Question

A certain atom can exist in one of four quantum states, with energy levels 0, E, 2E, and 4E. If all possible transitions between the four energy levels are allowed, how many lines will be present in the absorption spectrum of this atom?

Answer 1

The energy levels are arranged in the following ways for an atom with four different quantum states

Since there is no restriction on the possible transitions. the total numbe of possible transition is a combination

the six transitions are shown in the figure above.

Transiton
	E
	2E
	4E
	E
	3E
	2E

The lines that will appear in the absorption spectrum will be a representative of the difference in energy between two levels.

This is because the energy of the photon that carries out a transition must equal the energy difference between the levels in that particular transition.

From the table,we see that the transitons results in same energy difference. hence will be shown in the same line in the spectrum.

Similarly, the transitons results in same energy difference, hence, they will also be representaed by a single line.

Hence, the total number of lines that will be present in the absorption spectrum will be four.  

The four lines will corresppond to energies of E, 2E, 3E, and 4E.