A hydrogen atom with an elerctron in the first shell ( n = 1) absorbls ` UV` light of a wavelength
` 1. 03 xx 10^(-7) m` To what shell does the electron jumps ?

Explanation

` Delta E = (hc)/( lambda) = ( 6.626 xx 10^(-34) xx 3.0 xx 10^8)/( 1.03 xx 10^(-7))`
` = 1.93 xx 10^(-18) J`
` E_n -E_1 = 1 . 93 xx 10 ^(-18) J`
` E_1 -E_1 = 1. 93xx 10^(-18) J`
` E_1 - E_1/n^2 = 1 . 93 xx 10^(-18) J`
` or ( n^2 -1)/n^2 = ( 1.93 xx 10^(-18))/E_1`
` = (1. 93 xx 10^(-18))/( 13. 7 xx 1. 602 xx 10^(-19))`
` [E_1 = 13 . 7 eV = 13 . 7 xx 1. 602 xx 10^(-19) J]`
` ( n^2 -1)/n^2 =0. 88 therefore n= 2. 89 =3` .