The atomic radius of zinc is 137 pm .Estimate its density,Given that the metal has a close-packed structure.

Question

Quizplus · Accepted Answer

For a close-packed structure, the density ($\rho$) can be estimated using the formula $\rho = \frac{Z \cdot M}{a^3 \cdot N_A}$, where $Z$ is the number of atoms per unit cell, $M$ is the molar mass, $a$ is the edge length of the unit cell, and $N_A$ is Avogadro's number. For zinc, $Z = 4$ (since it's close-packed), $M = 65.38 \, \text{g/mol}$, and $a = 2 \sqrt{2} \cdot r = 2 \sqrt{2} \cdot 137 \times 10^{-10} \, \text{cm}$. Plugging these values into the formula and using $N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}$, the calculated density is closest to the value given in option A, 7.47 g/cm³.

The Atomic Radius of Zinc Is 137 Pm