Question

A formula analogous to the Rydberg formula applies to the series of spectral lines which arise from transitions from higher energy level to the lower energy level of hydrogen atom.
A muonic hydrogen atom is like a hydrogen atom in which the electron is replaced by a heavier particle, the 'muon'. The mass of the muon is about $207$ times the mass of an electron, while the charge remains same as that of the electron. Rydberg formula for hydrogen atom is:
$\frac{1}{\lambda }=R_H[\frac{1}{n_1^2}-\frac{1}{n_2^2}](R_H=109678{cm}^{-1})$

Angular momentum of 'muon' in muonic hydrogen atom may be given as:

• A. $\frac{h}{\pi }$
• B. $\frac{h}{2\pi }$
• C. $\frac{h}{4\pi }$
• D. $\frac{h}{6\pi }$

Answer 1

Answer: (B)

$\frac{h}{2\pi }$

Angular momentum of 'muon' in muonic hydrogen atom may be given as either $\frac{h}{\pi }$ or $\frac{h}{2\pi }$
Angular momentum of 'muon' in muonic hydrogen atom is an integral multiple of $\frac{h}{2\pi }$
$mvr=n\left(\frac{h}{2\pi }\right)$