The energy of the electron in the ground state of hydrogen is - 13.6 eV. Calculate the energy of the photon that would be emitted if the electron were to make a transition corresponding to the emission of the first line of the (i) Lyman series, (ii) Balmer series of the hydrogen spectrum.

Explanation

Energy of electron in ground state (n = 1) of hydrogen E, = - 13.6 eV.
(i) First line of Lyman series is emitted for transition n = 2 to n=1 . Hence .
`E_(2) = (E_(1))/((2)^(2)) = - (13.6)/(9) = - 3.4 eV`
`therefore ` Energy of the emitted photon `E_(1) = E_(3) - E_(2) = - 1.51 -(-3.4) = 1.89 eV`