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,

Bohr radius,

And, energy of a ground state electronic hydrogen atom,

We have the value of the first Bohr orbit,

Let r_μ be the radius of 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

2.56 × 10⁻¹³ m.

We have,

E_e= − 13.6 eV

Take the ratio of these energies as:

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