The de Broglie wavelength of a proton and $\alpha$- particle are equal. The ratio of their velocities is:

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Modern Physics

The de Broglie wavelength of a proton and

α

- particle are equal. The ratio of their velocities is:

(A) $4 : 2$
(B) $4 : 3$
(C) $4 : 1$ ✓ Correct
(D) $1 : 4$

Answer: (C)

Solution

Since

λ = \frac{h}{p}

, equal de Broglie wavelengths mean equal momenta, so

m_{p} v_{p} = m_{α} v_{α}

. An alpha particle contains four nucleons, so

m_{α} = 4 m_{p}

and

\frac{v _{p}}{v _{α}} = \frac{m _{α}}{m _{p}} = 4

The velocities of the proton and the alpha particle are in the ratio

4 : 1

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Single correct option

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