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

Question:

Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu)$

The mass of muon particle is 207 times that of an electron and charge is

equal to the charge of an electron. The ionization potential of this hydrogen

atom will be :-

  1. (1) $13.6 \mathrm{eV}$

  2. (2) $2815.2 \mathrm{eV}$

  3. (3) $331.2 \mathrm{eV}$

  4. (4) $27.2 \mathrm{eV}$


Correct Option: , 2

Solution:

(2)

$\mathrm{E} \propto \frac{1}{\mathrm{r}} \quad \mathrm{r} \propto \frac{1}{\mathrm{~m}}$

$\mathrm{E} \propto \mathrm{m}$

Ionization potential $=13.6 \times \frac{\left(\text { Mass }_{\mu}\right) \mathrm{eV}}{\left(\text { Mass }_{e}\right)}$

$=13.6 \times 207 \mathrm{eV}=2815.2 \mathrm{eV}$

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