Which of the following sets of quantum numbers is correct for an electron in 4 f-orbital?

Options

A. n=4,l=3,m=+4,s=`+1//2`
B. n=4,l=4,m=-4,s`-1//2`
C. n=4,l=3,m=+1, `s=+1//2`
D. n=3,l=2,m=-2,`s=+1//2`

Explanation

To determine the correct set of quantum numbers for an electron in a 4f-orbital, we need to understand the quantum numbers involved:

1. **Principal Quantum Number (n)**: This number indicates the energy level of the electron and is always a positive integer. For a 4f-orbital, the principal quantum number (n) is 4.

2. **Azimuthal Quantum Number (l)**: This number defines the shape of the orbital. The values of l are determined by the type of orbital:
- s-orbital: l = 0
- p-orbital: l = 1
- d-orbital: l = 2
- f-orbital: l = 3
Therefore, for a 4f-orbital, the azimuthal quantum number (l) is 3.

3. **Magnetic Quantum Number (m)**: This number describes the orientation of the orbital in space. The values of m range from -l to +l. For l = 3 (f-orbital), the possible values of m are -3, -2, -1, 0, +1, +2, +3.

4. **Spin Quantum Number (s)**: This number indicates the spin of the electron and can take on values of either +1/2 or -1/2.

Now, we can summarize the quantum numbers for an electron in a 4f-orbital:
- n = 4
- l = 3
- m = -3, -2, -1, 0, +1, +2, +3
- s = +1/2 or -1/2

Next, we will analyze the given options to find the correct set of quantum numbers.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- For a 4f-orbital, n = 4.

2. **Identify the Azimuthal Quantum Number (l)**:
- For f-orbitals, l = 3.

3. **Identify the Magnetic Quantum Number (m)**:
- The possible values for m are -3, -2, -1, 0, +1, +2, +3.

4. **Identify the Spin Quantum Number (s)**:
- The possible values for s are +1/2 or -1/2.

5. **Evaluate the Options**:
- Check each option to see if they match the identified quantum numbers.
- Eliminate any options that do not have n = 4 and l = 3.
- For the remaining options, check if the m and s values are valid.

6. **Select the Correct Option**:
- After evaluating the options, the correct set of quantum numbers will be the one that matches n = 4, l = 3, and has valid m and s values.

### Conclusion:
The correct set of quantum numbers for an electron in a 4f-orbital is found in option C.