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Q.

The kinetic energy of electrons is 10^-20 J and the photons also have the same energy. The wavelengths associated with these particles are $λ_{e}$ and $λ_{ph}$ respectively. These wavelengths are related in the following way

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a

$λ_{ph} = λ_{e}$

b

$λ_{ph} < λ_{e}$

c

$λ_{e} / λ_{ph} = c$

d

$λ_{ph} > λ_{e}$

answer is B.

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Detailed Solution

for photon $λ_{ph} = \frac{c}{v} = \frac{hc}{hv} = \frac{hc}{E}$
For electron $λ_{e} = \frac{h}{mv} = \frac{h}{\sqrt{(2 mE)}}$
$\frac{λ_{ph}}{λ_{e}} = c \sqrt{(\frac{2 m}{E})} = (3 \times 10^{8}) \sqrt{[\frac{2 \times (9 \times 10^{- 31})}{10^{- 20}}]} or \frac{λ_{ph}}{λ_{e}} > 1 or λ_{ph} > λ_{e}$

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