Ionisation energy values of an atom are 495 , 767 , 1250 and 4540 kJ `"mole"^(-1)` the formula of its sulphate is

Options

A. `MSO_(4)`
B. `M_(2)SO_(4)`
C. `M_(2)(SO_(4))_(3)`
D. `M(SO_(4))_(2)`

Answer

To determine the formula of the sulfate compound formed by the given atom based on its ionization energy values, we can follow these steps:

### Step 1: Analyze the Ionization Energies
The given ionization energy values are:
- First Ionization Energy (IE1) = 495 kJ/mol
- Second Ionization Energy (IE2) = 767 kJ/mol
- Third Ionization Energy (IE3) = 1250 kJ/mol
- Fourth Ionization Energy (IE4) = 4540 kJ/mol

### Step 2: Identify the Number of Valence Electrons
The significant increase in the fourth ionization energy (IE4 = 4540 kJ/mol) compared to the third ionization energy (IE3 = 1250 kJ/mol) indicates that the atom has three valence electrons. This is because it is relatively easy to remove the first three electrons, but removing the fourth electron requires a much larger amount of energy, suggesting that the fourth electron is being removed from a more stable electron configuration.

### Step 3: Determine the Charge of the Ion
Since the atom can lose three electrons to achieve a stable electron configuration, it will form a cation with a charge of +3. Therefore, we can represent the metal as M³⁺.

### Step 4: Write the Formula for Sulfate
The sulfate ion (SO₄²⁻) has a charge of -2. To balance the charges in the compound formed by the metal cation and the sulfate anion, we need to find the appropriate ratio of M³⁺ ions to SO₄²⁻ ions.

### Step 5: Balancing the Charges
To balance the charges:
- The charge from one sulfate ion (SO₄²⁻) is -2.
- The charge from three M³⁺ ions (3 × +3 = +9).

To balance the charges, we need two sulfate ions for every three M³⁺ ions:
- 3 M³⁺ ions will balance with 2 SO₄²⁻ ions.

### Step 6: Write the Final Formula
Thus, the formula for the sulfate compound will be:
\[ \text{M}_3(\text{SO}_4)_2 \]

### Conclusion
The formula of the sulfate is \( \text{M}_3\text{(SO}_4\text{)}_2 \).