Question

The most abundant isotope of strontium, Sr-88, contains thirty-eight protons and fifty neutrons and has a mass of 87.9056 u.

a)What is the mass defect for this nucleus in atomic mass units? In kilograms? atomic mass units u

b) kilograms kg

Answer 1

To calculate the mass defect:

• add up the masses of each proton and of each neutron that make up the nucleus,
• subtract the actual mass of the nucleus from the combined mass of the components to obtain the mass defect.

• Find the composition of the Sr-88 nucleus and determine the combined mass of its components.

Sr-88 has contains thirty-eight protons and fifty neutrons and has a mass of 87.9056 u.The mass of a proton is 1.00728 amu and a neutron is 1.00867 amu.
The combined mass is calculated:

38 protons(1.00728 amu/proton) + 50 neutrons(1.00867 amu/neutron)
or
88.7101 amu

• Calculate the mass defect.

Dm = 88.7101 amu - 87.9056 amu = 0.8045 amu

Conversion of Mass Defect into Energy

To convert the mass defect into energy:

• Convert the mass defect into kilograms (1 amu = 1.6606 x 10^-27 kg)
• Convert the mass defect into its energy equivalent using Einstein's equation.

• Convert the mass defect (calculated in the previous example) into kg.

(0.8045 amu/nucleus)(1.6606 x 10^-27 kg/amu) = 13.3595 x 10^-28 kg/nucleus

• Convert this mass into energy using DE = Dmc², where c = 2.9979 x 10⁸ m/s.

E = 13.3595 x 10^-28kg/nucleus)(2.9979 x 10⁸ m/s)² = 40.05 x 10^-11 J/nucleus