Chapter 21, Problem 21.19QP

Interpretation Introduction

Interpretation:

The nuclear binding energy and the binding energy per nucleon for the following isotope s should be calculated

Concept introduction:

• Nuclear binding energy: It is the minimum amount of energy required to disassemble the nucleus of an atom into its component parts.

• The component parts are neutrons and protons, which are collectively called as nucleons.

• Binding energy per nucleon:
• The maximum binding energy per nucleon occurs at around mass number A=50.

• Example –Iron nucleolus (${\text{Fe}}^{56}$) is located closed to the peak with a binding energy per nucleon value of approximately 8.8 MeV.

• Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy
• This quantity represents the conversion of mass to energy occurs during an exothermic reaction.
• Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is,$\Delta E=\left(\Delta m\right)c^2$

• Where, $\left(\Delta m\right)$ is called mass defect.

• The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

Formula:

Einstein mass energy relationship [$\text{ΔE}=({\text{ΔM)c}}^{\text{2}}$]

$\text{nuclear binding energy per nucleon =}\frac{\text{nuclear binding energy}}{\text{number of nucleons}}$