Question:
Potassium forms bcc unit cell structure with edge length of 522 pm. Find the radius of the potassium atom ?
Potassium forms bcc unit cell structure with edge length of 522 pm. Find the radius of the potassium atom ?
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In a bcc cell, the atoms touch along the body diagonal, so the radius is root 3 times a divided by 4.
Updated On: Nov 12, 2026
- 206 pm
- 226 pm
- 246 pm
- 286 pm
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
In a bcc unit cell, atoms touch along the body diagonal.
Body diagonal \(=\sqrt{3}\,a=4r\).
Step 2: Calculation
\(r=\dfrac{\sqrt{3}\,a}{4}=\dfrac{1.732\times 522}{4}\).
Step 3: Result
\(r\approx 226\) pm.
Final Answer:
The radius of the potassium atom is about 226 pm. \[ \boxed{\text{(B) }226\ \text{pm}} \]
In a bcc unit cell, atoms touch along the body diagonal.
Body diagonal \(=\sqrt{3}\,a=4r\).
Step 2: Calculation
\(r=\dfrac{\sqrt{3}\,a}{4}=\dfrac{1.732\times 522}{4}\).
Step 3: Result
\(r\approx 226\) pm.
Final Answer:
The radius of the potassium atom is about 226 pm. \[ \boxed{\text{(B) }226\ \text{pm}} \]
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