A photon and an electron (mass m) have the same energy E. The ratio \lambda{\text{photon}}/\lambda{\text{electron}} of their de Broglie wavelengths is (c is the speed of light):

C. Photon: \lambdap = \frac{hc}{E}. Electron: \lambdae = \frac{h}{\sqrt{2mE}}. Ratio = \frac{hc}{E}\cdot\frac{\sqrt{2mE}}{h} = c\sqrt{\frac{2m}{E}} = \sqrt{\frac{2mc^2}{E}}.

PhysicsNEET 2025Matter waves and de Broglie wavelength

Dual Nature of Radiation and Matter

A photon and an electron (mass $m$ ) have the same energy $E$ . The ratio $λ_{photon} / λ_{electron}$ of their de Broglie wavelengths is ( $c$ is the speed of light):

A. $\frac{2 E}{m}$
B. $c 2 m E$
C. $\frac{2 m c ^{2}}{E}$ ✓
D. $\frac{1}{c} \frac{2 E}{m}$

Solution

Photon: $λ_{p} = \frac{h c}{E}$ . Electron: $λ_{e} = \frac{h}{2 m E}$ . Ratio $= \frac{h c}{E} \cdot \frac{2 m E}{h} = c \frac{2 m}{E} = \frac{2 m c ^{2}}{E}$ .

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Dual Nature of Radiation and Matter

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