How many electrons in the 3d subshell of an atom can have a spin quantum number of +1/2?

• A. 10
• B. 3
• C. 5
• D. 1

Answer: (C)

Verified step by step guidance

1. Recall that the 3d subshell corresponds to the principal quantum number \(n=3\) and the azimuthal quantum number \(l=2\), which means it has 5 orbitals (since the number of orbitals in a subshell is given by \$2l + 1$).
2. Each orbital can hold a maximum of 2 electrons, one with spin quantum number \(+\frac{1}{2}\) and one with spin quantum number \(-\frac{1}{2}\).
3. Since there are 5 orbitals in the 3d subshell, and each orbital can have one electron with spin \(+\frac{1}{2}\), the maximum number of electrons with spin \(+\frac{1}{2}\) is equal to the number of orbitals.
4. Therefore, the number of electrons in the 3d subshell that can have a spin quantum number of \(+\frac{1}{2}\) is 5.
5. This is consistent with the Pauli exclusion principle, which states that no two electrons in the same atom can have the same set of four quantum numbers, so each orbital can only have one electron with a given spin.