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Q.

An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is (C-being the velocity of light)

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a

${(\frac{E}{2 m})}^{1 / 2}$

b

$\frac{1}{C} {(\frac{E}{2 m})}^{1 / 2}$

c

$C {(2 m E)}^{1 / 2}$

d

$\frac{1}{C} {(\frac{2 m}{E})}^{1 / 2}$

answer is B.

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Detailed Solution

$λ_{e} = \frac{h}{\sqrt{2 m E}}, λ_{p h} = \frac{h c}{E}$
$\frac{λ_{e}}{λ_{p h}} = \frac{1}{C} \sqrt{\frac{E}{2 m}}$

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