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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?

Asked in JEE Main 28th June 1st Shift 2022 · Matter wave against photon

Answer: (1) λₚ∝λₑ²

Step-by-step solution

Electron: λₑ=h/(√2mK), so K=(h²)/(2mλₑ²).

Photon: K=(hc)/(λₚ), so λₚ=(hc)/K.

Substituting: λₚ=(hc·2mλₑ²)/(h²)=(2mc)/hλₑ².

So λₚ∝λₑ².

Why the other options are wrong

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