MHT CET · Chemistry · Solid State
What is the number of unit cells present in a cubic pack crystal lattice having 4 atoms per unit cell and weighing \(0.60 \mathrm{~g}\) (molar mass \(\left.60 \mathrm{~g} \mathrm{~mol}^{-1}\right) ?\)
- A \(1 \times 10^{21}\)
- B \(1.5 \times 10^{21}\)
- C \(3.0 \times 10^{21}\)
- D \(6.0 \times 10^{21}\)
Answer & Solution
Correct Answer
(B) \(1.5 \times 10^{21}\)
Step-by-step Solution
Detailed explanation
Number of moles \(=\frac{0.6 \mathrm{~g}}{60 \mathrm{~g} \mathrm{~mol}^{-1}}=0.01 \mathrm{~mol}\)
Total number of atoms \(=0.01 \times 6.022 \times 10^{23}\)
Number of atoms per unit cell \(=4\) (Given)
\(\therefore\) Number of unit cells present in the given cubic crystal lattice
\(
\begin{aligned}
& =\frac{0.01 \times 6.022 \times 10^{23}}{4} \\
& =1.5 \times 10^{21} \text { unit cells }
\end{aligned}
\)
Total number of atoms \(=0.01 \times 6.022 \times 10^{23}\)
Number of atoms per unit cell \(=4\) (Given)
\(\therefore\) Number of unit cells present in the given cubic crystal lattice
\(
\begin{aligned}
& =\frac{0.01 \times 6.022 \times 10^{23}}{4} \\
& =1.5 \times 10^{21} \text { unit cells }
\end{aligned}
\)
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