Along the period, atomic/ionic radius and metallic character generally decreases, while IE, EN and nonmetallic character and oxidizing power increases.
  If the ionic radius of `M^(+)` and `X^(-)` are about 135 and 209 pm respectively, then the expected values of atomic radius of M and X may be respectively in pm)
(M and X are metal and non-metal, respectively of same period.) 

Options

A. 180,90
B. 135,209
C. 90, 180
D. Same radius which is average of 135 and 209 pm

Answer

To determine the expected atomic radius of the metal (M) and the non-metal (X) based on the given ionic radii of their respective ions (M^+ and X^-), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Ionic Radii**:
- The ionic radius of M^+ is given as 135 pm. Cations (positively charged ions) are smaller than their parent atoms because they lose electrons, resulting in a decrease in electron-electron repulsion and a stronger attraction between the remaining electrons and the nucleus.
- The ionic radius of X^- is given as 209 pm. Anions (negatively charged ions) are larger than their parent atoms because they gain electrons, which increases electron-electron repulsion and results in a larger size.

2. **Relate Ionic Radius to Atomic Radius**:
- For the metal M, since M^+ is smaller than M, we can conclude that the atomic radius of M (r_M) will be greater than 135 pm:
\[ r_M > 135 \text{ pm} \]
- For the non-metal X, since X^- is larger than X, we can conclude that the atomic radius of X (r_X) will be less than 209 pm:
\[ r_X < 209 \text{ pm} \]

3. **Estimate Atomic Radii**:
- In general, the atomic radius of metals tends to be larger than their ionic radius by a certain amount. A typical increase might be around 30-50 pm for metals. Therefore, we can estimate:
\[ r_M \approx 135 \text{ pm} + 30 \text{ pm} \text{ to } 50 \text{ pm} \implies r_M \approx 165 \text{ pm to } 185 \text{ pm} \]
- For non-metals, the atomic radius tends to be smaller than the ionic radius. A typical decrease might also be around 30-50 pm. Therefore, we can estimate:
\[ r_X \approx 209 \text{ pm} - 30 \text{ pm} \text{ to } 50 \text{ pm} \implies r_X \approx 159 \text{ pm to } 179 \text{ pm} \]

4. **Conclusion**:
- Based on the estimates, the expected atomic radius of M could be around 165-185 pm, and for X, it could be around 159-179 pm. However, since we need to provide specific values, we can summarize:
- Expected atomic radius of M: **greater than 135 pm** (let's say around 165 pm)
- Expected atomic radius of X: **less than 209 pm** (let's say around 179 pm)

### Final Answer:
- The expected values of atomic radius of M and X may be approximately **165 pm** and **179 pm**, respectively.