Which of the following sets of quantum numbers is correct for an electron in 4f 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`

Answer

To determine the correct set of quantum numbers for an electron in a 4f orbital, we need to understand the quantum numbers associated with this orbital. Let's break down the solution step by step:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the electron. For a 4f orbital, the value of n is:
- **n = 4**

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) defines the shape of the orbital. For the f subshell, the value of l is:
- **l = 3** (since f corresponds to l = 3)

### Step 3: Identify the Magnetic Quantum Number (m)
The magnetic quantum number (m) can take values from -l to +l. Therefore, for l = 3, the possible values of m are:
- **m = -3, -2, -1, 0, +1, +2, +3**

### Step 4: Identify the Spin Quantum Number (s)
The spin quantum number (s) can have two possible values:
- **s = +1/2 or -1/2**

### Step 5: Analyze the Options
Now we need to analyze the given options to find the correct set of quantum numbers:
1. **Option 1:** (n=4, l=3, m=+4, s=+1/2) - Incorrect because m cannot be +4.
2. **Option 2:** (n=4, l=4, m=0, s=+1/2) - Incorrect because l cannot be 4 for an f orbital.
3. **Option 3:** (n=4, l=3, m=+1, s=+1/2) - Correct because all values are valid.
4. **Option 4:** (n=4, l=3, m=0, s=-1/2) - Correct because all values are valid.

### Conclusion
The correct set of quantum numbers for an electron in a 4f orbital can be found in **Option 3** or **Option 4**. However, since the question asks for a single set, we can conclude that **Option 3** is a valid answer.

### Final Answer
The correct set of quantum numbers for an electron in a 4f orbital is **Option 3: (n=4, l=3, m=+1, s=+1/2)**.