CBSE Class 12 · 2017 · Modern PhysicsShort Answer

Draw a graph showing the variation of de-Broglie wavelength of a particle of charge

q

and mass

m

with the accelerating potential. A proton and a deuteron have the same de-Broglie wavelengths. Explain which has more kinetic energy.

Answer: $λ \propto 1/ V$ ; proton has more KE (lighter mass).

Solution

The de-Broglie wavelength is

λ = \frac{h}{2 m q V} \propto \frac{1}{V}

, so the graph of

λ

versus

V

is a decreasing curve (see figure).
For equal de-Broglie wavelengths,

λ = \frac{h}{2 m K}

gives

K = \frac{h ^{2}}{2 m λ ^{2}} \propto \frac{1}{m}

.
Since the deuteron is heavier than the proton (

m_{d} > m_{p}

), for the same

λ

the proton has the greater kinetic energy.

λ \propto 1/ V; K_{p} > K_{d}

CBSE Class 12 Board · 2017 · Subjective