Chapter 28, Problem 46A

To determine

The number of spectral line an atom having four energy levels can emit.

The transition that produces the photon with the highest energy.

Explanation of Solution

Introduction:

When an atom makes transition from one level to another it emits a photon of energy equal to the

energy difference between the two levels.

The atom has four energy levels, $E_4$ being the highest level and $E_1$ being the lowest. $E_2$ and $E_3$ are the two middle levels. The atom can make transition between any two levels.

The possible transitions are:

  $\begin{array}{l}{E}_4\to E_1\\ E_4\to E_2\\ E_4\to E_3\\ E_3\to E_1\\ E_3\to E_2\\ E_2\to E_1\end{array}$

  

Hence, the atom can emitsix possible spectral lines.

  $E_4$ being the highest energy level and $E_1$ being the lowest, their energy difference is the greatest from the rest. Therefore, the transition $E_4\to E_1$ emits the highest energy photon.

Conclusion:

The atom can emitsix possible spectral lines.

The transition $E_4\to E_1$ emits the highest energy photon.