The energy required to remove an electron from the outermost shell of an isolate gaseous atom is known as `IE_(1)` of that atom. Similarly, the enrgy required for the removal of the electron from the unipositive ion, diapositive ion and tripositive ion are known as `IE_(2),IE_(3)` and `IE_(4)` respectively, and are called successive ionisation energies. The magnitude of the charge depends on the size of the orbital of electron. Electrons in smaller orbitals are on average close with each other and have more repulsion. Thus for `Be(2s^(2))`, the `IE_(1)` and `IE_(2)` are `9.3` and `18.2 eV "atom"^(1)`, whereas for `Ca(4s^(2))`, the values are `6.1` and `11.9 eV`.
Four elemensts have the following first ionization energies in `KJmol^(-1): 762, 709, 59` and `558`. The elements are `Ca, Ge`. `In` and `Sn` (not in order). Which of these elements has the ionisation energy of `762 KJ mol^(-1)`?

Options

A. `In`
B. `Ga`
C. `Sn`
D. `Ge`

Explanation

To determine which of the given elements has the first ionization energy of 762 KJ mol^(-1), we will analyze the ionization energies of the elements provided: Calcium (Ca), Germanium (Ge), Indium (In), and Tin (Sn).

### Step-by-Step Solution:

1. **Identify the Elements and Their Groups**:
- Calcium (Ca) is in Group 2 (alkaline earth metals).
- Germanium (Ge) is in Group 14 (metalloids).
- Indium (In) is in Group 13 (post-transition metals).
- Tin (Sn) is also in Group 14 (metalloids).

2. **Understand the Trends in Ionization Energy**:
- Ionization energy generally increases across a period (from left to right) due to increasing nuclear charge.
- Ionization energy generally decreases down a group due to increasing atomic size and shielding effect.

3. **Compare the Given Ionization Energies**:
- The first ionization energies provided are: 762 KJ mol^(-1), 709 KJ mol^(-1), 559 KJ mol^(-1), and 558 KJ mol^(-1).
- We need to identify which element corresponds to the highest ionization energy of 762 KJ mol^(-1).

4. **Analyze Each Element's Position**:
- **Calcium (Ca)**: Being in Group 2, it is expected to have a lower ionization energy compared to elements in Groups 13 and 14.
- **Germanium (Ge)**: As a metalloid in Group 14, it is likely to have a higher ionization energy than metals.
- **Indium (In)**: Being in Group 13, it should have a lower ionization energy than germanium.
- **Tin (Sn)**: Also in Group 14, but below Ge, it is expected to have a lower ionization energy than Ge.

5. **Determine the Element with 762 KJ mol^(-1)**:
- Since Ge and Sn are in Group 14, they will have higher ionization energies compared to Ca and In.
- Among Ge and Sn, Ge being higher in the group will have a higher ionization energy than Sn.
- Therefore, the element with the highest ionization energy of 762 KJ mol^(-1) is likely **Germanium (Ge)**.

### Conclusion:
The element with the first ionization energy of 762 KJ mol^(-1) is **Germanium (Ge)**.