Question

A muonic atom contains a nucleus of charge Ze and a negative muon, ${\mu }^{-}$, moving about it. The ${\mu }^{-}$ is an elementary charge with -e and a mass that is approximately 200 times as large as an electron mass.
Calculate the binding energy of a muonic atom(in eV) with $Z=1$.

Answer 1

General equation of binding energy is
$E=-\frac{m{k}^2{e}^4}{2h^2}$

For regular electron model, $E_{binding}=-13.6eV$
Hence for muonic atom, $E_{binding}=-13.6\times 200eV=2720eV$
(as $E_{muonic}=-\frac{\mu k^2{e}^4}{2h^2}$, where $\mu =200m_e$)