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A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as

Asked in JEE Main 9th April 1st Shift 2024 · Same or changed energy

(1) λₑ>λ_α>λₚ
(2) λₚ>λₑ>λ_α
(3) λ_α<λₚ<λₑ
(4) λₚ<λₑ<λ_α

Answer: (3) λ_α<λₚ<λₑ

Step-by-step solution

At the same energy, p=√2mE, so λ=h/(√2mE)∝1/(√m).

Masses run mₑ<mₚ<m_α.

So the wavelengths run the other way: λ_α<λₚ<λₑ.

Why the other options are wrong

(1) comes from puts the alpha particle ahead of the proton, though it is the heavier of the two
(2) comes from puts the proton ahead of the electron, reversing the mass order
(4) comes from reverses the order completely, as if the heaviest particle had the longest wavelength

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