The positronium consisting of an electron and a positron corresponding binding energy and wavelength of first line in Lyman series of such a system.

Answer

`- 6.8 eV, 2430 Å`

Explanation

The reduced mass of the system (electron and positron ) is given by
`mu = (mm)/(m + m) = (m)/(2)`
where `m = mass` of electron or positron.
The radius of first Bohr's orbit is given by
`r_(1) = (h^(2))/(4 pi^(2) Ke^(2) (m//2))`
`= 2 xx `Radius of first Bohr's orbit of hydrogen
`= 2 xx 0.529 = 1.058 Å`
Energy of first Bohr's orbit is given as
`E_(1) = (2 pi^(2) K^(2) z^(2) e^(2) (m//2))/(h^(2))`
`= - (1)/(2) xx ` ground state of hydrogen
` = - (1)/(2) xx 13.6 eV`
`= - 6.8 eV` (Binding energy)
The wavelength of Lyman series is given by
`(1)/(lambda) = R_(1) [(1)/(1^(2)) - (1)/(2^(2))] = R_(1) ((1)/(1^(2)) - (1)/(2^(2)))`
`lambda = (4)/(3 R_(1))`
`R_(mu) = (2 pi^(2) K^(2) e^(2) mu)/(3) = (R)/(m_(e)) mu = (1)/(2) R`
`= 10967800 xx (1)/(2) = 5483900 m^(-1)`
or `lambda = (4)/(3 xx 5483900) m`
`= 2430 Å`