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 be19.4 g cm^(-3) and its atomic mass is 197 a.m.u. The length of the edge of the unit cell will be

By X-ray studies, the packing atoms, in a crystal of gold is found to

1.	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 be19.4 g cm^(-3) and its atomic mass is 197 a.m.u. The length of the edge of the unit cell will be
Answer» <P>407pm 189 pm 814 pm 204 pm Solution :` p = (Z xx M)/( a^(3)xx N_(0) xx 10^(-30))or a^(3) = (Z xx M)/( p xx N_(0) xx 10^(-30))` For CCP , i.e, f.c.c , Z= 4 Hence , ` a^(3) = ( 4xx 197)/( 19.4 xx 6.02 xx 10^(23) xx 10^(-30))` ` = 6.747 xx 10^(7) = 67.47 xx 10^(6)` ` a = (67.47)^(1//3) xx 10^(2)` ` 4.07 xx 10^(2) "pm" = 407 "pm"`