The correct set of four quantum numbers for the outermost electron of sodium (Z = 11) is

Options

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

Explanation

To determine the correct set of four quantum numbers for the outermost electron of sodium (Z = 11), we can follow these steps:

### Step 1: Determine the electron configuration of sodium.
- Sodium has an atomic number of 11, which means it has 11 electrons.
- The electron configuration for sodium is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^1 \]
- The outermost electron is in the 3s subshell.

### Step 2: Identify the principal quantum number (n).
- The principal quantum number (n) indicates the main energy level of the electron.
- For the outermost electron in the 3s subshell, \( n = 3 \).

### Step 3: Determine the azimuthal quantum number (l).
- The azimuthal quantum number (l) indicates the subshell type.
- For s orbitals, \( l = 0 \).

### Step 4: Find the magnetic quantum number (m).
- The magnetic quantum number (m) can take values from \(-l\) to \(+l\).
- Since \( l = 0 \), the only possible value for \( m \) is:
\[ m = 0 \]

### Step 5: Determine the spin quantum number (s).
- The spin quantum number (s) can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
- For this example, we can choose \( s = +\frac{1}{2} \) (though it could also be \( -\frac{1}{2} \), we typically choose the positive value).

### Final Set of Quantum Numbers
- Therefore, the complete set of quantum numbers for the outermost electron of sodium is:
\[ n = 3, \, l = 0, \, m = 0, \, s = +\frac{1}{2} \]

### Summary of Quantum Numbers
- The quantum numbers are:
- \( n = 3 \)
- \( l = 0 \)
- \( m = 0 \)
- \( s = +\frac{1}{2} \)