Which of the following is correct in order of increasing size ?

Options

A. `I^(o+) lt I lt I^(ɵ)`
B. `Fe lt Fe^(2+) lt Fe^(3+)`
C. `Fe^(3+) lt Fe^(2+) lt Fe`
D. All of these

Explanation

To determine the correct order of increasing size among the given ions, we can use the concept of the Z/E ratio, where Z is the atomic number and E is the number of electrons. The size of an ion is inversely proportional to this ratio. Let's analyze the options step by step.

### Step-by-Step Solution:

1. **Identify the Ions and Their Atomic Numbers:**
- For the first option, we have I⁻, I, and I⁺. The atomic number (Z) of iodine (I) is 53.
- For the second option, we have Fe, Fe²⁺, and Fe³⁺. The atomic number (Z) of iron (Fe) is 26.

2. **Calculate the Z/E Ratios:**
- **For Iodine:**
- I⁻: Z/E = 53/(n + 1)
- I: Z/E = 53/n
- I⁺: Z/E = 53/(n - 1)
- Since the atomic number is constant (53), the number of electrons (E) changes:
- I⁻ has the most electrons, followed by I, and then I⁺ has the least.
- Therefore, the Z/E ratio increases in the order: I⁺ < I < I⁻.
- This means the size order is: I⁺ < I < I⁻.

3. **For Iron:**
- **For Iron Ions:**
- Fe: Z/E = 26/n
- Fe²⁺: Z/E = 26/(n - 2)
- Fe³⁺: Z/E = 26/(n - 3)
- Here, Fe has the most electrons, followed by Fe²⁺, and Fe³⁺ has the least.
- Therefore, the Z/E ratio increases in the order: Fe³⁺ < Fe²⁺ < Fe.
- This means the size order is: Fe³⁺ < Fe²⁺ < Fe.

4. **Combine the Results:**
- From the first option, we have the order: I⁺ < I < I⁻.
- From the second option, we have the order: Fe³⁺ < Fe²⁺ < Fe.
- Thus, the correct order of increasing size for both sets of ions is:
- I⁺ < I < I⁻ and Fe³⁺ < Fe²⁺ < Fe.

5. **Conclusion:**
- The correct options that show the order of increasing size are:
- I⁺ < I < I⁻ for iodine ions.
- Fe³⁺ < Fe²⁺ < Fe for iron ions.