How many electron in copper atom `(._(29)Cu)` have `(n+l) = 4`

Options

A. 6
B. 7
C. 8
D. 4

Explanation

To determine how many electrons in a copper atom (Cu) have \( n + l = 4 \), we can follow these steps:

### Step 1: Determine the Electron Configuration of Copper
Copper has an atomic number of 29, which means it has 29 electrons. The electron configuration of copper is:

\[ \text{Cu: } 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 3d^{10}, 4s^1 \]

### Step 2: Identify the Values of \( n \) and \( l \)
In the electron configuration:
- The principal quantum number \( n \) indicates the energy level.
- The azimuthal quantum number \( l \) corresponds to the type of orbital:
- \( l = 0 \) for s orbitals
- \( l = 1 \) for p orbitals
- \( l = 2 \) for d orbitals
- \( l = 3 \) for f orbitals

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

1. **For 1s orbital**:
- \( n = 1 \), \( l = 0 \) → \( n + l = 1 + 0 = 1 \)
2. **For 2s orbital**:
- \( n = 2 \), \( l = 0 \) → \( n + l = 2 + 0 = 2 \)
3. **For 2p orbital**:
- \( n = 2 \), \( l = 1 \) → \( n + l = 2 + 1 = 3 \)
4. **For 3s orbital**:
- \( n = 3 \), \( l = 0 \) → \( n + l = 3 + 0 = 3 \)
5. **For 3p orbital**:
- \( n = 3 \), \( l = 1 \) → \( n + l = 3 + 1 = 4 \)
6. **For 3d orbital**:
- \( n = 3 \), \( l = 2 \) → \( n + l = 3 + 2 = 5 \)
7. **For 4s orbital**:
- \( n = 4 \), \( l = 0 \) → \( n + l = 4 + 0 = 4 \)

### Step 4: Count the Electrons with \( n + l = 4 \)
From the calculations:
- The 3p orbital contributes 6 electrons (since it can hold a maximum of 6).
- The 4s orbital contributes 1 electron.

Thus, the total number of electrons for which \( n + l = 4 \) is:

\[ 6 \text{ (from 3p)} + 1 \text{ (from 4s)} = 7 \]

### Final Answer
The number of electrons in a copper atom that have \( n + l = 4 \) is **7**.

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