Answer –
We are given that the mass of a negatively charged muon is mμ = 207 me
Now, According to Bohr’s model bohr’s radius is given by –
The energy of a ground state muonic hydrogen atom is such that Eμ α mμ
We are given the value of the first Bohr orbit,
re = 0.53 A = 0.53 × 10-10 m
Let rμ represent the radius of muonic hydrogen atom.
Now, writing the equation at the equilibrium –
Therefore, 2.56 × 10−13 m is the value of first Bohr radius for a muonic hydrogen atom.
We know that,
Ee= − 13.6 eV
Applying the ratio of the energies we get the relation –
The ground state energy of a muonic hydrogen atom is -2.81keV.