Question

Stronium metal is found to have a face centered cubic crystal structure. It is measured to have a density of 2.54g/mL. What is the length of the unit cell in pm?

Answer 1

We know that,

d = zM/N​​​​​​a​​​​​a​3

Or

a​​​​​​3 = zM/Na​​​​​d ............(1)

Where,

a = length of unit cell

Z = atoms contribution per unit cell

For FCC

Z = 4atoms

M = molar mass of element

For strontium

M = 87.62g/mol

N​​​​​​a = Avogadro's constant = 6.022×1023atoms/mol

d = density of element = 2.54g/ml

We know that

1ml = 1cm3

So,

d = 2.54g/cm​​​​​3

putting the all value in formula

a​​​​​​3 = [(4atoms)(87.62g/mol)]/[(6.022×10-23atoms/mol)(2.54g/cm​​​​​3​)]

a​​​​​​3 = 22.913×10-23cm3

a​​​​​​3 = 229.13×10-24cm3

taking cube root on both side

a = 6.119×10-8cm

(Note:- 1cm = 10-2m = 1010pm)

so,

a = 6.119×10-8×1010pm

a = 611.9pm

hence,

length of unit cell = 611.9pm