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>>Dual Nature of Radiation and Matter
>>Wave Nature of Matter
>> $An alpha - particle and a proton are acc$

Question

An $α$ -particle and a proton are accelerated from rest by a potential difference of $100 V$ . 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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Updated on : 2022-09-05

Solution

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Correct option is A)

We have, $\frac{1}{2} m v^{2} = e V$

De broglie wavelength= $λ = \frac{h}{m v}$

$λ = \frac{h}{2 m e V}$

$λ_{p} = \frac{h}{2 ( m ) e V}$ ....(1)

$λ_{α} = \frac{h}{2 ( 4 m ) 2 e V}$ ....(2)

Now, $\frac{λ _{p}}{λ _{α}} = 8 ≃ 3$

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