Question

A particular term in an atom in which LS coupling is a good approximation splits into three levels, each having the same L and same S but different J. If the relative spacings between the levels are in the proportion 5:3, find L and S.

Answer 1

Step-by-step explanation:

From the information given;

Consider using Lande's Interval rule which can be expressed as:

`\Delta E = E_(j+1) - E_jj \ = \alpha (j+1)`

here;

`j+1` = highest level of j

and

`(\Delta E_1)/(\Delta E_2) = ((j+2))/((j+1))`

`(5)/(3) = ((j+2))/((j+1))`

`5(j+1) = 3(j+2)`

`5j+5 = 3j+6`

`2j = 1\\ \\ j = (1)/(2)`

recall that:

`j = |S-L| \ \to \ |S+L |`

So;

`S-L = (1)/(2) --- (1)`; &

`S+L = (5)/(2) --- (1)`

Using the elimination method, we have:

`2S = (6)/(2)`

`S = (3)/(2)`

Since
`S = (3)/(2)`; then from (1)

`(3)/(2) -L = (1)/(2)`

`L = (2)/(2)`

`L = 1`