JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Modern Physics

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of

λ

. An alpha particle having certain kinetic energy has the same de-Brogle wavelength

λ

. The ratio of kinetic energy of proton and that of alpha particle is:

(A) $2 : 1$
(B) $4 : 1$ ✓ Correct
(C) $1 : 2$
(D) $1 : 4$

Answer: (B)

Solution

Equal de Broglie wavelengths mean equal momenta, since

λ = \frac{h}{p}

. Kinetic energy in terms of momentum is

K = \frac{p ^{2}}{2 m}

, so for a shared

p

the energies are inversely proportional to the masses,

\frac{K _{p}}{K _{α}} = \frac{m _{α}}{m _{p}}

. With the alpha particle four times as heavy as the proton,

\frac{K _{p}}{K _{α}} = \frac{4 m _{p}}{m _{p}} = 4 : 1.

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Single correct option

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