How many electrons in zinc `(Z = 30)` have `n + l` value equal to 4 ?

Answer

To determine how many electrons in zinc (Z = 30) have an n + l value equal to 4, we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number (n) indicates the energy level or shell of an electron.
- The azimuthal quantum number (l) indicates the subshell and can take values from 0 to (n-1).
- The n + l rule is used to determine the energy of orbitals: the lower the sum of n + l, the lower the energy.

### Step 2: Write the Electron Configuration of Zinc
- The electron configuration of zinc (Z = 30) is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \]

### Step 3: Identify the Values of n and l for Each Subshell
- For each subshell, we can identify n and l:
- 1s: n = 1, l = 0 → n + l = 1 + 0 = 1
- 2s: n = 2, l = 0 → n + l = 2 + 0 = 2
- 2p: n = 2, l = 1 → n + l = 2 + 1 = 3
- 3s: n = 3, l = 0 → n + l = 3 + 0 = 3
- 3p: n = 3, l = 1 → n + l = 3 + 1 = 4
- 4s: n = 4, l = 0 → n + l = 4 + 0 = 4
- 3d: n = 3, l = 2 → n + l = 3 + 2 = 5

### Step 4: Find Electrons with n + l = 4
- From the above calculations, we see that:
- For 3p: n + l = 4, and there are 6 electrons.
- For 4s: n + l = 4, and there are 2 electrons.

### Step 5: Calculate the Total Number of Electrons
- Total electrons with n + l = 4:
\[ 6 \, (\text{from } 3p) + 2 \, (\text{from } 4s) = 8 \]

### Final Answer
Thus, the total number of electrons in zinc that have an n + l value equal to 4 is **8**.

---