By X-ray studies, the packing 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 idenctical. 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

Options

A. 407 pm
B. 189 pm
C. 814 pm
D. 204 pm

Answer

A

Explanation

`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