Total number of electrons having `n + l = 3` in `Cr(24)` atom in its ground state is.

Explanation

To solve the question of determining the total number of electrons in a chromium (Cr) atom with atomic number 24 that satisfy the condition \( n + l = 3 \), we will follow these steps:

### Step 1: Determine the Electronic Configuration
First, we need to write the electronic configuration of chromium (Cr). The atomic number of chromium is 24, which means it has 24 electrons. The ground state electronic configuration of chromium is:

\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^1 \]

### Step 2: Identify the Values of \( n \) and \( l \)
In the electronic configuration, \( n \) represents the principal quantum number (the shell number), and \( l \) represents the azimuthal quantum number (the subshell type). The values of \( l \) are as follows:
- \( s \) subshell: \( l = 0 \)
- \( p \) subshell: \( l = 1 \)
- \( d \) subshell: \( l = 2 \)

### Step 3: Calculate \( n + l \) for Each Subshell
Now, we will calculate \( n + l \) for each subshell in the electronic configuration:

1. **1s**:
- \( n = 1 \), \( l = 0 \)
- \( n + l = 1 + 0 = 1 \)

2. **2s**:
- \( n = 2 \), \( l = 0 \)
- \( n + l = 2 + 0 = 2 \)

3. **2p**:
- \( n = 2 \), \( l = 1 \)
- \( n + l = 2 + 1 = 3 \)

4. **3s**:
- \( n = 3 \), \( l = 0 \)
- \( n + l = 3 + 0 = 3 \)

5. **3p**:
- \( n = 3 \), \( l = 1 \)
- \( n + l = 3 + 1 = 4 \)

6. **3d**:
- \( n = 3 \), \( l = 2 \)
- \( n + l = 3 + 2 = 5 \)

7. **4s**:
- \( n = 4 \), \( l = 0 \)
- \( n + l = 4 + 0 = 4 \)

### Step 4: Identify Electrons with \( n + l = 3 \)
From the calculations, we find that \( n + l = 3 \) occurs in the following subshells:
- **2p**: \( n + l = 3 \) with 6 electrons
- **3s**: \( n + l = 3 \) with 2 electrons

### Step 5: Total the Electrons
Now, we sum the number of electrons from the subshells where \( n + l = 3 \):

\[ \text{Total electrons} = 6 \, (\text{from } 2p) + 2 \, (\text{from } 3s) = 8 \]

### Final Answer
The total number of electrons having \( n + l = 3 \) in a chromium (Cr) atom in its ground state is **8**.

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