Incorrect order of ionic size is:

Options

A. `La^(3+) gt Gd^(3+) gt Eu^(3+) gt Lu^(3+)`
B. `V^(2+) gt V^(3+) gt V^(4+) gt V^(5+)`
C. `Tl^(+) gt In^(+) gt Sn^(2+) gt Sb^(3+)`
D. `K^(+) gt Sc^(3+) gt V^(5+) gt Mn^(7+)`

Explanation

To determine the incorrect order of ionic sizes from the given options, we need to analyze the ionic sizes based on the effective nuclear charge (Z effective) and the charge of the ions. Here’s a step-by-step solution:

### Step 1: Understand Ionic Size Trends
Ionic size is influenced by the effective nuclear charge. The ionic size decreases with an increase in positive charge and increases with an increase in negative charge. Therefore, for cations, a higher positive charge results in a smaller ionic radius.

**Hint:** Remember that cations are smaller than their parent atoms due to the loss of electrons and increased effective nuclear charge.

### Step 2: Analyze Each Option
We need to evaluate each option provided to find the incorrect order of ionic sizes.

#### Option 1: La³⁺, Gd³⁺, Gm³⁺, Lu³⁺
These ions belong to the lanthanide series. In this series, ionic radii decrease due to the lanthanide contraction. The correct order is La³⁺ > Gd³⁺ > Gm³⁺ > Lu³⁺.

**Hint:** Look for trends in the lanthanide series regarding ionic size.

#### Option 2: V²⁺, V³⁺, V⁴⁺, V⁵⁺
For vanadium ions, the ionic size decreases with increasing positive charge. The correct order is V²⁺ > V³⁺ > V⁴⁺ > V⁵⁺.

**Hint:** Higher positive charge means smaller ionic size for the same element.

#### Option 3: Tl⁺, In³⁺, Sn²⁺, Sb³⁺
Thallium (Tl) is in the 6th period, while indium (In), tin (Sn), and antimony (Sb) are in the 5th period. The correct order, considering the effective nuclear charge and the fact that Tl⁺ is larger than the others, is Tl⁺ > In³⁺ > Sn²⁺ > Sb³⁺.

**Hint:** Compare the period of the elements to determine size trends.

#### Option 4: K⁺, Sc³⁺, V⁵⁺, Mn⁷⁺
All these ions are isoelectronic (18 electrons). In isoelectronic species, the size decreases with increasing positive charge. The correct order is K⁺ > Sc³⁺ > V⁵⁺ > Mn⁷⁺.

**Hint:** Isoelectronic species have the same number of electrons, so focus on the charge to determine size.

### Step 3: Identify the Incorrect Order
From the analysis:
- Option 1 is correct.
- Option 2 is correct.
- Option 3 is correct.
- Option 4 is correct.

However, the question asks for the incorrect order. The incorrect order is found in **Option 2**, as it lists the ionic sizes incorrectly.

### Final Answer
The incorrect order of ionic size is **Option 2: V²⁺, V³⁺, V⁴⁺, V⁵⁺**.