Answer:
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Explanation:
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Answer : The radii of the two ions Cl⁻ ion and Na⁺ ion is, 181 and 102 pm respectively.
Explanation :
As we are given that the Na⁺ radius is 56.4% of the Cl⁻ radius.
Let us assume that the radius of Cl⁻ be, (x) pm
So, the radius of Na⁺ = ![x\times \frac{56.4}{100}=(0.564x)pm](https://tex.z-dn.net/?f=x%5Ctimes%20%5Cfrac%7B56.4%7D%7B100%7D%3D%280.564x%29pm)
In the crystal structure of NaCl, 2 Cl⁻ ions present at the corner and 1 Na⁺ ion present at the edge of lattice.
Thus, the edge length is equal to the sum of 2 radius of Cl⁻ ion and 2 radius of Na⁺ ion.
Given:
Distance between Na⁺ nuclei = 566 pm
Thus, the relation will be:
![2\times \text{Radius of }Cl^-+2\times \text{Radius of }Na^+=\text{Distance between }Na^+\text{ nuclei}](https://tex.z-dn.net/?f=2%5Ctimes%20%5Ctext%7BRadius%20of%20%7DCl%5E-%2B2%5Ctimes%20%5Ctext%7BRadius%20of%20%7DNa%5E%2B%3D%5Ctext%7BDistance%20between%20%7DNa%5E%2B%5Ctext%7B%20nuclei%7D)
![2\times x+2\times 0.564x=566](https://tex.z-dn.net/?f=2%5Ctimes%20x%2B2%5Ctimes%200.564x%3D566)
![2x+1.128x=566](https://tex.z-dn.net/?f=2x%2B1.128x%3D566)
![3.128x=566](https://tex.z-dn.net/?f=3.128x%3D566)
![x=180.9\approx 181pm](https://tex.z-dn.net/?f=x%3D180.9%5Capprox%20181pm)
The radius of Cl⁻ ion = (x) pm = 181 pm
The radius of Na⁺ ion = (0.564x) pm = (0.564 × 181) pm =102.084 pm ≈ 102 pm
Thus, the radii of the two ions Cl⁻ ion and Na⁺ ion is, 181 and 102 pm respectively.
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