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Obtain the first Bohr’s radius and the g...

Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon `(mu^(–))` of mass about `207m_e` orbits around a proton].

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All that is needed is to replace `m_e` by `m_(mu)` in the formulas of the Bohr model. We note that keeping other factors fixed, `r prop (1//m) ` and `E prop m`. Therefore ,
`r_(mu) = (r_e m_e)/(m_(mu)) = (0.53 xx 10^(13))/(207) = 2.56 xx 10^(-13)m`
`E_(mu) = (E_(e)m_(mu))/(m_e) = (13.6 xx 207) eV = -2.8 keV`.
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