The four quantum number of the valence electron of potassium are.

Options

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

Answer

To determine the four quantum numbers of the valence electron of potassium (K), we can follow these steps:

### Step 1: Identify the Atomic Number
Potassium has an atomic number of 19. This means it has 19 electrons.

### Step 2: Write the Electronic Configuration
The electronic configuration of potassium can be written as:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹

### Step 3: Identify the Valence Electron
The valence electron for potassium is the one in the highest energy level, which is the 4s orbital.

### Step 4: Determine the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the electron. For the valence electron in the 4s orbital:
- n = 4

### Step 5: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) describes the subshell of the electron. For an s orbital:
- l = 0 (since s orbitals have l = 0)

### Step 6: Determine the Magnetic Quantum Number (m)
The magnetic quantum number (m) describes the orientation of the orbital. For an s orbital, which has only one orientation:
- m = 0

### Step 7: Determine the Spin Quantum Number (s)
The spin quantum number (s) describes the spin of the electron. For a single electron, it can either be +1/2 or -1/2. We can assign:
- s = +1/2 (commonly chosen for the first electron)

### Summary of Quantum Numbers
Thus, the four quantum numbers for the valence electron of potassium (4s¹) are:
1. n = 4
2. l = 0
3. m = 0
4. s = +1/2

### Final Answer
The four quantum numbers of the valence electron of potassium are:
- (n, l, m, s) = (4, 0, 0, +1/2)