A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of . An alpha particle having certain kinetic energy has the same de-Broglie wavelength . The ratio of kinetic energy of proton and that of alpha particle is

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Solution

Q.
A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $λ$ . An alpha particle having certain kinetic energy has the same de-Broglie wavelength $λ$ . The ratio of kinetic energy of proton and that of alpha particle is [2023]

1 2 : 1

2 4 : 1

3 1 : 2

4 1 : 4

Ans.
(2)

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

$\frac{{KE}_{p}}{{KE}_{α}} = \frac{m_{α}}{m_{p}} = 4 : 1$

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