Which of the following is the correct set of quantum numbers for the outer shell electrons of `._(21)Sc`

Options

A. `3, 2,0, +(1)/(2)`
B. `4, 0,0, +(1)/(2)`
C. `3, 0,0, -(1)/(2)`
D. `4 ,0,-1, +(1)/(2)`

Explanation

To determine the correct set of quantum numbers for the outer shell electrons of Scandium (Sc, atomic number 21), we will follow these steps:

### Step 1: Determine the Electron Configuration
The electron configuration for Scandium (Sc) is:
- The first 18 electrons fill up to Argon (Ar): 1s² 2s² 2p⁶ 3s² 3p⁶
- The next 3 electrons fill the 3d and 4s subshells: 3d¹ 4s²

Thus, the outermost electrons for Scandium are in the 3d and 4s subshells.

### Step 2: Identify the Outer Shell Electrons
The outer shell electrons for Scandium are:
- 3d¹ (1 electron)
- 4s² (2 electrons)

Since we are only interested in the outermost shell, we focus on the 4s² electrons.

### Step 3: Assign Quantum Numbers
Quantum numbers consist of four values:
1. **Principal Quantum Number (n)**: This indicates the energy level of the electron. For the 4s electrons, n = 4.
2. **Azimuthal Quantum Number (l)**: This indicates the subshell. For s orbitals, l = 0.
3. **Magnetic Quantum Number (m)**: This indicates the orientation of the orbital. For an s orbital (l = 0), m can only be 0.
4. **Spin Quantum Number (s)**: This indicates the spin of the electron. It can be either +1/2 or -1/2.

### Step 4: Compile the Quantum Numbers
For the 4s² electrons, the quantum numbers are:
- For the first electron: n = 4, l = 0, m = 0, s = +1/2
- For the second electron: n = 4, l = 0, m = 0, s = -1/2

### Conclusion
The correct set of quantum numbers for the outer shell electrons of Scandium (Sc) is:
- (n = 4, l = 0, m = 0, s = +1/2) for one electron
- (n = 4, l = 0, m = 0, s = -1/2) for the other electron

### Final Answer
The correct set of quantum numbers for the outer shell electrons of Scandium (Sc) is:
- (4, 0, 0, +1/2) and (4, 0, 0, -1/2)

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