Question:medium

What type of crystal structure from following has 52.36% packing efficiency?

Show Hint

Remember the three milestone numbers for cubic cell packing efficiencies: Simple Cubic = 52.4
Updated On: Jun 3, 2026
  • FCC
  • BCC
  • Hexagonal cubic
  • Simple cubic
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Recall the standard values.
FCC packs at about 74 percent, BCC at about 68 percent, and simple cubic at about 52 percent.

Step 2: Check simple cubic.
In a simple cubic cell there is 1 atom and the edge is $a = 2r$. The efficiency is \[ \frac{\frac{4}{3}\pi r^3}{(2r)^3}\times 100 = \frac{\pi}{6}\times 100 \approx 52.36\% \]

Step 3: Match.
The value 52.36 percent belongs to simple cubic.
\[ \boxed{\text{Simple cubic, option 4}} \]
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