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 (μ^–1) of mass about 207m_e orbits around a proton].

Answer 1

Let m be the mass of the electron the first Bohr radius of H-atom is given by,

in a muonic hydrogen atom, in place of an electron, a negatively charged muon having mass 207m_e. revolves around the nucleus of hydrogen i.e. proton.
If r₁‘ is first Bohr’s radius of muonic hydrogen atom,