Question

The density of an unknown metal is 7.21 g cm-3 and its atomic radius is 127 pm. Its crystal structure has a body-centered cubic (bcc) lattice.

a) How many atoms of the metal are in a unit cell of the unknown metal?

b) What is the length of a side of the unit cell?

c) What is the atomic mass of this metal?

d) Which is the name of this metal?

Answer 1

a)

2

b)

For BCC

a = (√16/3) r

where,

a = length of a side of the unit cell

r = atomic radius , 127pm = 127 ×10^-10 cm

a = (√16/3) × 127 × 10^-10 cm

a = 2.93×10^-8cm

c)

a³ = (2.93 ×10^-8)³ = 2.515×10^-23cm³

mass per uint cell = 7.21g /cm³ × 2.515 ×10^-23cm³

mass per unit cell = 1.813×10^-22g

mass per atom = 1.813× 10^-22g /2 = 9.065×10^-23

atomic mass of the metal = 9.065×10^-23g × 6.023×10²³

atomic mass of the metal = 54.60g/mol

d)

Manganese