Question

In the above question, if ground state energy of electron is $- 13.6\text{ eV}$ then what is the ground state energy of muonic hydrogen atom?

• A. 1.8 keV
• B. $- 2.8\text{ keV}$
• C. $- 3.8\text{ keV}$
• D. 4.8 keV

Answer 1

Answer: (B)

$- 2.8\text{ keV}$

Answer 2

According to Bohr’s atomic model energy

$E \propto m$

$\therefore\frac{E_{\mu}}{E_{e}} = \frac{m_{\mu}}{m_{e}}$

Here, $E_{e} = - 13.6eV$

$m_{\mu} = 207m_{e}$

$\therefore E_{\mu} = \frac{m_{\mu}}{m_{e}}E_{e} = \frac{207m_{e}}{m_{e}} \times ( - 13.6)eV$

$= - 2815.2eV = - 2.8KeV.$