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:

• A. $27.2\text{eV}$
• B. $331.2\text{eV}$
• C. $13.6\text{eV}$
• D. $2815.2\text{eV}$

Answer 1

The correct option is D $2815.2\text{eV}$

Orbital energy, $E$ $\propto$ $\frac{1}{r}$ and Radius, $r$ $\propto$ $\frac{1}{m}$
So, $E$ $\propto$ $m$

Ionization potential $=13.6\times \frac{\left({\text{mass}}_{\mu }\right)}{\left({\text{mass}}_e\right)}$ $eV$$=13.6\times 207$ $eV$ $=2815.2$ $eV$