Calculate the wavelength of radiation emitted producing a line in the Lyman series ,when an electron falls from fourth stationary level in hydrogen atom `(R_(H) = 1.1 xx 10^(7)m^(-1))`

Explanation

According to Rydberg equation,
`1/lambda = R_H (1/(n_1^2) - 1/(n_2^2))`
For Lyman series, `n_1 = 1 and n_2 = 4`
`:. 1/lambda = 1.1 xx 10^7 (1/(1^2) - 1/(4^2)) m^(-1)`
`1/(lambda) = 1.1 xx 10^(7) xx 15/16`
or `lambda = (1 xx 6)/(1.1 xx 10^7 xx 15)= 9.70 xx 10^(-8) m`
or `lambda = 97.0 nm`.