Consider a nucleus of mass number and atomic number .

CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear

Problem

Consider a nucleus of mass number

A

and atomic number

Z

. (a) Starting from the definition of mass defect, obtain an expression for the mass defect

\Delta M

in terms of

Z

A

, the rest masses of proton and neutron, and the experimental mass of the nucleus. (b) Hence derive the relation between the nuclear binding energy

E_{b}

and the mass defect

\Delta M

. (c) The experimental mass of the

^{4}_{\ 2}\text{He}

nucleus is

4.002603\,\text{u}

. Using the values

m_{p}=1.007276\,\text{u}

m_{n}=1.008665\,\text{u}

, calculate (i) the mass defect of the

^{4}_{\ 2}\text{He}

nucleus, (ii) its total binding energy, and (iii) its binding energy per nucleon. Take

1\,\text{u}=931\,\text{MeV}