Step 1: Formula for Density:
Density \( \rho = \frac{Z \cdot M}{N_A \cdot a^3} \)
Where \( Z \) is the number of atoms per unit cell, \( M \) is molar mass, \( a \) is edge length.
Since the metal is the same, \( M \) and \( N_A \) are constant.
Ratio: \( \frac{\rho_{fcc}}{\rho_{bcc}} = \frac{Z_{fcc}}{Z_{bcc}} \times \left( \frac{a_{bcc}}{a_{fcc}} \right)^3 \)
Step 2: Values:
For FCC: \( Z_{fcc} = 4 \), \( a_{fcc} = 3.5 \) \AA.
For BCC: \( Z_{bcc} = 2 \), \( a_{bcc} = 3.0 \) \AA.
Step 3: Calculation:
\[ \text{Ratio} = \frac{4}{2} \times \left( \frac{3.0}{3.5} \right)^3 \]
\[ \text{Ratio} = 2 \times \left( \frac{30}{35} \right)^3 = 2 \times \left( \frac{6}{7} \right)^3 \]
\[ \text{Ratio} = 2 \times \frac{216}{343} \]
\[ \text{Ratio} = \frac{432}{343} \]
\[ \text{Ratio} \approx 1.259 \]
Step 4: Match Option:
Approximately 1.26. Matches Option (B).