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Find the average binding energy per nucl...

Find the average binding energy per nucleon of `._7N^14` and `._8O^16`. Their atomic masses are 14.008 u and 16.000 u. The mass of `._1H^1`atom is 1.007825 u and the mass of neutron is 1.008665 u. Which is more stable?

Text Solution

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The average binding energy per nucleon
`= ([Zm_(H) +(A-Z) m_(n) - M^A])/A`
The average binding energy per nucleon of `""_(7)N^(14)`
`=([7xx1.007825+7xx1.008665-14.008]uxxc^2)/14`
= `([14.115430-14.008]931.5)/14 MeV`
`=(0.10743xx931.5)/14 MeV = 7.148 MeV`
The average binding energy per nucleon of `""_(8)O^(16)`
`=([8xx1.007825+8xx1.008665-16.000]uxxc^2)/A`
`= (0.131920xx931.5)/16 MeV = 7.680MeV`
`:. ""_(8)O^(16)` is more stable than `""_(7)N^(14)` .
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