The maximum no . Electrons in phosphorous atom for which n+l+m =3 will be :

Options

A. 6
B. 5
C. 4
D. 3

Explanation

To determine the maximum number of electrons in a phosphorus atom for which \( n + l + m = 3 \), we will follow these steps:

### Step 1: Understand the Electron Configuration of Phosphorus
Phosphorus has an atomic number of 15, which means it has 15 electrons. The electron configuration of phosphorus is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^3 \]

### Step 2: Identify Quantum Numbers
For each subshell, we need to identify the quantum numbers \( n \), \( l \), and \( m \):
- \( n \) = principal quantum number
- \( l \) = azimuthal quantum number (0 for s, 1 for p, 2 for d, etc.)
- \( m \) = magnetic quantum number (ranges from \(-l\) to \(+l\))

### Step 3: Calculate \( n + l + m \) for Each Subshell
1. **For 1s**:
- \( n = 1 \), \( l = 0 \), \( m = 0 \)
- \( n + l + m = 1 + 0 + 0 = 1 \)

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

3. **For 2p**:
- \( n = 2 \), \( l = 1 \)
- Possible \( m \) values: -1, 0, +1
- Calculate:
- For \( m = -1 \): \( n + l + m = 2 + 1 - 1 = 2 \)
- For \( m = 0 \): \( n + l + m = 2 + 1 + 0 = 3 \) (valid)
- For \( m = +1 \): \( n + l + m = 2 + 1 + 1 = 4 \) (not valid)
- **Electrons in 2p contributing to \( n + l + m = 3 \)**: 2 electrons (for \( m = 0 \))

4. **For 3s**:
- \( n = 3 \), \( l = 0 \), \( m = 0 \)
- \( n + l + m = 3 + 0 + 0 = 3 \) (valid)
- **Electrons in 3s**: 2 electrons

5. **For 3p**:
- \( n = 3 \), \( l = 1 \)
- Possible \( m \) values: -1, 0, +1
- Calculate:
- For \( m = -1 \): \( n + l + m = 3 + 1 - 1 = 3 \) (valid)
- For \( m = 0 \): \( n + l + m = 3 + 1 + 0 = 4 \) (not valid)
- For \( m = +1 \): \( n + l + m = 3 + 1 + 1 = 5 \) (not valid)
- **Electrons in 3p contributing to \( n + l + m = 3 \)**: 1 electron (for \( m = -1 \))

### Step 4: Total Electrons for \( n + l + m = 3 \)
Now we sum the contributions:
- From 2p: 2 electrons
- From 3s: 2 electrons
- From 3p: 1 electron

Total = \( 2 + 2 + 1 = 5 \) electrons

### Conclusion
The maximum number of electrons in a phosphorus atom for which \( n + l + m = 3 \) is **5**.

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