1.

Define mass defect and nuclear binding energy. For a nucleus ""_(Z)^(A)X, write the value of mass defect and nuclear binding energy.

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Solution :Binding energy in terms of mass defect can be defined as the energy equivalent to the mass defect, is called binding energy of the nucleus.
If `Deltam` is the mass defect, then
Binding energy, `B.E.=Deltam C^(2)` (in joule) `=Zm_(p)+(A-Z)M_(n)-M_("nucleus")`
Ifmass defect is in a.m.u. then
`B.E.=(Deltamxx931.5)` M EV
Expression for binding energy. The mass defect `(Deltam)` OFA nucleus containing Z protons and (A-Z) neutrons is given by
`Deltam=ZM_(p)+(A-Z)M_(n)-M_("nucleus")` ...(1)
where m is mass of the nucleus.
So `M_("nucleus")=(ZM_(p)+(A-Z)M_(n))-DELTA m` ...(2)
Since mass of atom `M(""_(Z)X^(A))` is given by
`M=M_("nucleus")+ZM_(e)`
Using eq (2), we get
`M=(ZM_(p)+(A-Z)M_(n))-Deltam+ZM_(e)`
`:.` Mass defect, `Deltam=Z(M_(p)+M_(e))+(A-Z)M_(n)-M`
`=ZM_(H)+(A-Z)M_(n)-M [ :.M_(p)+M_(e)=M_(H)]`
`:.B.E.=Delta mc^(2)`
or `B.E.=[ZM_(H)+(A-Z)M_(n)-M]c^(2)`


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