UPSEE Solved Model Paper 7

Given:
Molecular weight = 200 g/mole
Edge length = 3

0

A

Avogadro's number = 6 × 1023mol−1
We have to find the density of the element
The density of an element is given by the formula
ρ =

Z×M

a3×N0

... (i)
where, Z = Number of atoms per unit cell (for simple cubic unit cell, Z = 1)
M = Molecular weight
a = Edge length
N。= Avogadro's number = 6 × 1023mol−1
Now, a = 3

0

A

= 3 × 10−8 cm (Since 1

0

A

= 10−8 cm)
Substituting all the values in equation (i). we get
ρ =

1×200

(3×10−8)3×6×1023

ρ =

200

27×6×10−1

g∕cm3
ρ =

2000

27×6

g∕cm3
ρ = 12.345 g∕cm3
~ 12.29 g∕cm3
Therefore, the density of the element is 12.29 g∕cm3.
Hence, option 'C' is correct