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 $(r_e = 0.53 \times 10^{-10} m)$

• A. $2.56 \times 10^{-10}\,m$
• B. $2.56 \times 10^{-11}\,m$
• C. $2.56 \times 10^{-12}\,m$
• D. $2.56 \times 10^{-13}\,m$

Answer 1

Answer: (D)

According to Bohr’s atomic model,
$r\propto \frac{1}{m}$
$\Rightarrow \frac{r_{\mu}}{r_{e}} = \frac{m_{e}}{m_{\mu}}\quad...\left(i\right) $
Here, $r_{e} = 0.53 \times10^{-10} m ;$
$ m_{\mu} = 207 m_{e}$
$\therefore r_{\mu} = \frac{m_{e}}{207 m_{e}} \times0.53 \times10^{-10} $ (using $(i)$)
$ = 2.56\times10^{-13}m $