JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Modern Physics

The ratio of de-Broglie wavelength of an

α

-particle and a proton accelerated from rest by the same potential is

\frac{1}{m}

, the value of m is

(A)4
(B)16
(C)8✓ Correct
(D)2

Answer: (C)

Solution

For a particle accelerated from rest through potential

V

, the de-Broglie wavelength is

λ = \frac{h}{2 m q V}

. The ratio for the

α

-particle and proton is

\frac{λ _{α}}{λ _{p}} = \frac{m _{p} q _{p}}{m _{α} q _{α}}

. Using

m_{α} = 4 m_{p}

and

q_{α} = 2 q_{p}

\frac{λ _{α}}{λ _{p}} = \frac{1}{4 \times 2} = \frac{1}{8}

. Comparing with

\frac{1}{m}

, the value of

m

8

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Single correct option

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