Question

An element crystallises in a bcc structure with a unit cell edge
length of 150 pm. If the density of the element is 7.5 g/cm³,
then the number of atoms present in 150 g of the element is

i.1.18 x 10²⁴atoms
ii.1.18×10²⁵ atoms
iii.2.37 x 10²⁵atoms
iv.5.9 x 10²⁴atoms

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Answer 1

Answer:

Solution

verified

The edge length, a=500pm=500×10

−12

m=5×10

−8

cm

The volume of the unit cell =a

3

=(5×10

−8

cm)

3

=1.25×10

−22

cm

3

For b.c.c unit cell, the number of atoms per unit cell Z=2

Volume occupied by each atom =

2

1.25×10

−22

cm

3

=6.25×10

−23

cm

3

The density d=7.5g/cm

3

Mass of sample =300g

Volume of sample =

density

mass

=

7.5

300

=40cm

3

The number of atoms present in 300 g of the element =

6.25×10

−23

cm

3

40cm

3

=6.4×10

23

atoms.