For a 3s^2 electron in phosphorus (atomic number 15, electron configuration: 1s^2 2s^2 2p^6 3s^2 3p^3), what is the value of the third quantum number (magnetic quantum number, m_l) for this electron?

• A. 1
• B. 2
• C. -1
• D. 0

Answer: (D)

Verified step by step guidance

1. Identify the principal quantum number (n) for the electron. Since the electron is in the 3s orbital, n = 3.
2. Determine the azimuthal quantum number (l) for the 3s orbital. For s orbitals, l = 0.
3. Recall that the magnetic quantum number (m_l) can take integer values from -l to +l, including zero. Since l = 0, m_l can only be 0.
4. Therefore, the magnetic quantum number (m_l) for the 3s^2 electron in phosphorus is 0.
5. This means the electron's orbital orientation in space is unique and not degenerate with other orientations, as s orbitals are spherical.