An $\alpha$ particle and a proton are accelerated from rest by a potential difference of 200 V . After this, their de Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{\mathrm{P}}$ respectively. The ratio $\frac{\lambda_{\mathrm{P}}}{\lambda_{\alpha}}$ is :

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Modern Physics

α

particle and a proton are accelerated from rest by a potential difference of 200 V . After this, their de Broglie wavelengths are

λ_{α}

and

λ_{P}

respectively. The ratio

\frac{λ _{P}}{λ _{α}}

is :

(A)3.8
(B)7.8
(C)2.8✓ Correct
(D)8

Answer: (C)

Solution

A particle of charge

q

and mass

m

starting from rest and falling through a potential difference

V

gains kinetic energy

q V

, so its momentum is

2 m q V

and

λ = \frac{h}{2 m q V}

Both particles cross the same

V

, so the ratio depends only on mass and charge. With

m_{α} = 4 m_{P}

and

q_{α} = 2 q_{P}

\frac{λ _{P}}{λ _{α}} = \frac{m _{α} q _{α}}{m _{P} q _{P}} = 4 \times 2 = 22

The ratio

\frac{λ _{P}}{λ _{α}}

is therefore

2.8

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

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