Question

The binding energy per nucleon of ${}_5{B}^{10}$ is $8.0$MeV and that of ${}_5{B}^{11}$ is $7.5$MeV. The Energy required to remove a neutron from ${}_5{B}^{11}$ is (mass of electron and proton are $9.11\times {10}^{-31}$kg and $1.67\times {10}^{-27}$kg).

• A. $2.5$MeV
• B. $8.0$MeV
• C. $0.5$MeV
• D. $7.5$MeV

Answer 1

Answer: (A)

$2.5$MeV

The nuclear reaction is ${}_5{B}^{11}{\to }_5{B}^{10}{+}_0{n}^1$

Binding energy per nucleon of ${}_5{B}^{11}$ $E_1^{\prime }=7.5MeV$

Its binding energy $E_1=7.5\times 11=82.5MeV$

Binding energy per nucleon of ${}_5{B}^{10}$ $E_2^{\prime }=8.0MeV$

Its binding energy $E_2=8.0\times 10=80MeV$

Energy required to remove a neutron $\Delta E=E_1-E_2$

$\therefore$ $\Delta E=82.5-80=2.5MeV$