. Firstly, with the xenon gas present, measure both I p and I s as a function of the applied voltage. Range the voltage from 0 Volts - 10 Volts and take readings in.2 volt intervals up to 1 and then 1 volt intervals up to 10. Now invert the tube and place it in contact with the liquid nitrogen so as to reduce the pressure of the xenon gas. Repeat the same process as without the liquid nitrogen, i.e measure I p and I s using the same voltage intervals. Measure the contact potential and mean thermionic energy by reversing the polarity of the accelerating voltage. Results and Analysis The first plot illustrates I P and I P as a function of applied voltage. 2

4 As we can see the presence of the xenon gas drastically impacts the behaviour of the electrons in the tube. We can see that as we increase the voltage IP increases quite quickly as opposed to the almost constant I P in comparison. This indicates that a very low temperatures the electrons move freely throughout the tube, rarely being scattered and the more energy they are given the larger the current induced at the plate. The following graph illustrates the Ramsauer-Townsend effect: It shows clearly a minimum quite close to zero. The minimum was found to correspond with and energy of 0.7 ± 0.1eV. Since the quoted value is near 1eV it can be concluded that the Ramsauer- Townsend effect was successfully observed. The probability maximum and minimum corresponded to 0.13 and 0.9, respectively. Hence using: λ = l log(p S ) 3

5 with l = 0.7cm we get the range for the mean free path to be: 3.43x10 3 m λ m The final plot illustrates the effect of the retarding potential. From the plot we can calculate the contact potential by the finding the point of intersection of the lines the characterise the two seperate regions. It can be read off the plot that the contact potential is.404 ± 0.004V Given that the total kinetic energy of the electron is given by: V tot = V + V C + V V can be read from the slope of the second line which is given by y = 3.77x and thus the mean kinetic is given by ev T ot = 1.5 ± 0.02eV Now using that and the De Broglie relation p = 2m e E λ = h p we find that the momentum of the electrons is given by p = 5.25x10 25 kg m s 1 and that the wavelength of the electrons is given by λ = 1.22x10 9 m. Conclusions Overall, the experiment was a success. The Ramsauer- Townsend effect was observed and the energy where the probability of scattering was successfully located near 1 ev. The range of the mean free path of the electrons was found to be 3.43x10 3 m λ m. As well as this, various other properties of the electrons were discovered, such as it s wavelength λ = 1.22x10 9 m and momentum p = 5.25x10 25 kg m s 1. Perhaps the most significant result of this experiment is the demonstration that classical physics fails in certain instances and a quantum mechanical treatment must be utilised in order to provide an explanation. 4