When a particle as an electron exist in a box, three quantum numbers are necessary to describe the spatial distributioni fo electrons in atoms. The describe an electron in an atom completely, a fourth quantum number, `m_(s)` called the spin quantum number must be specified. This is because every electron has magnetic moment associated with it which is quantized in one of two possible orientations. Electrons having the same spin strongly repel each other and tend to occupy different region of space. This result of a fundamental law of nature is known as Pauli exclusion principle.
The valence shell electron of sodium has the quantum numbers (n,l,m,s)

Options

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

Answer

To determine the quantum numbers for the valence shell electron of sodium, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Number of Sodium**:
Sodium (Na) has an atomic number of 11, which means it has 11 electrons.

2. **Write the Electron Configuration**:
The electron configuration for sodium is:
- 1s² 2s² 2p⁶ 3s¹
This shows that the valence electron is in the 3s orbital.

3. **Determine the Principal Quantum Number (n)**:
The principal quantum number (n) indicates the energy level of the electron. For the 3s orbital, n = 3.

4. **Determine the Azimuthal Quantum Number (l)**:
The azimuthal quantum number (l) describes the shape of the orbital. For s orbitals, l = 0.

5. **Determine the Magnetic Quantum Number (m)**:
The magnetic quantum number (m) indicates the orientation of the orbital. For s orbitals, m = 0.

6. **Determine the Spin Quantum Number (s)**:
The spin quantum number (s) describes the spin of the electron. It can take one of two values: +1/2 or -1/2. Since we cannot determine the specific spin without additional information, we can state that s can be either +1/2 or -1/2.

### Summary of Quantum Numbers:
- Principal Quantum Number (n) = 3
- Azimuthal Quantum Number (l) = 0
- Magnetic Quantum Number (m) = 0
- Spin Quantum Number (s) = +1/2 or -1/2

### Final Answer:
The quantum numbers for the valence shell electron of sodium are:
- (n, l, m, s) = (3, 0, 0, +1/2 or -1/2)