If muonic hydrogen atom is an atom in which a negatively charged muon ( $\mu$ ) of mass about $207 m

Question

If muonic hydrogen atom is an atom in which a negatively charged muon ( $\mu$ ) of mass about $207 m_e$ revolves around a proton, then first Bohr radius of this atom is $\left(r_e=0.53 	imes 10^{-10} \mathrm{~m}ight)$

Professor PC Thomas Classes · Answer

(d) : According to Bohr's atomic model,
$
r \propto \frac{1}{m} \Rightarrow \frac{r_\mu}{r_e}=\frac{m_e}{m_\mu} ...(i)
$
Here, $r_e=0.53 	imes 10^{-10} \mathrm{~m} ; m_\mu=207 m_e$
$
\begin{aligned}
	herefore \quad r_\mu & =\frac{m_e}{207 m_e} 	imes 0.53 	imes 10^{-10} ..using(i)\
& =2.56 	imes 10^{-13} \mathrm{~m} .
\end{aligned}
$