A positronium "atom" is a system that consists of a positron and an electron that orbit each other. Campare the wavelengths of the spectral lines of positronium with those of ordinary hydrogen.

Explanation

Here the two particle have the same mass `m`, so the reduced mass is
`mu=(mM)/(m+M)=(m^(2))/(2m)=(m)/(2)`
where `m` is the electron mass. We know that `E_(n)propm`
`:. (E'_(n))/(E_(n))=(mu)/(m)=(1)/(2)` energy of each level is halved `:.` Their difference will also be halved.
Hence `lambda'_(n)=2 lambda_(n)`