CBSE Class 12 · 2016 · All India · Modern PhysicsShort Answer

A proton and an

α

-particle are accelerated through the same potential difference. Which one of the two has
(i) the greater de-Broglie wavelength, and
(ii) less kinetic energy? Justify your answer.

Answer: Proton has the greater $λ$ and the smaller KE.

Solution

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

. Taking proton units,

m q = 1

for the proton and

m q = 4 \times 2 = 8

for the

α

-particle.
(i)

\frac{λ _{p}}{λ _{α}} = 8 > 1

, so the proton has the greater de-Broglie wavelength.
(ii) Kinetic energy

K = q V

. With the same

V

K_{p} = e V

and

K_{α} = 2 e V

, so the proton has the smaller kinetic energy.

Proton: larger λ and smaller K

CBSE Class 12 Board · 2016 · All India · Subjective

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