A proton and an -particle are accelerated from rest by 2V and 4V potential, respectively. The ratio of their de-Broglie wavelength is: [2023]

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Solution

Q.
A proton and an $α$ -particle are accelerated from rest by 2V and 4V potential, respectively. The ratio of their de-Broglie wavelength is: [2023]

1 4 : 1

2 2 : 1

3 8 : 1

4 16 : 1

Ans.
(1)

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m K}} = \frac{h}{\sqrt{2 m q Δ V}}$

$\frac{λ_{α}}{λ_{p}} = \sqrt{\frac{m_{p} V_{p} q_{p}}{m_{α} V_{α} q_{α}}}$

$\Rightarrow \frac{λ_{α}}{λ_{p}} = \sqrt{\frac{1 \times 2 \times 1}{4 \times 4 \times 2}} = \frac{1}{4}$

$\Rightarrow λ_{p} : λ_{α} = 4 : 1$

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