The ionic radii `(A^@)`of `C^(-4)` and `O^(-2)` are 2.60 and 1.40 respectively .The ionic radius of the isoelectronic ion `N^(-3)` would be

Options

A. 2.6
B. 1.71
C. 1.4
D. 0.95

Answer

To find the ionic radius of the isoelectronic ion \( N^{3-} \), we will follow these steps:

### Step 1: Understand the concept of isoelectronic ions
Isoelectronic ions are ions that have the same number of electrons. In this case, \( C^{4-} \), \( O^{2-} \), and \( N^{3-} \) are all isoelectronic with neon (\( Ne \)), having the same electron configuration.

### Step 2: Analyze the given ionic radii
We have the following ionic radii:
- \( C^{4-} \): 2.60 Å
- \( O^{2-} \): 1.40 Å

### Step 3: Relate ionic radius to charge
The ionic radius is influenced by the charge of the ion. Generally, as the negative charge increases, the ionic radius also increases. This is because more negative charge leads to greater electron-electron repulsion, which expands the size of the ion.

### Step 4: Determine the order of ionic radii
From the given data:
- \( C^{4-} \) has the highest negative charge and the largest radius (2.60 Å).
- \( O^{2-} \) has a lower negative charge and a smaller radius (1.40 Å).
- \( N^{3-} \) has a negative charge between \( C^{4-} \) and \( O^{2-} \).

### Step 5: Estimate the ionic radius of \( N^{3-} \)
Since \( N^{3-} \) has a charge that is more negative than \( O^{2-} \) but less negative than \( C^{4-} \), we can estimate its ionic radius to be between the radii of \( C^{4-} \) and \( O^{2-} \).

### Step 6: Calculate the ionic radius
To find a reasonable estimate for the ionic radius of \( N^{3-} \), we can take the average of the two ionic radii:
\[ \text{Average radius} = \frac{(2.60 + 1.40)}{2} = \frac{4.00}{2} = 2.00 \, \text{Å} \]
However, since \( N^{3-} \) is expected to be larger than \( O^{2-} \) but smaller than \( C^{4-} \), a more accurate estimate would be around 1.71 Å, which is closer to the average but accounts for the charge influence.

### Conclusion
The ionic radius of \( N^{3-} \) is approximately **1.71 Å**.

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