A proton, a neutron, an electron and an $\alpha$-particle have same energy. If $\lambda_{\mathrm{p}}, \lambda_{\mathrm{n}}, \lambda_{\mathrm{e}}$ and $\lambda_{\alpha}$ are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose the correct relation from the following:

(B) $\lambda_{\alpha}<\lambda_{\mathrm{n}}<\lambda_{\mathrm{p}}<\lambda_{\mathrm{e}}$

(A) $\lambda_{\mathrm{p}}=\lambda_{\mathrm{n}}>\lambda_{\mathrm{e}}>\lambda_{\alpha}$

(C) $\lambda_{\text {e }} \lambda_{\alpha}$

(D) $\lambda_{\mathrm{e}}=\lambda_{\mathrm{p}}=\lambda_{\mathrm{n}}=\lambda_{\alpha}$

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Modern Physics

A proton, a neutron, an electron and an

α

-particle have same energy. If

λ_{p}, λ_{n}, λ_{e}

and

λ_{α}

are the de Broglie's wavelengths of proton, neutron, electron and

α

particle respectively, then choose the correct relation from the following:

Answer: (B)

The de Broglie wavelength is

λ = \frac{h}{2 E m}

. For particles with the same energy

E

λ \propto \frac{1}{m}

. The masses are:

m_{e} < m_{p} \approx m_{n} < m_{α}

(where

m_{α} \approx 4 m_{p}

). Therefore, the wavelengths are ordered as

λ_{e} > λ_{p} \approx λ_{n} > λ_{α}

, which matches option (B):

λ_{α} < λ_{n} < λ_{p} < λ_{e}

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Single correct option