JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Modern Physics

Imagine that the electron in a hydrogen atom is replaced by a muon

(μ)

. The mass of muon particle is 207 times that of an electron and charge is equal to the charge is of an electron. The ionization potential of this hydrogen atom will be :

(A)13.6 eV
(B)2815.2 eV✓ Correct
(C)331.2 eV
(D)27.2 eV

Answer: (B)

Solution

The ionisation energy of a hydrogen-like atom is

E = \frac{m e ^{4}}{8 ε _{0}^{2} h ^{2}}

, which is proportional to the mass of the orbiting particle when the charges are unchanged. Replacing the electron by a muon of mass

207 m_{e}

and the same charge multiplies the ionisation energy by

207

E = 207 \times 13.6 = 2815.2 eV

The ionisation potential of such an atom corresponds to

2815.2

eV.

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Single correct option

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