- #1

Kara386

- 208

- 2

## Homework Statement

The spectrum of barium contains the following series of energy levels (given relative to ground):

1.521, 1.567, 1.676 (all in eV)

What are the most likely values of L, S, J?

## Homework Equations

## The Attempt at a Solution

I tried using the Lande interval rule, giving the lowest state the value j, then the 1.567 level j+1 and j+2 for 1.676. If the change between 1.521 and 1.567 is ##\Delta E = 0.046## and the change between 1.567 and 1.676 is ##\Delta E_2 = 0.109##, then ##\Delta E_2 \approx \frac{12}{5} \Delta E##. So by the interval rule

##\Delta E = 2B(j+1)## (1)

##\frac{12}{5}\Delta E = 2B(j+2)## (2)

Dividing (1) by (2) to get rid of the constant,

##\frac{5}{12} = \frac{j+1}{j+2}## which would give me ##j = -\frac{2}{7}##. Which is wrong. But that's the only method I can think of! Have I made a mistake or should I be using a different approach?

I'm also very confused by the phrase 'most likely' values; should the method I'm meant to use give multiple possibilities? Thanks for any help!