# How can only one valence electron in sodium cause doublet in spectrum?

The valence electron in sodium atom gets excited and moves to higher orbital say $3P$ and it then comes to the lower energy state $3S$ thus there should be only one line in spectrum (regarding this particular transition). But my book says since $3P$ can exist in 2 states $3P_{1/2}$ and $3P_{3/2}$ so there are doublet in the spectrum but how can only one electron make two transitions - from $3P_{1/2}$ to $3S$ and from $3P_{3/2}$ to $3S$ ?

• $\uparrow$ Which book? – Qmechanic Mar 21 '16 at 18:11
• chapter 5 from the book Atomic physics (volume 2) by John Yarwood – shivani Mar 22 '16 at 7:00

But my book says since 3P can exist in 2 states 3P1/2 and 3P3/2 so there are doublet in the spectrum but how can only one electron make two transitions - from 3P1/2 to 3S and from 3P3/2 to 3S ?

Actually your book is saying correctly that there are two levels belonging to P-state i.e. l=1 state -its happening due to coupling of spin and orbital state of electron given by quantum numbers namely l and s respectively.

Spin orbit coupling can give those two P-state belonging to two j-values ;

namely j= l + 1/2 and j= l - 1/2 ;With same (l=1)orbital state the electron can stay in two spin states +1/2 and -1/2 in the unit of hbar. This gives us the two 3Pj state namely j=3/2 and j=1/2 only.

As the energy level differ slightly for the above two j-values. The electron has two options to stay with definite probability i any one of them and the transitions to the 3Sj-state leads to two emission lines (D1 and D2) separated by approximately 5 Angstrom which we know as sodium doublet. This is clear evidence/effect of spin orbit interaction or l-s coupling.

• I understood that the two states are arising due to spin-orbit coupling but i was confused that how can both transition be possible if there is a single electron. so if i want to know how actually this is working then for electron to be in two states it should be either parallel or anti-parallel i.e. it should have spin wither $+1/2$ or $-1/2$. but how can a electron have simultaneously two spin quantum numbers? is there any clear mechanism that explains these transitions? or we just know the probability that electron can be in both states that's why we see the doublet? – shivani Mar 22 '16 at 6:59
• @earthling ,the 'microsystems' explained by quantum picture -a particular electron can stay in possible states with finite probability but as soon as one measures its state it will be found in one of the possible state-so simultaneously its not present in the two state-suppose somebody makes several measurements on a particular atom then for some it will be found in Ist state and for the rest it may be in IInd state, However in spectra production a very large number of Na atoms are involved and a good number of them can stay in either state and provide transition opportunity.. – drvrm Mar 22 '16 at 8:27

It is not one electron making the transitions. For each atom electrons can exist in two P states and if a transition to an S state is possible the one of quantum jumps occurs. So when you see the spectrum doublet it is the result of these quantum jumps by electrons in different atoms.