Calculate the binding energy per nucleon for `C^(12),N^(14), O^(16)`, and comment on their relative magnitudes. Masses of proton and neutron are `1.0078` and `1.0087m_(u)`, respectively.
`(m_(u)=931MeV)`

Answer

`C^(12)=7.68MeV`
`N^(14)=7.68MeV`
`O^(16)=7.68MeV`
Stability is same.

Explanation

`a. C^(12),` proton `=6`, neutron `=6`
`Delta_(m)=(6xx1.0078+6xx1.0087)-12`
`=(6.0468+6.0522)-12`
`=12.099-12=0.099m _(u)`
`BE` per nucleus
`=(0.099xx931)/(12)MeV=7.68MeV`
`b.` `N^(14), proton =7`, neutron `=7`
`Delta m=(7xx1.0078+7xx1.0087)-14`
`=(7.0546+7.0609)-14`
`=14.1155-14=0.1155m_(u)`
`BE` per nucleus
`=(0.1155xx931)/(14)MeV=7.68m_(u)`
`c.` `O^(16),` proton `=8` neutron `=8`
`Delta_(m)=(8xx1.0078+8xx1.0087)-16`
`=(8.0624+8.0696)-16`
`=0.132m_(u)`
`BE` per nucleus
`=(0.132xx931)/(16)MeV=7.68MeV`