The energy of a photon is equal to the kinetic energy of a proton. The energy of photon is E. Let $λ_{1} and λ_{2}$ be the de Broglie wave length of the proton and photon respectively. Then $\frac{λ_{1}}{λ_{2}}$ is proportional to

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$E^{0}$

$E^{1 / 2}$

$E^{- 1}$

$E^{- 2}$

answer is B.

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Detailed Solution

$\begin{array}{l} λ_{1} = \frac{h}{p} = \frac{h}{\sqrt{2 mE}} and λ_{2} = \frac{hc}{E} \\ So, \frac{λ_{1}}{λ_{2}} \propto \frac{E}{\sqrt{E}} \Rightarrow \frac{λ_{1}}{λ_{2}} \propto {(E)}^{1 / 2} . \end{array}$

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