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

Energy of first Bohr orbit of muonic hydrogen atom is

• A. $-\frac{13.6}{207}eV$
• B. $-13.6\times 207eV$
• C. $+\frac{13.6}{207}eV$
• D. $+13.6\times 207eV$

Answer 1

The correct option is B $-13.6\times 207eV$

$E\propto m$
m is the mass of the particle (electron or muon) and E is the energy of first orbit of the atom.

$\frac{E_{muonic}}{E_{electronic}}=\frac{m_{muon}}{m_{electron}}$

$\frac{E_{muonic}}{-13.6eV}=\frac{207}{1}$

$E_{muonic}=-13.6\times 207eV$
Option B is correct.