Question

An element of atomic mass 125 crystallizes in simple cubic structure the diameter of the largest atom which can be placed without disturbing unit cell is 366 pm if the densities is X then find the value of x

Answer 1

Explanation:

The largest sphere which can be fit in the simple cubic crystal without altering the crystal could be fitted in a cubic void.

The radius of cubic void is given by r=(

3

−1) R, where r is the radius of void and R is the radius of element.

Radius of largest sphere = 366/2 = 183 pm

⟹183=0.732×R

⟹R=250 pm

So, the edge length of cubic unit cell (a) = 2R = 500 pm = 500×10

−10

cm

Density of a crystal is given by d=

N A

×a 3

Z×M

g cm −3

Z for simple cubic crystal = 1

⟹d= 6×10 23×(500×10 −10 ) 31×125

Value of 300d = 300× 6×10 23×(500×10 −10) 31×125

⟹300d=500