If the ionic radii of each `K^(+)` and `F^(-)` are `1.34Å`, then tha atomic radii of `K` and `F` will be respectively:

Options

A. 1.34 Å, 1.34 Å
B. 0.72 Å, 1.96 Å
C. 1.96 Å, 0.72 Å
D. 1.96 Å, 1.34 Å

Answer

To find the atomic radii of potassium (K) and fluorine (F) given their ionic radii, we can follow these steps:

### Step 1: Understand Ionic and Atomic Radii
- The ionic radius of an ion is the measure of the size of the ion in a crystal lattice. For potassium (K⁺), when it loses one electron, its size decreases. For fluorine (F⁻), when it gains one electron, its size increases.
- Given that the ionic radii of both K⁺ and F⁻ are 1.34 Å, we need to relate this to their atomic radii.

### Step 2: Analyze Potassium (K)
- Potassium (K) in its neutral state has one more electron than K⁺. When an electron is removed to form K⁺, the effective nuclear charge on the remaining electrons increases, pulling them closer to the nucleus. Therefore, the atomic radius of K will be larger than its ionic radius.
- Since K⁺ has a radius of 1.34 Å, the atomic radius of K will be slightly larger than this value. We can estimate it to be around 1.5 Å.

### Step 3: Analyze Fluorine (F)
- Fluorine (F) in its neutral state has one less electron than F⁻. When an electron is added to form F⁻, the effective nuclear charge experienced by the remaining electrons decreases, allowing them to be further from the nucleus. Therefore, the atomic radius of F will be smaller than its ionic radius.
- Since F⁻ has a radius of 1.34 Å, the atomic radius of F will be slightly smaller than this value. We can estimate it to be around 0.7 Å.

### Step 4: Conclusion
- Therefore, the atomic radii of potassium (K) and fluorine (F) are approximately:
- Atomic radius of K: ~1.5 Å
- Atomic radius of F: ~0.7 Å

### Final Answer
The atomic radii of K and F are approximately 1.5 Å and 0.7 Å, respectively.

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