Which of the following excited electrons has the lowest energy?

• A. An electron in the n = 2 energy level
• B. An electron in the n = 3 energy level
• C. An electron in the n = 5 energy level
• D. An electron in the n = 4 energy level

Answer: (A)

Verified step by step guidance

1. Recall that the energy of an electron in a hydrogen-like atom is given by the formula \(E_n = -\frac{R_H}{n^2}\), where \(R_H\) is the Rydberg constant and \(n\) is the principal quantum number (energy level).
2. Understand that the energy levels are quantized and negative, meaning that as \(n\) increases, the energy becomes less negative and thus higher in energy.
3. Compare the energy levels for the given values of \(n\): 2, 3, 4, and 5. Since energy is inversely proportional to \(n^2\), the smallest \(n\) corresponds to the lowest (most negative) energy.
4. Identify that the electron in the \(n=2\) level has the lowest energy among the excited states listed because \(E_2 < E_3 < E_4 < E_5\) in terms of energy values (more negative means lower energy).
5. Conclude that the electron in the \(n=2\) energy level is the excited electron with the lowest energy compared to the others.