Positronium emitted wavelengths

[stefan.t1990]

Hey everyone so I'm having some trouble figuring out how to approach this question. I don't need a step by step solution just an idea of how I should approach the question and maybe some specifics on how to apply needed concepts such as reduced mass. Thank you.

"Assuming positronium were a normal atom, show that the wavelengths of the emitted lines would be double those emitted by a hydrogen atom ( assuming an infinitely heavy nucleus)."

 

[stefan.t1990]

I used reduced mass to model the electron as orbiting the nucleus(positron). I used the formula: (M/m+M)Rinf=Rm, and then used the new value of Rm along with the Balmer formula to obtain emitted wavelengths. Can somebody confirm this is correct?