Question

Determine the packing efficiency of a simple cubic unit cell that contains one atom with a metallic radius of 175 pm.

Answer 1

Answer:

the packing efficiency is 52.36%

Explanation:

Given the data in the question;

simple cubic unit cell that contains one atom with a metallic radius of 175 pm;

we know that;

Edge length of Simple cubic (a) is related to radius of atom (r) as follows;

a = 2r

since radius r = 175 pm

we substitute

a = 2 × 175 pm

a = 350 pm

Now we get the volume unit;

Volume of unit cell = a³ = ( 350 pm ) = 42875000 pm³

Next we get Volume of sphere;

Volume of Sphere = $\frac{4}{3}$πr³

Volume occupied by 1 atom = $\frac{4}{3}$ × π × ( 175 pm )³

=  $\frac{4}{3}$ × π × 5359375 pm³

= 22449297.5 pm³

Now, the packing efficiency = ( Volume occupied by 1 atom / Volume of unit cell ) × 100

we substitute;

packing efficiency = ( 22449297.5 pm³ / 42875000 pm³ ) × 100

= 0.523598 × 100

= 52.36%

Therefore, the packing efficiency is 52.36%