Element Hg has two oxidation states `Hg^(+)` & `Hg^(+2)` the right order of radii of these ions is :

Options

A. `Hg^(+) gt Hg^(-2)`
B. `Hg^(+2) gt Hg^(-)`
C. `Hg^(+) = Hg^(+2)`
D. `Hg^(+2) ge Hg^(+)`

Answer

To determine the correct order of ionic radii for the oxidation states of mercury (Hg), namely \(Hg^+\) and \(Hg^{2+}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Oxidation States**:
- Mercury has two oxidation states: \(Hg^+\) (mercury(I)) and \(Hg^{2+}\) (mercury(II)).

2. **Understand Ionic Radius and Nuclear Charge**:
- The ionic radius is influenced by the effective nuclear charge (Z_eff) experienced by the electrons. The greater the nuclear charge, the more strongly the electrons are attracted to the nucleus, resulting in a smaller ionic radius.

3. **Determine the Number of Protons and Electrons**:
- Mercury (Hg) has an atomic number of 80, meaning it has 80 protons and, in its neutral state, 80 electrons.
- For \(Hg^+\): It loses one electron, resulting in 80 protons and 79 electrons.
- For \(Hg^{2+}\): It loses two electrons, resulting in 80 protons and 78 electrons.

4. **Calculate Effective Nuclear Charge**:
- The effective nuclear charge increases as electrons are removed because the number of protons remains constant while the number of electrons decreases.
- For \(Hg^+\): Z_eff is higher than for neutral Hg because there are fewer electrons (79).
- For \(Hg^{2+}\): Z_eff is even higher because there are even fewer electrons (78).

5. **Compare Ionic Radii**:
- Since \(Hg^{2+}\) has a higher effective nuclear charge than \(Hg^+\), it will attract its remaining electrons more strongly, resulting in a smaller ionic radius.
- Therefore, the order of ionic radii is \(Hg^+ > Hg^{2+}\).

6. **Conclusion**:
- The correct order of radii of these ions is:
\[ \text{Ionic radius order: } Hg^+ > Hg^{2+} \]

### Final Answer:
The right order of radii of these ions is \(Hg^+ > Hg^{2+}\).

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