In a protonium atom, a proton and an antiproton orbit each other. What is the energy of a photon emitted in transition of a protonium atom from the first excited state to the  ground state?

In protonium atom, proton and antiproton rotate about the centre of mass. Applying Bohr’s model, we realize that energy in an orbit is $\frac{m_P}{2m_e}$ times that of electron in hydrogen atom. Hence, the deexcitation from first to ground state results in $\frac{m_P}{2m_e}$ times that of 10.2 eV