How many 3d electrons can have spin quantum number `- (1)/(2)` ?

Options

A. 5
B. 7
C. 8
D. 10

Answer

To determine how many 3d electrons can have a spin quantum number of -1/2, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the d-subshell**: The d-subshell consists of 5 orbitals. Each orbital can hold a maximum of 2 electrons.

2. **Total electrons in the d-subshell**: Since there are 5 orbitals, the total number of electrons that can occupy the d-subshell is 5 orbitals × 2 electrons/orbital = 10 electrons.

3. **Spin quantum number**: Each electron can have one of two possible spin quantum numbers: +1/2 (up spin) or -1/2 (down spin).

4. **Filling of orbitals**: According to Hund's rule, electrons will fill each of the 5 orbitals singly with up spin (+1/2) before any orbital is doubly occupied with down spin (-1/2).

5. **Distribution of spins**:
- Initially, the 5 orbitals will each have 1 electron with spin +1/2, totaling 5 electrons with spin +1/2.
- After the first 5 electrons are placed, the next 5 electrons will start to fill the orbitals again, this time with spin -1/2.

6. **Counting down spin electrons**: Since there are 5 orbitals, each can accommodate 1 electron with spin -1/2. Therefore, all 5 orbitals can have 1 electron with spin -1/2.

7. **Conclusion**: Thus, the total number of 3d electrons that can have a spin quantum number of -1/2 is 5.

### Final Answer:
There can be **5 electrons** in the 3d subshell that have a spin quantum number of -1/2.

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