Which one of the following sets of quantum number is possible for electron in a 4f- orbital?

Options

A. `{:(n,l,m,s),(4,3,+4,+1//2):}`
B. `{:(n,l,m,s),(4,3,+1,-1//2):}`
C. `{:(n,l,m,s),(4,4,+4,-1//2):}`
D. `{:(n,l,m,s),(4,2,+4,+1//2):}`

Answer

To determine which set of quantum numbers is possible for an electron in a 4f orbital, we need to analyze the quantum numbers 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, n = 4.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) determines the shape of the orbital. For f orbitals, l = 3.

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

### Step 4: Determine the Spin Quantum Number (s)
The spin quantum number (s) can take values of +1/2 or -1/2.

### Step 5: Analyze the Options
Now we need to analyze the given options based on the values we have determined:
1. The principal quantum number (n) must be 4.
2. The azimuthal quantum number (l) must be 3.
3. The magnetic quantum number (m) must be between -3 and +3.
4. The spin quantum number (s) must be either +1/2 or -1/2.

### Conclusion
After checking all the options, we find that the only set of quantum numbers that fits all the criteria for an electron in a 4f orbital is the second option.