The de Broglie wavelengths for an electron and a photon are λe and λp, respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?
\(λ_p ∝ λ^{2}_e\)
\(λ_p ∝ λ_e\)
\(λ_p ∝ \sqrtλ_e\)
\(λ_p ∝ \sqrt{\frac{1}{λ_e}}\)
The Correct Option is A
Solution and Explanation
The correct answer is (A) : \(λ_p ∝ λ^{2}_e\)
\(λ_p = \frac{h}{p} = \frac{hc}{E} .... (i)\)
\(λ_e = \frac{h}{\sqrt{2mE}} .... (ii)\)
From (i) and (ii)
\(λ_p ∝ λ^{2}_e\)
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