The `I.E_(1)` among the group 13 member follows as

Options

A. `B gt Al lt Ga lt Tl`
B. `B gt Al gt Ga gt Tl`
C. `B gt Ga gt Al gt Tl`
D. `B gt Ga lt Al lt Tl`

Explanation

To determine the order of first ionization energy (I.E.) among the group 13 elements (Boron, Aluminium, Gallium, and Thallium), we need to consider the factors affecting ionization energy, such as atomic size and effective nuclear charge.

### Step-by-Step Solution:

1. **Understanding Ionization Energy**:
- Ionization energy is the energy required to remove the most loosely bound electron from an atom in its gaseous state. Generally, ionization energy increases with decreasing atomic size and increasing effective nuclear charge.

2. **Group 13 Elements**:
- The group 13 elements include Boron (B), Aluminium (Al), Gallium (Ga), and Thallium (Tl).

3. **Trends in Atomic Size**:
- As we move down the group from Boron to Thallium, the atomic size increases due to the addition of electron shells. This generally leads to a decrease in ionization energy.

4. **Effective Nuclear Charge**:
- Despite the increase in atomic size, Gallium has a higher effective nuclear charge compared to Aluminium. This is due to the presence of d-electrons in Gallium which do not shield the nucleus effectively, resulting in a stronger attraction between the nucleus and the valence electrons.

5. **Comparison of Ionization Energies**:
- **Boron (B)**: Has the highest ionization energy due to its small size and high effective nuclear charge.
- **Gallium (Ga)**: Has a higher ionization energy than Aluminium because its valence electrons are held more tightly due to the effective nuclear charge.
- **Aluminium (Al)**: Has a lower ionization energy than Gallium but higher than Thallium.
- **Thallium (Tl)**: Has the lowest ionization energy among these due to its larger atomic size and lower effective nuclear charge.

6. **Conclusion**:
- The actual order of first ionization energy among the group 13 elements is:
- Boron (B) > Gallium (Ga) > Aluminium (Al) > Thallium (Tl).

### Final Order:
- **Correct Order**: Boron > Gallium > Aluminium > Thallium