Write down electronic configuration of `Fe^(3+)` ion and anwer the following:
(i) What is the number of electrons having `n+l=3` in it?
(ii) How many electrons in it have `n=3` and `m=0`?

Answer

To solve the problem, we need to follow these steps:

### Step 1: Determine the electronic configuration of `Fe^(3+)`
1. The atomic number of iron (Fe) is 26, which means it has 26 electrons in its neutral state.
2. The electronic configuration of neutral Fe is:
\[ \text{Fe: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^6 \]
3. To find the electronic configuration of `Fe^(3+)`, we need to remove 3 electrons from the neutral configuration:
- The 2 electrons from the 4s subshell (outermost shell) are removed first.
- Then, 1 electron is removed from the 3d subshell.
4. Therefore, the electronic configuration of `Fe^(3+)` is:
\[ \text{Fe}^{3+}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^0 \, 3d^5 \]

### Step 2: Calculate the number of electrons having `n + l = 3`
1. We need to find the values of `n` and `l` such that `n + l = 3`.
- For `l = 0` (s subshell), `n` can be 3 (3s).
- For `l = 1` (p subshell), `n` can be 2 (2p).
- For `l = 2` (d subshell), `n` cannot be 1 (1d is not possible).
- For `l = 3` (f subshell), it is not applicable here.
2. Now we check the electrons in the relevant subshells:
- **3s**: 2 electrons (from `3s^2`)
- **2p**: 6 electrons (from `2p^6`)
3. Total number of electrons having `n + l = 3`:
\[ 2 \, (\text{from } 3s) + 6 \, (\text{from } 2p) = 8 \]

### Step 3: Calculate the number of electrons with `n = 3` and `m = 0`
1. For `n = 3`, we consider the subshells: 3s, 3p, and 3d.
2. We need to find the number of electrons with `m = 0` in these subshells:
- **3s**: 1 orbital with `m = 0` and has 2 electrons.
- **3p**: 3 orbitals, 1 of which has `m = 0` and has 6 electrons (2 in each of the 3 orbitals).
- **3d**: 5 orbitals, 1 of which has `m = 0` and has 5 electrons (according to Hund's rule).
3. Total number of electrons with `m = 0`:
\[ 2 \, (\text{from } 3s) + 2 \, (\text{from } 3p) + 1 \, (\text{from } 3d) = 5 \]

### Final Answers
- (i) The number of electrons having `n + l = 3` is **8**.
- (ii) The number of electrons having `n = 3` and `m = 0` is **5**.