1. The problem statement, all variables and given/known data One of the n=5 states of hydrogen is split by spin-orbit coupling into two levels with an energy difference of 0.0039 cm^-1 . Determine the 'l' quantum number for this state and predict the analogous splitting for doubly ionised Li . 2. Relevant equations The fine structure constant is 0.007 297 3. 3. The attempt at a solution Ok I did the first part and I got l=3 basically I use the spin orbit coupling energy equation and set j= l + 1/2 and j= l-1/2 find the difference between both of them and then work out the value of 'l' knowing that the wave number is 0.0039. What I dont understand is the second part. Do I use n=5 and l=3 and do the same thing? Thanks.