How many electron in K (Z =19) have n = 3, l = 1 ?

Options

A. 2
B. 4
C. 6
D. 8

Explanation

To solve the question of how many electrons in potassium (K, Z = 19) have the principal quantum number \( n = 3 \) and azimuthal quantum number \( l = 1 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The principal quantum number \( n \) indicates the energy level of the electron. Here, \( n = 3 \) means we are looking at the third energy level.
- The azimuthal quantum number \( l \) indicates the shape of the orbital. For \( l = 1 \), the corresponding orbital is the p orbital.

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

3. **Identify the Electrons in the n = 3 Level**:
- In the electronic configuration, the electrons in the \( n = 3 \) level are found in the \( 3s \) and \( 3p \) orbitals.
- The \( 3s \) orbital has 2 electrons, and the \( 3p \) orbital has 6 electrons.

4. **Count the Electrons in the 3p Orbital**:
- Since we are specifically interested in the \( l = 1 \) (which corresponds to the \( 3p \) orbital), we see that there are 6 electrons in the \( 3p \) orbital.

5. **Conclusion**:
- Therefore, the total number of electrons in potassium that have \( n = 3 \) and \( l = 1 \) is 6.

### Final Answer:
The number of electrons in potassium (K, Z = 19) with \( n = 3 \) and \( l = 1 \) is **6**.

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