Effective nuclear charge `(Z_(eff))` is the net attractive force
on electrons under consideration and is equal to:
`Z_(eff) = Z - sigma` (nuclear charge - screening constant). `Z_(eff)` or `sigma` is calculated by Slater's formula, as given.
If one electrons is present in the outermst orbit, there will be no screening in that orbital. Each electrons contribute, `0.35` (total electrons minus one electron) present in the outermost shell.
A contribution of `0.85` for each electrons is taken in the `(n - 1)th` shell.
Which of the following statement is wrong?

Options

A. `IE_(1)` of `Ga gt Al`, due ot imperfect shielding of `3d`-orbitals in `Ga`.
B. `IE_(1)` of `Ga lt Al`, due ot perfect shielding of `3d`-orbitals in `Ga`.
C. The atomic size of `Ga` and `Al` are almost same because of poor shielding effect of electrons in `d`-orbitals as the effective nuclear
charge increases in `Ga`.
D. `IE_(1)` of group `16` elements is less than that of group `15` elements.

Explanation

To solve the question regarding the effective nuclear charge `(Z_eff)` and identify the wrong statement among the given options, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Effective Nuclear Charge**:
The effective nuclear charge `(Z_eff)` is defined as the net attractive force on electrons in an atom. It is calculated using the formula:
\[ Z_{eff} = Z - \sigma \]
where `Z` is the nuclear charge (number of protons) and `σ` is the screening constant that accounts for the shielding effect of other electrons.

2. **Review Slater's Rules**:
According to Slater's rules:
- For each electron in the outermost shell (n), there is no screening.
- Each electron in the same shell contributes `0.35` to the screening constant.
- Each electron in the (n-1) shell contributes `0.85` to the screening constant.

3. **Analyze the Statements**:
We need to evaluate the given statements one by one to identify which one is incorrect.

- **Statement 1**: "The first ionization energy of gallium is greater than that of aluminium due to the imperfect shielding of 3D orbitals in gallium."
- This statement is **correct**. Gallium has a filled 3D subshell which leads to poor shielding, resulting in a higher ionization energy compared to aluminium.

- **Statement 2**: "Gallium is smaller than aluminium."
- This statement is **incorrect**. Gallium has a larger atomic radius than aluminium due to the presence of 3D electrons which do not shield the nucleus effectively.

- **Statement 3**: "The atomic sizes of gallium and aluminium are almost the same because of poor shielding effect as effective nuclear charge increases in gallium."
- This statement is **correct**. The atomic sizes are similar due to the effective nuclear charge being higher in gallium, despite the presence of 3D electrons.

- **Statement 4**: "The ionization energy of group 16 is less than that of group 15."
- This statement is **correct**. Group 15 elements have half-filled p orbitals which are more stable and require more energy to remove an electron compared to group 16 elements.

4. **Conclusion**:
The only incorrect statement among the options is **Statement 2**.

### Final Answer:
The wrong statement is **Statement 2**: "Gallium is smaller than aluminium."