what is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n=4 to and energy level with n=2 ?
`{:((e),n=3, l=3,m_(1)=-3,m_(s)=+1//2), ((f), n=3, l=1, m_(1)=0, m_(s)=+1//2):}`

Explanation

The energy of the nth shell in hydrogen is given by
`E_(n)=-(2.178 xx 10^(-18))/(n^2)"J atom"^(-1)`
Thus, `E_(2)=-(2.178 xx 10^(-18))/((2)^2) and E_4=-(2.178 xx 10^(-18))/((4)^2)`
`triangle E=E_(4)-E_(2)=2.178 xx 10^(-18) (1/2^2-1/4^2)`
`=4.08 xx 10^(-19)" J atom"^(-1)`
Moreover `triangleE=hv=(hc)/lambda`
`lambda=(hc)/(triangleE)=(6.626 xx 10^(-34) xx 3 xx 10^(8))/(4.08 xx 10^(-19))`
`=4.87 xx 10^(-7) m=487nm`