Question

Sodium crystallizes in a bcc unit cell. calculate the approximate number of unit cells in 9.2g of sodium?

Answer 1

Answer:

no. of unit cells in 9.2 g Na

=9.2*6.022*10^22/23*2

=1.204*10^23

Answer 2

Given:

Sodium crystallizes in a bcc unit cell

To Find:

The approximate number of unit cells in 9.2g of sodium

Solution:

There will be approximately 6.9 X 10²² unit cells in 9.2g of Sodium.

In the bcc structure, 8 atoms are present at the 8 corners and a single atom at the center of the lattice.

The contribution of atoms on the corners = 1/8

The contribution of atoms in the center = 1

Total number of effective atoms in a bcc cell = 8 X 1/8 + 1 X1

= 2

So two Na atoms are present in one unit cell.

Number of moles of Na in a sample with 9.2g of sodium =  Given mass/ Molar mass

= 9.2 / 40

= 0.23 moles

Since one mole of a substance has 6.022 X 10²³ atoms,

⇒ 0.23 moles will have 0.23 X 6.022 X 10²³ atoms

= 1.38 X 10²³ atoms

As proved above, one unit cell has two atoms

⇒ 1.38 X 10²³ atoms will be present in 1.38 X 10²³ / 2 unit cells

= 0.69 X 10²³

= 6.9 X 10²² unit cells