For a 3s^2 electron in a phosphorus atom, what is the value of the third quantum number (magnetic quantum number, m_l)?

• A. 1
• B. 0
• C. 2
• D. -1

Answer: (B)

Verified step by step guidance

1. Identify the principal quantum number (n) and the azimuthal quantum number (l) for the given electron. For a 3s^2 electron, n = 3 (the shell number) and s corresponds to l = 0 (the subshell type).
2. Recall that the magnetic quantum number (m_l) depends on the azimuthal quantum number l and can take integer values from -l to +l, including zero.
3. Since l = 0 for an s orbital, the possible values of m_l are limited to just one value: 0.
4. Therefore, for the 3s^2 electron in phosphorus, the magnetic quantum number m_l must be 0.
5. This means the electron's orbital orientation in space is uniquely defined for an s orbital, which has spherical symmetry.