CBSE Class 12 · 2003 · Modern PhysicsShort Answer

Derive the expression for the de-Broglie wavelength of an electron moving under a potential difference of

V

volts. Describe the Davisson and Germer experiment to establish the wave nature of electrons. Draw a labelled diagram of the apparatus used.

Answer: $λ = h / 2 m e V$ ; Davisson–Germer diffraction peak confirms wave nature.

Solution

Wavelength: An electron accelerated through

V

gains kinetic energy

e V = \frac{1}{2} m v^{2}

, so its momentum is

p = m v = 2 m e V

and

λ = \frac{h}{p} = \frac{h}{2 m e V} = \frac{12.27}{V} \overset{˚}{A} .

Davisson–Germer experiment: Electrons from a heated filament are accelerated through a known potential and directed as a fine beam onto a nickel crystal. The scattered electrons are collected by a movable detector that measures their intensity as a function of scattering angle. A sharp peak in intensity (observed at

54 V

and

5 0^{\circ}

) occurs exactly where constructive interference (diffraction) of matter waves is predicted; the measured wavelength agrees with

λ = h / 2 m e V

, confirming the wave nature of electrons.

λ = \frac{h}{2 m e V}; diffraction peak confirms matter waves

CBSE Class 12 Board · 2003 · Subjective

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CBSE Class 12 · 2003 · Modern PhysicsShort Answer

Solution

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