Question 376: Atoms & Nuclei

Question

A nucleus with mass number 242 and binding energy per nucleon as $$7.6~ \mathrm{MeV}$$ breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as $$8.1 ~\mathrm{MeV}$$, the total gain in binding energy is _________ $$\mathrm{MeV}$$.

Accepted Answer

The total binding energy of a nucleus is the binding energy per nucleon multiplied by the number of nucleons (protons and neutrons), which is the mass number.
The initial total binding energy of the nucleus is $242 	imes 7.6 \, 	ext{MeV}$.
After the break, each fragment has a total binding energy of $121 	imes 8.1 \, 	ext{MeV}$.
Since there are two such fragments, the final total binding energy is $2 	imes 121 	imes 8.1 \, 	ext{MeV}$.
The gain in binding energy is the final total binding energy minus the initial total binding energy. Therefore, the gain in binding energy is:
$2 	imes 121 	imes 8.1 \, 	ext{MeV} - 242 	imes 7.6 \, 	ext{MeV} = 1960.2 \, 	ext{MeV} - 1839.2 \, 	ext{MeV} = 121 \, 	ext{MeV}$.
Therefore, the total gain in binding energy is $121 \, 	ext{MeV}$.

Atoms & Nuclei

A nucleus with mass number 242 and binding energy per nucleon as $7.6~ \mathrm{MeV} breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 ~\mathrm{MeV}, the total gain in binding energy is _________ \mathrm{MeV}$.

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