The longest wavelenght doublet absorption transition is observed at 589 and 589.6 nm. Energy difference between two excited states is

Explanation

For first transition :
`lambda_(1)=589 nm=589 xx 10^(-9)m`
`v_(1)=c/lambda_(1)=(3.0 xx 10^(8))/(589 xx 10^(-9)) 1 =5.093 xx 10^(14) s^(-1)`
and `E_(1)=hv_(1)=(6.626 xx 10^(-34)) xx (5.093 xx 10^(14))`
`=3.37462 xx 10^(-19)J`
For second transition :
`v_(2)=c/lambda_2=(3.0 xx 10^(8))/(589.6 xx 10^(-9))`
`=5.088 xx 10^(14) s^(-1)`
and `E_(2)=hv_(2)=(6.626 xx 10^(-34)) xx (5.088 xx 10^(14))`
`=3.37131 xx 10^(-19)J`
The energy difference between the two excited states
`=E_(1)-E_(2)`
`=(3.37462 xx 10^(-19)) -(3.37131 xx 10^(-19))`
`=3.311 xx 10^(-22)J`