Successive ionisation energies of an element is represented as follows
`A underset(IE_1)(rarr)A^(+)underset(IE_2)(rarr)A^(2+)underset(IE_3)(rarr)A^(3+) to ….A^(n +)`
Which of the following statement is correct? 

Options

A. In some of the elements `IE_2` values may be negative.
B. `IE_ of A^(3+) = IE_2` of `A^(+)`.
C. Successive electron affinity of `A^(n+)` is gradually decreasing.
D. None of these is correct.

Answer

To solve the question regarding the successive ionization energies of an element and determine which statement is correct, we will analyze each statement step by step.

### Step 1: Understand Ionization Energy
**Definition**: Ionization energy is the energy required to remove an electron from an atom or ion. The first ionization energy (IE1) refers to the energy needed to remove the outermost electron, while the second ionization energy (IE2) refers to the energy needed to remove the next electron from the resulting ion, and so on.

**Hint**: Remember that ionization energy is always a positive value because energy must be supplied to remove an electron.

### Step 2: Analyze the First Statement
**Statement**: In some elements, the second ionization energy value may be negative.

**Analysis**: This statement is incorrect. Ionization energies cannot be negative because they represent the energy required to remove an electron. Therefore, the first statement is false.

**Hint**: Ionization energy values are always positive; think about the energy required to overcome the attraction between the electron and the nucleus.

### Step 3: Analyze the Second Statement
**Statement**: The ionization energy of A^(3+) is equal to the second ionization energy of A^(+).

**Analysis**: This statement is also incorrect. The ionization energy of A^(3+) (which has fewer electrons) will be higher than that of A^(+) because the nuclear charge remains the same while the number of electrons decreases, leading to a stronger attraction between the nucleus and the remaining electrons. Thus, the second statement is false.

**Hint**: Consider how the number of electrons affects the attraction to the nucleus; fewer electrons mean a stronger pull from the nucleus.

### Step 4: Analyze the Third Statement
**Statement**: Successive electron affinity of A^(n) is gradually decreasing.

**Analysis**: This statement is correct. As electrons are added to an ion with a positive charge (like A^(n)), the effective nuclear charge increases, making it harder to add additional electrons. Therefore, the energy released (or the affinity) when adding an electron decreases as more electrons are added to the ion. Thus, this statement is true.

**Hint**: Think about how adding electrons affects the stability of the ion; more electrons lead to increased repulsion and decreased electron affinity.

### Conclusion
After analyzing all the statements, we conclude that the third statement is the only correct one.

### Final Answer
The correct statement is: "Successive electron affinity of A^(n) is gradually decreasing."