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Nuclear Stability

A nucleus Z...

Question

A nucleus $_{Z}^{A} X$ has mass represented by $M (A, Z)$ . If $M_{p}$ and $M_{n}$ denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then:

B . E = M (A, Z) Z M p (A - Z) M_{n}

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B . E = [M (A, Z) - Z M_{p} - (A - Z) M_{n}] c^{2}

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B . E = [Z M_{p} + (A - Z) M_{n} - M (A, Z)] c^{2}

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B . E = [Z M_{p} + A M_{n} - M (A, Z)] c^{2}

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Solution

The correct option is A $B . E = [Z M_{p} + (A - Z) M_{n} - M (A, Z)] c^{2}$
Nuclear Binding Energy is the energy required to split a nucleus of an atom into its component parts : protons and neutrons
It is directly linked with mass defect.
$Δ m = [{Z M}_{p} + (A - Z) M_{n} - M (A, Z)] .$
Binding Energy = $(Δ m) c^{2}$
$B \circ E \circ = [{Z M}_{P} + (A - Z) M_{n} - M (A, Z)] C^{2}$

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