Step 1: Find the first Bohr's orbit of a muon.
Mass of a negatively charged muon,
According to Bohr's model,
And, the energy of a ground state electronic hydrogen atom,
Also, the energy of a ground state muonic hydrogen atom,
We have the value of the first Bohr orbit,
Let , be the radius of the muonic hydrogen atom.
At equilibrium, we can write the relation as:
Hence, the value of the first Bohr radius of a muonic hydrogen atom is .
Step 2: Find the ground state energy of muon.
Take the ratio of these energies as:
Hence, the ground state energy of a muonic hydrogen atom is -2.81 keV.