A photon and an electron have equal energy E , then the ratio λ photon λ electron is proportional to

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Question: Answered & Verified by Expert

A photon and an electron have equal energy

E

, then the ratio

\frac{λ_{photon}}{λ_{electron}}

is proportional to

PhysicsDual Nature of MatterNEET

Options:

A $\sqrt{E}$
B $\frac{1}{\sqrt{E}}$
C $\frac{1}{E}$
D does not depend upon $E$

Solution:

2836 Upvotes Verified Answer

The correct answer is:

\frac{1}{\sqrt{E}}

λ_{photon} = \frac{hc}{E}

λ_{electron} = \frac{h}{\sqrt{2 mE}}

\Rightarrow \frac{λ_{photon}}{λ_{electron}} = c \sqrt{\frac{2 m}{E}}

\frac{λ_{photon}}{λ_{electron}} \propto \frac{1}{\sqrt{E}}

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