Question

calculate the packing fraction ,mass defect and energy released in the formation of argon atom ​

Answer 1

We have to calculate the packing fraction, mass defect and energy released in the formation of argon atom.

solution : argon atom is stable in face centered cubic lattice at all temperature.

let r is radius of atom and a is edge length of lattice.

from FCC structure,

4r = √2a ⇒a = 2√2

no of atoms per unit cell = 4

now packing fraction = volume of atoms/volume of lattice × 100

= (4 × 4/3 πr³)/(a³) × 100

= (16/3πr³)/(16√2r³) × 100

= π/3√2 × 100

= 74.04 %

mass defect , ∆m = 18 × mass of proton + 18 × mass of neutron - mass of atom

= 18 × 1.007276 + 18 × 1.008664 - 35.967

= 36.28692 - 35.967

= 0.31992 u

energy released in the formation of argon atom = ∆mc²

= 0.31992 u × 931.5 MeV/u

= 298.00548 MeV