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)

Physics · Atomic Physics

NEET (UG) 2025 — Question 35

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)

Option A:
$\sqrt{\frac{E}{2m}}$
Option B:
$c \sqrt{2mE}$
Option C:
$c \sqrt{\frac{2m}{E}}$
Correct
Option D:
$\frac{1}{c} \sqrt{\frac{E}{2m}}$

Answer: C

Step-by-step solution

Energy of photon: $E = \frac{hc}{\lambda_{\text{photon}}}$ ⇒ $\lambda_{\text{photon}} = \frac{hc}{E}$ . Energy of electron: $E = \frac{p^2}{2m}$ ⇒ $p = \sqrt{2mE}$ ⇒ de Broglie wavelength $\lambda_{\text{electron}} = \frac{h}{p} = \frac{h}{\sqrt{2mE}}$ . Ratio: $\frac{\lambda_{\text{photon}}}{\lambda_{\text{electron}}} = \frac{hc/E}{h/\sqrt{2mE}} = \frac{hc}{E} \times \frac{\sqrt{2mE}}{h} = \frac{c \sqrt{2mE}}{E} = c \sqrt{\frac{2m}{E}}$ .

Answer key and solution verified before publishing.

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Exam: NEET (UG) 2025
Paper: 2025 paper
Subject: Physics
Chapter: Atomic Physics
Topic: Dual Nature of Matter

Answer: C

Step-by-step solution

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