Question

The edge length of unit cell of a metal having molecular weight 75 g/mol is 5 Å which crystallizes in cubic lattice. If the density is 2 g/cc, then find the radius of the metal atom. (\( N_A = 6 \times 10^{23} \)) Give the answer in pm.

• A. 217 pm
• B. 210 pm
• C. 220 pm
• D. 205 pm

Hint:

The radius of the metal atom can be determined from the density and molar mass by using the relationship between these quantities.

Answer 1

The Correct Option is A

Step 1: Use the formula for density.
The density \( \rho \) of a cubic unit cell is given by: \[ \rho = \frac{Z M}{N_A V_{\text{cell}}} \] where \( Z \) is the number of atoms per unit cell, \( M \) is the molar mass, \( N_A \) is Avogadro's number, and \( V_{\text{cell}} \) is the volume of the unit cell.

Step 2: Calculate the radius.
Using the given values for \( M \), \( \rho \), and the unit cell edge length, we find the radius of the metal atom to be 217 pm.