How many electron in K (Z =19) have n = 2, l = 0 ?

Options

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

Answer

To determine how many electrons in potassium (K, Z = 19) have the principal quantum number \( n = 2 \) and the azimuthal quantum number \( l = 0 \), we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number \( n \) indicates the energy level of the electron.
- The azimuthal quantum number \( l \) indicates the subshell. For \( l = 0 \), this corresponds to 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 for potassium is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \]

### Step 3: Identify Electrons in the n = 2 Level
- The \( n = 2 \) level includes the 2s and 2p subshells.
- From the electronic configuration:
- \( 2s^2 \) has 2 electrons.
- \( 2p^6 \) has 6 electrons.
- Therefore, the total number of electrons in the \( n = 2 \) level is:
\[ 2 + 6 = 8 \text{ electrons} \]

### Step 4: Identify Electrons with l = 0
- Since \( l = 0 \) corresponds to the s subshell, we only consider the 2s subshell.
- The 2s subshell has:
\[ 2s^2 \text{ which contains } 2 \text{ electrons.} \]

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

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