Question

By X-ray studies, the packing of atoms in a crystal of gold is found to be in layers such that starting from any layer, every fourth layer is found to be exactly identical . The density of gold is found to be `19.4 g cm^(-3)` and its atomic mass is 197 a.m.u.
The length of the edge of the unit cell will be
A. 407 pm
B. 189 pm
C. 814 pm
D. 204 pm

Answer 1

Correct Answer - A
`rho=(ZxxM)/(a^3xxN_0xx10^(-30))`
or `a^3=(ZxxM)/(rhoxxN_0xx10^(-30))`
For ccp, i.e., f.c.c., Z=4.
Hence,`a^3=(4xx197)/(19.4xx6.02xx10^23xx10^(-30))`
`=6.747xx10^7`
=`67.47xx10^6`
or `a=(67.47)^(1//3)xx10^2`
`=4.07xx10^2` pm
=407 pm