An electron has spin quantum number (s) `+ 1//2` and magnetic quantum number is `1` it can be present in

Options

A. s orbital
B. d orbital
C. p orbital
D. f orbital

Answer

To determine where an electron with a spin quantum number of \( +\frac{1}{2} \) and a magnetic quantum number of \( m = +1 \) can be present, we will analyze the possible orbitals based on the values of the angular momentum quantum number \( l \) and the magnetic quantum number \( m \).

### Step-by-Step Solution:

1. **Identify the Spin Quantum Number**:
- The spin quantum number \( s \) is given as \( +\frac{1}{2} \). This indicates the direction of the electron's spin.

2. **Identify the Magnetic Quantum Number**:
- The magnetic quantum number \( m \) is given as \( +1 \).

3. **Determine Possible Orbitals**:
- **s Orbital**:
- For the s orbital, the angular momentum quantum number \( l = 0 \).
- The possible values of \( m \) for \( l = 0 \) are only \( 0 \) (i.e., \( m \) can take values from \( -l \) to \( +l \)).
- Therefore, \( m = +1 \) is **not possible** in the s orbital.

- **p Orbital**:
- For the p orbital, the angular momentum quantum number \( l = 1 \).
- The possible values of \( m \) for \( l = 1 \) are \( -1, 0, +1 \).
- Therefore, \( m = +1 \) is **possible** in the p orbital.

- **d Orbital**:
- For the d orbital, the angular momentum quantum number \( l = 2 \).
- The possible values of \( m \) for \( l = 2 \) are \( -2, -1, 0, +1, +2 \).
- Therefore, \( m = +1 \) is **possible** in the d orbital.

- **f Orbital**:
- For the f orbital, the angular momentum quantum number \( l = 3 \).
- The possible values of \( m \) for \( l = 3 \) are \( -3, -2, -1, 0, +1, +2, +3 \).
- Therefore, \( m = +1 \) is **possible** in the f orbital.

4. **Conclusion**:
- The electron with spin quantum number \( +\frac{1}{2} \) and magnetic quantum number \( +1 \) can be present in the following orbitals:
- **p orbital**
- **d orbital**
- **f orbital**

### Final Answer:
The electron can be present in the p, d, and f orbitals.