Calculate frequency, energy and wavelength of the radiation corresponding to the speciral line of the lowest frequency in lyman series in the spectrum of a hydrogen atom .Also calculate the energy for the coresponding line in the spectrum of `Li^(2+).(R_(H) = 109677 cm^(-1), c = 3 xx 10^(8) m s^(-1), Z = 3)`

Explanation

Accroding to Rydberg equation,
`barv = R(1/(n_1^2) - 1/(n_2^2))`
For lowest frequency (or energy) in Lyman series:
`n_1 = 1, n_2 = 2`
`:. barv = 1.09678 xx 10^(7) (1/(1^2) - 1/(2^2))`
`= 1.09678 xx 10^7 xx 3/4`
`= 0.8226 xx 10^(7) m^(-1)`
Now, `barv = 1/lambda`
`:. lambda = 1/(barv) = 1/(0.8226 xx 10^7)`
`=1.216 xx 10^(-7) m`
`=121.6 nm`
Now, `v = c/lambda`
`=(3.0 xx 10^8)/(1.216 xx 10^(-7))`
`=2.47 xx 10^(15) s^(-1)`
Now, `E = hv`
`=6.625 xx 10^(-34) xx 2.47 xx 10^(15)` `= 1.636 xx 10^(-18) J`
For `Li^(2+) , Z = 3`
`:. E_(Li^(2+)) = (3)^2 xx 1.636 xx 10^(-18)`
`=1.47 xx 10^(-17) J`.