Question

Define mass defect of a nucleus. Binding energy of ${}_8{O^{16}}{\text{ is 127}}{\text{.5MeV}}$. Write the value of its ‘binding energy per nucleon.’ Write the value of 1eV energy in joule.

Answer 1

Hint: Mass of the nucleus is less than the nucleon. Hence mass defect has been introduced. Binding energy of oxygen has given. Binding energy per nucleon is given by binding energy divided by the mass number. The value obtained must be in mega electron-volt. Convert MeV in joule by multiplying $1.602 \times {10^{ - 19}}$ to the calculated value of binding energy per nucleon.

Formula used:
${\text{Binding energy per nucleon}} = \dfrac{{{\text{binding energy of nucleus}}}}{A}$
where A represents the mass number of the atom

Complete step by step answer:
It is observed that the mass of the nucleus is less than the sum of the masses of constituent nucleons in the free State.
The difference between the actual mass of the nucleus and the sum of masses of constituent nucleons is called the mass defect.
The mass defect is given by,
$\vartriangle m = [Z{m_p} + (A - Z){m_n}] - M$
where,
M- The measured mass of the nucleus
Z- Atomic number (number of protons)
A- Mass number (mass of nucleons in a free state)
${m_p}$- Mass of proton
${m_n}$- Mass of a free neutron
(A-Z)- Number of neutrons
The amount of energy required to separate all the nucleons from the nucleus is called binding energy.
In the given question, the oxygen element has given $\left( {{}_8{O^{16}}} \right)$ .
Atomic number = 8
Mass number = 16
The binding energy of oxygen is given by ${\text{127}}{\text{.5MeV}}$.
Now the binding energy per nucleon is given as
$\eqalign{
  & {\text{Binding energy per nucleon}} = \dfrac{{{\text{binding energy of nucleus}}}}{A} \cr
  & \Rightarrow {\text{Binding energy per nucleon}} = \dfrac{{127.5MeV}}{{16}} \cr
  & \therefore {\text{Binding energy per nucleon}} = 7.969MeV \cr} $
The value of binding energy per nucleon is$7.969MeV$.
The value of 1eV energy in joule: $1eV = 1.602 \times {10^{ - 19}}joule$

Note:
Nucleus is nothing but protons and neutrons. Whereas nucleons are protons or neutrons. Neutrons are charged with less quantity present in the nucleus of an atom. Do you know, the binding energy per nucleon is calculated to separate a nucleon from the nucleus. The amount of energy required to separate all the nucleons from the nucleus is called binding energy. You can also calculate the mass defect by the formula $\vartriangle m = [Z{m_p} + (A - Z){m_n}] - M$. Mega is equal to the power of 6. Now to convert eV into joule, multiply the value by the charge of the electron $1.602 \times {10^{ - 19}}$.