Question

Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon (μ⁻) of mass about 207m_e orbits around a proton].

Answer 1

Mass of a negatively charged muon
According to Bohr’s model,

Hence, the value of the first Bohr radius of a muonic hydrogen atom is 2.56 × 10⁻¹³ m.
We have,

Ee= − 13.6 eV
Take the ratio of these energies as:

Hence, the ground state energy of a muonic hydrogen atom is −2.81 keV.