Question # An element ( x ) (atomic wt. ( =125 ) ) crystallises in simple cubic structure. If diameter of the largest atom which can be placed without disturbing unit cell is 366 pm. Find the density of pure element ( X ) in

# An element ( x ) (atomic wt. ( =125 ) ) crystallises in simple cubic structure. If diameter of the largest atom which can be placed without disturbing unit cell is 366 pm. Find the density of pure element ( X ) in

( mathrm{gm} / mathrm{cm}^{3} )

Solution

For Simple cubic unit cell

( 2 r=a )

( r=r a d i u s ) of atoms ( X )

If Radius of the largest atom that can be

placed ( =mathrm{R} )

( 2 R=366 p m )

( 2 r+2 R=a sqrt{3} )

( a+366=a(sqrt{3}-1) )

( 366=a(sqrt{3}-1) )

( begin{aligned} a &=frac{366}{0.732} &=500 mathrm{pm} end{aligned} )

Answer: 0500