Which of the following quantum numbers are correct for the outermost electorn of sodium atom?

Options

A. `n=4,l=0,m=0,s=+1//2`
B. `n=3,l=0,m=0,s=+1//2`
C. `n=3,l=1,m=+1,s=+1//2`
D. `n=3,l=2,m=-1,s=-1//2`

Explanation

To determine the correct quantum numbers for the outermost electron of a sodium atom, we can follow these steps:

### Step 1: Identify the Atomic Number
The atomic number of sodium (Na) is 11. This means that a sodium atom has 11 electrons.

### Step 2: Write the Electronic Configuration
The electronic configuration of sodium can be written as follows:
- 1s² (2 electrons)
- 2s² (2 electrons)
- 2p⁶ (6 electrons)
- 3s¹ (1 electron)

So, the full electronic configuration is: **1s² 2s² 2p⁶ 3s¹**. The outermost electron is in the 3s orbital.

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

### Step 4: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) defines the shape of the orbital. For s orbitals, l = 0. Therefore, for the 3s orbital, l = 0.

### Step 5: Determine the Magnetic Quantum Number (m)
The magnetic quantum number (m) describes the orientation of the orbital. For an s orbital (where l = 0), the only possible value for m is 0. Thus, m = 0.

### Step 6: Determine the Spin Quantum Number (s)
The spin quantum number (s) can have values of +1/2 or -1/2. Since the outermost electron in sodium is the first electron in the 3s orbital, it will have an upward spin. Therefore, s = +1/2.

### Step 7: Compile the Quantum Numbers
Now we have determined the quantum numbers for the outermost electron in sodium:
- n = 3
- l = 0
- m = 0
- s = +1/2

### Step 8: Check the Options
Now we can check the options given in the question:
- Option A: n = 4, l = 0, m = 0, s = +1/2 (Incorrect)
- Option B: n = 3, l = 0, m = 0, s = +1/2 (Correct)
- Option C: n = 3, l = 1, m = +1, s = +1/2 (Incorrect)
- Option D: n = 3, l = 2, m = -1, s = -1/2 (Incorrect)

The correct option is **Option B**.