Chapter 24, Problem 24.80P

(a)

Interpretation Introduction

Interpretation:

Binding energy per nucleon of ${}^{206}Pb$ has to be calculated in $MeV.$

Concept Introduction:

Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.

Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.

  $\text{Nucleus + nuclear binding energy }\underset{}{\to }\text{ nucleons}$

It can be calculated in $MeV$ using the given formula,

  $\text{Binding energy = }\Delta \text{m}\left(\text{in amu}\right)\times \frac{\text{931}\text{.5 MeV}}{1\text{ amu}}$

Nucleon: Nucleon is the collective name given to the members of the nucleus that is protons and neutrons.

The difference between mass of an atom and the sum of the masses of its proton and neutron is called Mass difference.

Binding Energy per Nucleon can be determined as follows:

  $\text{Binding energy per nucleon = }\frac{\text{Binding energy}}{\text{No}\text{. of nucleons}}$

(b)

Interpretation Introduction

Interpretation:

Binding energy per atom of ${}^{206}Pb$ has to be calculated in $MeV.$

Concept Introduction:

Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.

Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.

  $\text{Nucleus + nuclear binding energy }\underset{}{\to }\text{ nucleons}$

It can be calculated in $MeV$ using the given formula,

  $\text{Binding energy = }\Delta \text{m}\left(\text{in amu}\right)\times \frac{\text{931}\text{.5 MeV}}{1\text{ amu}}$

The difference between mass of an atom and the sum of the masses of its proton and neutron is called Mass difference.

(c)

Interpretation Introduction

Interpretation:

Binding energy per mole of ${}^{206}Pb$ has to be calculated in $kJ.$

Concept Introduction:

Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.

Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.

  $\text{Nucleus + nuclear binding energy }\underset{}{\to }\text{ nucleons}$

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is,

  $\begin{array}{l}\Delta \text{E = }\Delta {\text{mc}}^2\\ \\ where,\\ \Delta \text{m = Mass Difference}\\ c=\text{ Speed of light}\end{array}$

The difference between mass of an atom and the sum of the masses of its proton and neutron is called Mass difference.