In an ordianary atom, as a first approximation, the motion of the nucleus can be ignored. In a positronium atom a positronreplaces the proton of hydrogen atom. The electron and positron masses are equal and , therefore , the motion of the positron cannot be ignored. One must consider the motion of both electron and positron about their center of mass. A detailed analyasis shows that formulae of Bohr's model apply to positronium atom provided that we replace `m_(e)` by what is known reduced mass is `m_(e)//2`.
When system de-excites from its first excited state to ground state, the wavelngth of radiation is

Explanation

In an ordinary atom, as a first approximation, we ignore the motion of the nucleus, being too heavy. In a positronium atom, a positron replaces proton of hydrogen atom. As electron and positron masses are equal, the motion of the positron cannot be ignored.
We consider motion of electron and positron about their centre of mass. A detailed analysis (beyond the scope of this book) shows that formulae of Bohr model apply to positronium atom provided that we replace `m_(e)` by what is known is reduced mass of the electron. emitted is double than that of the corresponding radiation emitted for a similar transition in hydrogen atom, which has a wavelength of `1217Å`, and hence is equal to `2xx1217=2434Å`. This radiation lies in the ultra-violet part of the electromagnetic spectrum.