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.

What is the wavelength of the first line($\text{in}\stackrel{\circ }{A}$) in the Lyman series for such an atom?

Answer 1

For regular electron atom wavelength of first line in Lyman series ,
$\frac{1}{\lambda }=R_H(1-\frac{1}{4})$
$\lambda =1216\stackrel{\circ }{A}$

Since $R_H=\frac{m{k}^2{e}^4}{2h^4}$

Hence for muonic atom, $R_H=\frac{\mu k^2{e}^4}{2h^4}$
$\therefore \lambda =\frac{1216}{200}=6.5\stackrel{\circ }{A}$