# Drawing spectral lines

1. Jan 21, 2012

### v_pino

1. The problem statement, all variables and given/known data

A meteorite found in Antarctica contains a trace of a mysterious element. Its spectral lines are all multiples of a frequency f0. The multiples are:
1, 2, 3, 5, 6, 8, 10, 11, 13, 16, 18, 19, 21, 26, 29, 31, 32, 34, 42, 47, 50, 52, 53 .

The frequencies in bold have twice the intensity expected from the pattern of intensities of
the other lines. The investigating spectroscopists assume that these are cases in which two
distinct transitions have the same frequency.

(a) Find the simplest set of energy levels that will produce the frequency spectrum.
Assume that transitions between all levels occur, and that the energy levels (like those of
hydrogen) get closer together as the energy increases.

(b) Draw with care the energy-level diagram. To the right, draw the frequency spectrum,
scaled (as in Fig. 5) to the highest frequency.

(c) The symbol given to the new element is Fb. What is its name?

2. Relevant equations

$$hf=-13.6\left ( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right )eV$$

3. The attempt at a solution

If the spectral lines, like that of hydrogen, get smaller, how can I double the frequency? For example, assuming it is like hydrogen, the ground level is -13.6eV and the second is -3.4eV and the third is -1.51eV. If I take the transition of ground to first level as f0, then 2*f0 has to be from ground level to infinity.

How can I draw such spectral line?

Thanks