An \alpha-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de-Broglie wavelengths are \left(\lambda\right)_{\alpha} and \left(\lambda\right)_{p} respectively. The ratio \frac{\left(\lambda\right)_{p}}{\left(\lambda\right)

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An $α$ -particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de-Broglie wavelengths are $λ_{α} and λ_{p}$ respectively. The ratio $\frac{λ_{p}}{λ_{α}}$ , to the nearest integer, is

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$KE = \frac{1}{2} {mv}^{2} = \frac{1}{2 m} p^{2}$

$p = \sqrt{2 mKE}$

2e $\to_{}^{} α \to_{}^{}$ 4m

e p $\to_{}^{}$ m

KE = 2 e × 100

Ke = e × 100

$λ= \frac{h}{p} = \frac{h}{\sqrt{2 m KE}}$

$\frac{λ_{p}}{λ_{α}} = \sqrt{\frac{2 \times 4 m \times 2 \times e \times 100}{2 \times m \times e \times 100}} = 2 \times 1 .414 = 2 .8 \to 3$

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