Which one of the following sets of quantum numbers represents an electron with the highest energy?

• A. n = 1, l = 0, m_l = 0, m_s = -1/2
• B. n = 3, l = 2, m_l = +1, m_s = +1/2
• C. n = 4, l = 0, m_l = 0, m_s = +1/2
• D. n = 2, l = 1, m_l = 0, m_s = -1/2

Answer: (C)

Verified step by step guidance

1. Understand that the principal quantum number \(n\) primarily determines the energy level of an electron in an atom. Higher \(n\) values generally correspond to higher energy levels.
2. Recall that the azimuthal quantum number \(l\) defines the subshell (s, p, d, f) and slightly affects energy within the same principal level, but \(n\) has a greater impact on energy than \(l\).
3. Compare the given sets of quantum numbers by their principal quantum number \(n\): \(n=1\), \(n=3\), \(n=4\), and \(n=2\). The electron with the highest \(n\) will have the highest energy.
4. Since \(n=4\) is the highest principal quantum number among the options, the electron with \(n=4, l=0, m_l=0, m_s=+1/2\) will have the highest energy.
5. Note that the magnetic quantum number \(m_l\) and spin quantum number \(m_s\) do not significantly affect the energy ordering compared to \(n\) and \(l\) in this context.