1. Davisson and Germer experiment.
2. Aim:
To confirm the wave nature of electron. Experimental setup:
The Davisson and Germer Experiment consists of lament ‘F’, which is connected to a low tension battery. The Anode Plate (A) is used to accelerate the beam of electrons. A high voltage is applied in between A and C. ’N’ is a nickel crystal. D is an electron detector. It can be rotated on a circular scale. Detector produces current according to the intensity of incident beam.
Working:
The electron beam is produced by passing current through lament F. The electron beam is accelerated by applying a voltage in between A (anode) and C. The accelerated electron beam is made to fall on the nickel crystal.
The nickel crystal scatters the electron beam to different angles The crystal is fixed at an angle of Φ = 50° to the incident beam. The detector current for different values of the accelerating potential ‘V’ is measured. A graph between detector current and voltage (accelerating) is plotted. The shape of the graph is shown in figure.
Analysis of graph:
The graph shows that the detector current increases with accelerating voltage and attains maximum value at 54V and then decreases. The maximum value of current at 54 V is due to the constructive interference of scattered waves from nickel crystal (from different planes of crystal). Thus wave nature of electron is established.
Experimental wavelength of electron:
The wave length of the electron can be found from the formula
2d sinθ = n λ ………..(1)
From the figure, we get
θ + Φ + θ = 180°
2θ = 180 – Φ, 2θ = 180 – 50°
θ = 65°
for n = 1
equation (1) becomes
λ = 2d sinθ ………(2)
for Ni crystal, d = 0.91 A°
Substituting this in eq. (2), we get
wavelength λ = 1.65 A°
Theoretical wave length of electron:
The accelerating voltage is 54 V
Energy of electron E = 54 × 1.6 × 10-19 J
∴ Momentum of electron P = \(\sqrt{2mE}\)
P = \(\sqrt{2\times9.1\times10^{-31}\times54\times1.6\times10^{-19}}\)
= 39.65 × 10-25 Kg ms-1
∴ De Broglie wavelength λ = \(\frac{h}{p}\)
λ = \(\frac{6.63\times10^{-35}}{39.65\times10^{-25}}\) = 1.67 A0
The experimentally measured wavelength is found in agreement with de Broglie wave length. Thus wave nature of electron is confirmed.
3. λ = \(\frac{h}{p}\)
k = \(\frac{p^2}{2m}\)
P = \(\sqrt{2mK}\)
λ = \(\frac{h}{\sqrt{2mK}}\)
λ ∝ \(\frac{h}{\sqrt{m}}\)
Mass of alpha particle is more than that of proton, hence it has shortest wavelength.
