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

First method:
`bar(v)=(3.289xx10^(15) s^(-1))xx(1/n_(low)^(2)1/n_(high)^(2))`
`=3.289xx10^(15) s^(-1)xx(1/2^(2)-1/4^(2))`
`=3.289xx10^(15) s^(-1)xx(1/4-1/16)`
`=3.289xx10^(15) s^(-1)xx3/16`
`=6.17xx10^(14) s^(-1)`
Since `c=vlambda`
or `lambda=c/v=(3.00xx10^(8)m s^(-1))/(6.17xx10^(14) s^(-1))=4.86xx10^(-7)m=486 nm`.
The colour of light corresponding to `486 nm` wavelength id blue.
Second method: `bar(v)=1/lambda=R(1/n_(1)^(2)-1/n_(2)^(2))=109677 cm^(-1)xx(1/2^(2)-1/4^(2))`
`=(109677xx3)/(16)`
`:. lambda=(16)/(109677xx3)=0.0000486`
`=486xx10^(-7) cm`
`=186xx10^(-9) m=486 nm`