How many electron in K (Z =19) have n = 3, l = 0 ?

Options

A. 1
B. 4
C. 3
D. 2

Explanation

To determine how many electrons in potassium (K, atomic number 19) have the principal quantum number \( n = 3 \) and azimuthal quantum number \( l = 0 \), we can follow these steps:

### Step 1: Understand Quantum Numbers
The principal quantum number \( n \) indicates the energy level of the electron, while the azimuthal quantum number \( l \) indicates the subshell. For \( l = 0 \), the subshell is the s subshell.

### Step 2: Write the Electronic Configuration of Potassium
The atomic number of potassium (K) is 19, which means it has 19 electrons. The electronic configuration of potassium can be written as:
- \( 1s^2 \)
- \( 2s^2 \)
- \( 2p^6 \)
- \( 3s^2 \)
- \( 3p^6 \)
- \( 4s^1 \)

So, the complete electronic configuration is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \]

### Step 3: Identify Electrons in the Relevant Shell and Subshell
From the electronic configuration:
- The electrons in the \( n = 3 \) level are found in the \( 3s \) and \( 3p \) subshells.
- For \( l = 0 \) (which corresponds to the \( s \) subshell), we look at the \( 3s \) subshell.

### Step 4: Count the Electrons in the \( 3s \) Subshell
The \( 3s \) subshell contains:
- \( 3s^2 \) which means there are 2 electrons in the \( 3s \) subshell.

### Conclusion
Thus, the number of electrons in potassium (K) that have \( n = 3 \) and \( l = 0 \) is **2**.

### Summary
The answer is:
**2 electrons in potassium (K) have \( n = 3 \) and \( l = 0 \).**