Platinum has a face-centered cubic crystal structure and a density of 21.5 g/cm3.What is the radius of a platinum atom?
A)69 pm
B)98 pm
C)139 pm
D)196 pm
E)277 pm

Question

Quizplus · Accepted Answer

The density of platinum can be related to the atomic radius using the formula: d = (4M)/(a^3*N*_A), where d is density, M is molar mass, a is the length of one side of the cubic unit cell, and N*_A is Avogadro's number. Rearranging this formula to solve for the atomic radius (a), we get: a = [(4M)/(d*N*_A)]^(1/3). Plugging in the values given for platinum, we get: a = [(4*195.08 g/mol)/(21.5 g/cm3 * 6.022 x 10^23 atoms/mol)]^(1/3) = 1.39 x 10^-8 cm = 139 pm. Therefore, the answer is choice C.

Platinum Has a Face-Centered Cubic Crystal Structure and a Density