Question

Calculate the mass loss in the following:
${}_1^2{\text{H}} + {}_1^3{\text{H}} \to {}_4^2{\text{He}} + {}_0^1{\text{n}}$
Given the masses: ${}_1^2{\text{H}} = 2.014{\text{amu}},{}_1^3{\text{H}} = 3.016{\text{amu}},{}_2^4{\text{He}} = 4.004{\text{amu}},{}_0^1{\text{n}} = 1.008{\text{amu}}$
A. $0.018{\text{amu}}$
B. $0.18{\text{amu}}$
C. $0.0018{\text{amu}}$
D. $1.8{\text{amu}}$
E. $18{\text{amu}}$

Answer 1

Hint: Mass defect is the difference in the mass of the nucleus and the mass of free nucleons. It is used further to calculate the binding energy. It holds a considerable amount of mass.

Complete step by step answer:
Given data:
Masses of ${}_1^2{\text{H}} = 2.014{\text{amu}},{}_1^3{\text{H}} = 3.016{\text{amu}},{}_2^4{\text{He}} = 4.004{\text{amu}},{}_0^1{\text{n}} = 1.008{\text{amu}}$

Atom has a nucleus at the center. This nucleus has protons and neutrons in it. Different nuclei are called nuclides.
There are two types of nuclear forces-strong and weak. Strong nuclear force is an attractive force between all the protons and neutrons. They are greater than electric force. Weak nuclear force is less than strong nuclear force. Atomic mass units are used to specify the nuclear masses.
Mass defect is defined as the amount by which the sum of individual masses of the protons and neutrons exceeds the mass of intact nucleus. It is also known as the difference in the mass of the nucleus. The mass of a stable nucleus of an atom is always less than the sum of masses of individual nucleons. Atomic mass is the sum of protons and electrons in the atom. Mass defect can be expressed as $\Delta {\text{m}}$
Mass defect, $\Delta {\text{m}} = $ Total mass of reactants $ - $ total mass of products
${}_1^2{\text{H}} + {}_1^3{\text{H}} \to {}_4^2{\text{He}} + {}_0^1{\text{n}}$
From the reaction above, the reactants are ${}_1^2{\text{H}}$and ${}_1^3{\text{H}}$ and the products are ${}_2^4{\text{He}}$and ${}_0^1{\text{n}}$.
It is given that the masses of ${}_1^2{\text{H}} = 2.014{\text{amu}},{}_1^3{\text{H}} = 3.016{\text{amu}},{}_2^4{\text{He}} = 4.004{\text{amu}},{}_0^1{\text{n}} = 1.008{\text{amu}}$
Total mass of reactants $ = $ mass of ${}_1^2{\text{H}}$$ + $ mass of ${}_1^3{\text{H}}$
i.e. total mass of reactants $ = 2.014{\text{amu}} + 3.016{\text{amu = 5}}{\text{.030amu}}$
Total mass of products $ = $ mass of ${}_2^4{\text{He}}$$ + $mass of ${}_0^1{\text{n}}$
i.e. total mass of products $ = 4.004{\text{amu}} + 1.008{\text{amu = 5}}{\text{.012amu}}$
$\therefore $Mass defect, $\Delta {\text{m}} = 5.030{\text{amu}} - 5.012{\text{amu = 0}}{\text{.018amu}}$
So the mass defect value is $0.018{\text{amu}}$
Hence, Option A is the correct option.

Additional information:
The energy required to decompose the nucleus to its constituent nucleons is called binding energy. Binding energy is related to mass defect.

Note:
Mass defect keeps the nucleons bound together. Mass defects can also be expressed in terms of atomic number, mass of proton, mass number, mass of neutron and mass of bounded nucleus. This is in the form of energy. From this value, mass can be converted to energy using Einstein’s equation.