Which of the following correctly describes the allowed values for the four quantum numbers n, l, m_l, and m_s for an electron in an atom?

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

Answer: (C)

Verified step by step guidance

1. Understand that the four quantum numbers describe the unique quantum state of an electron in an atom: the principal quantum number \(n\), the azimuthal (angular momentum) quantum number \(l\), the magnetic quantum number \(m_l\), and the spin quantum number \(m_s\).
2. Recall the allowed values for each quantum number: \(n\) is a positive integer starting from 1, so \(n = 1, 2, 3, \ldots\).
3. The azimuthal quantum number \(l\) depends on \(n\) and can take integer values from 0 up to \(n-1\), so \(l = 0, 1, 2, \ldots, n-1\).
4. The magnetic quantum number \(m_l\) depends on \(l\) and can take integer values from \(-l\) to \(+l\), including zero, so \(m_l = -l, -(l-1), \ldots, 0, \ldots, (l-1), +l\).
5. The spin quantum number \(m_s\) describes the electron spin and can only be \(+\frac{1}{2}\) or \(-\frac{1}{2}\).