Question

Sodium forms bcc structure. The molar mass of sodium is \(23\) g/mol. What is the mass of \(3\) unit cells of sodium?

• A. \(2.2915\times 10^{-22}\) g
• B. \(7.638\times 10^{-23}\) g
• C. \(3.819\times 10^{-23}\) g
• D. \(1.5277\times 10^{-22}\) g

Hint:

A bcc unit cell has 2 atoms, so find the mass of one sodium atom and multiply by the number of atoms in three cells.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A body-centred cubic unit cell contains \(8\times\dfrac{1}{8}+1=2\) atoms. So 3 unit cells contain \(3\times2=6\) atoms.

Step 2: Mass of one atom
Mass of one Na atom \(=\dfrac{23}{6.022\times10^{23}}=3.819\times10^{-23}\) g.

Step 3: Calculation
Mass of 3 unit cells \(=6\times3.819\times10^{-23}=2.2915\times10^{-22}\) g.

Final Answer:
Three unit cells of sodium weigh 2.2915 times 10 to the power minus 22 g. \[ \boxed{\text{(A) }2.2915\times10^{-22}\ \text{g}} \]