Postronium consists of an electron and a position (same mass apposite charge) orbiting around their common center of mass .The specitum is, therefore expected to be hydrogen like , the difference arining from the mass difference .Calculate the wavelength of the first three line of the balmer series of positrunium

Explanation

The masses of the electron are comparable and in into system the mass of the nucless is also to the taken into account in the energy equation instead of the mass of the electron the redation mass is to be taken by defination tredaced mass `mu` is
`(1)/(mu) = (1)/(m) + (1)/(M)`
`m` is the mass of the electron and M is the mass of the necless
`mu= ( m xx M)/(m + M)`
Since the mass of position = mass of electron
`mu = ( m xx m)/(2m ) = (m)/(2)`ltMbrgt Therefore the Ryudbery constant for possitronium is `R_(pos)= (2 pi^(2)mue^(4)k^(2))/(h^(3)c) = (2pi^(2)(m//2)e^(4)k^(2))/(h^(3)c)`
`= (R_(H))/(2) = (109737)/(2) = 54868.5 cm^(-1)`
From line of Balmer series
`bar v_(1) = 54868.5 ((1)/(2^(2)) - (1)/(3^(2))) = 7620.6 cm^(-1)`
sercond line
`bar v_(2) = 549868.5((1)/(2^(2)) - (1)/(4^(2))) = 10288cm^(-1)`
Third line
`bar v_(3) = 549868.5 ((1)/(2^(2)) - (1)/(5^(2))) = 11522 cm^(-1)`