Which of the following best describes the partial energy level diagram for a hydrogen atom?

• A. The energy levels are evenly spaced and each can hold up to two electrons.
• B. The energy levels become closer together as n increases, and each level can hold up to two electrons with opposite spins.
• C. The energy levels become closer together as n increases, and each level can hold only one electron.
• D. The energy levels are equally spaced and each can hold an unlimited number of electrons.

Answer: (B)

Verified step by step guidance

1. Recall that the hydrogen atom's energy levels are quantized and described by the principal quantum number \( n \). The energy of each level is given by the formula \( E_n = -\frac{13.6\,\text{eV}}{n^2} \), where \( n = 1, 2, 3, \ldots \).
2. Understand that as \( n \) increases, the energy difference between consecutive levels decreases because the energy depends on \( 1/n^2 \). This means the levels get closer together at higher \( n \) values.
3. Remember that each energy level (or shell) can hold electrons according to the Pauli exclusion principle, which states that each orbital can hold up to two electrons with opposite spins.
4. Note that for the hydrogen atom, which has only one electron, the concept of electron capacity per level is theoretical, but the rule still applies: each orbital can hold two electrons with opposite spins.
5. Combine these points to conclude that the correct description is that the energy levels become closer together as \( n \) increases, and each level can hold up to two electrons with opposite spins.