A photon and an electron have equal energy E. The ratio of λ (electron) to λ (photon) is proportional to (a) 1: √(E) (b) √(E): 1 (c) 1: E (d) 1: E²

Answer: (b). λe = (h)/(√(2mE)), λph = hc/E. λeλph = (E)/(c√(2mE)) = (√(E))/(c√(2m)) ∝ √(E) So the answer is (b) √(E): 1.

A photon and an electron have equal energy E. The ratio of λ… | MHT CET 2026 (11 Apr, Shift 1)

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Matter Waves: de Broglie Wavelength

A photon and an electron have equal energy E. The ratio of $\lambda$ (electron) to $\lambda$ (photon) is proportional to

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Answer: (b)

$\lambda_e = \dfrac{h}{\sqrt{2mE}}$ , $\lambda_{ph} = \dfrac{hc}{E}$ .
$\dfrac{\lambda_e}{\lambda_{ph}} = \dfrac{E}{c\sqrt{2mE}} = \dfrac{\sqrt{E}}{c\sqrt{2m}} \propto \sqrt{E}$
So the answer is (b) $\sqrt{E} : 1$ .

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