Introduction:
In a muonic atom, a muon (μ-) replaces the electron (e-) in a hydrogen atom. The muon is 207 times heavier than the electron, which results in significant changes in the energy levels of the atom. We need to express the energy levels (En) of the muonic atom in terms of the binding energy (Eo) of ordinary hydrogen.

Derivation:

1. Energy Levels of Hydrogen Atom:
The energy levels of a hydrogen atom are given by the equation:
En = - Eo / n²
where Eo is the binding energy of the hydrogen atom and n is the principal quantum number.

2. Mass of Muonic Atom:
The mass of a muonic atom (mμ) is given as 207 times the mass of an electron (me):
mμ = 207me

3. Reduced Mass:
The reduced mass (μ) of a muonic atom is given by the equation:
μ = (mp * mμ) / (mp + mμ)
where mp is the mass of the proton.

4. Substituting Values:
Substituting the values of mμ and mp into the equation for reduced mass, we have:
μ = (mp * 207me) / (mp + 207me)

5. Energy Levels of Muonic Atom:
The energy levels (En') of the muonic atom can be expressed in terms of the binding energy (Eo') of ordinary hydrogen using the reduced mass (μ') of the muonic atom:
En' = - Eo' / n²
where Eo' is the binding energy of the muonic atom and n is the principal quantum number.

6. Relationship between Binding Energies:
The binding energy of the muonic atom (Eo') can be related to the binding energy of ordinary hydrogen (Eo) using the reduced mass (μ') of the muonic atom:
Eo' = Eo * (μ' / μ)
Substituting the values of μ' and μ, we have:
Eo' = Eo * ((mp + 207me) / (mp * 207me))

7. Expressing Energy Levels in terms of Binding Energy:
Substituting the value of Eo' into the equation for En', we get:
En' = - (Eo * ((mp + 207me) / (mp * 207me))) / n²
Simplifying further, we have:
En' = - (Eo / n²) * ((mp + 207me) / (mp * 207me))

Conclusion:
The energy levels (En') of the muonic atom can be expressed in terms of the binding energy (Eo) of ordinary hydrogen using the equation:
En' = - (Eo / n²) * ((mp + 207me) / (mp * 207me))
where n is the principal quantum number.