Question:
A metal crystallizes in bcc lattice with an edge length of 4 \AA. How many metal atoms can be placed in a two-dimensional open box of length 35 \AA and width 35 \AA?
A metal crystallizes in bcc lattice with an edge length of 4 \AA. How many metal atoms can be placed in a two-dimensional open box of length 35 \AA and width 35 \AA?
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For lattice-based packing problems, first determine the spacing between neighbouring atoms and then calculate the number of atoms that fit along each dimension.
Updated On: Jun 17, 2026
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The Correct Option is C
Solution and Explanation
Concept:
For a BCC lattice,
\[
4r=\sqrt{3}a
\]
where \(a\) is edge length.
Atoms arranged in a two-dimensional layer occupy approximately a square grid of side equal to the lattice parameter.
Step 1: Determine number of atoms along one side.
Given, \[ a=4\AA \] Length of box \[ =35\AA \] Number of atoms along one side \[ \approx \frac{35}{4}+1 \] \[ \approx 8.75+1 \] \[ \approx 10 \]
Step 2: Determine total atoms in the square layer.
\[ N=10\times10 \] \[ N=100 \]
Step 3: Final answer.
\[ \boxed{100} \]
Step 1: Determine number of atoms along one side.
Given, \[ a=4\AA \] Length of box \[ =35\AA \] Number of atoms along one side \[ \approx \frac{35}{4}+1 \] \[ \approx 8.75+1 \] \[ \approx 10 \]
Step 2: Determine total atoms in the square layer.
\[ N=10\times10 \] \[ N=100 \]
Step 3: Final answer.
\[ \boxed{100} \]
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