Question

The radius of the hydrogen atom in its ground state is $a_0$. The radius of a muonic hydrogen atom in which the electron is replaced by an identically charged $a_ \mu$ with mass 207 times that of an electron, is am equal to

• A. $20\,a_0$
• B. $\frac{a_{0}}{207}$
• C. $\frac{a_{0}}{\sqrt{207}}$
• D. $a_{0}\sqrt{207}$

Answer 1

Answer: (B)

$a_{0} = \frac{h^{2}\varepsilon_{0}}{\pi me^{2}}$
$a_{\mu} = \frac{h^{2}\varepsilon _{0}}{\pi \left(207\,m\right)e^{2}}$
Dividing $\left(ii\right)$ by $\left(i\right)$, we get, $\frac{a_{\mu }}{a_{0 }} = \frac{1}{207}$ or $a_{\mu } = \frac{a_{0 }}{207}$