The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25 % of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be

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Solution

Q.
The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25 % of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be [2024]

1 1/1

2 1/8

3 8/1

4 1/4

Ans.
(2)

For photon, $E_{p} = \frac{h c}{λ_{p}} \Rightarrow λ_{p} = \frac{h c}{E_{p}}$

For electron, $λ_{e} = \frac{h}{m_{e} v_{e}} = \frac{h v_{e}}{2 K_{e}}$

Given $v_{e} = 0.25 c$

$λ_{e} = \frac{h \times 0.25 c}{2 K_{e}} = \frac{h c}{8 K_{e}}$

Also $\frac{h c}{E_{p}} = \frac{h c}{8 K_{e}} \Rightarrow \frac{K_{e}}{E_{p}} = \frac{1}{8}$

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