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:
$\frac{1}{\lambda }=R_H[\frac{1}{n_1^2}-\frac{1}{n_2^2}](R_H=109678{cm}^{-1})$

Radius of first Bohr orbit of muonic hydrogen atom is

• A. $\frac{0.259}{207}\mathring{A}$
• B. $\frac{0.529}{207}\mathring{A}$
• C. $0.529\times 207\mathring{A}$
• D. $0.259\times 207\mathring{A}$

Answer 1

Answer: (B)

$\frac{0.529}{207}\mathring{A}$

$r\propto \frac{1}{m}$
m is the mass of the particle (electron or muon) and r is the radius of the first orbit of the atom.
$\frac{r_{muonic}}{r_{electronic}}=\frac{m_{electron}}{m_{muon}}$
$\frac{r_{muonic}}{0.529A^o}=\frac{1}{207}$
$r_{muonic}=\frac{0.529A^o}{207}$