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  • The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei _13 ^27 Al from the following data:

Q.13.24 (ii) The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei _{13}^{27}\textrm{Al} from the following data:

                   m(_{20}^{40}\textrm{Ca})=39.962591\; u

                    m(_{20}^{41}\textrm{Ca})=40.962278 \; u

                    m(_{13}^{26}\textrm{Al})=25.986895 \; u

                     m(_{13}^{27}\textrm{Al})=26.981541 \; u

Answers (1)

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The reaction showing the neutron separation is

_{13}^{27}\textrm{Al}+E\rightarrow _{13}^{26}\textrm{Al}+_{0}^{1}\textrm{n}

\\E=(m(_{13}^{26}\textrm{Ca})+m(_{0}^{1}\textrm{n})-m(_{13}^{27}\textrm{Ca}))c^{2}\\ E=(25.986895+1.008665-26.981541)c^{2}\\ E=(0.014019)u\times c^{2}

But 1u=931.5 MeV/c2

Therefore E=(0.014019)\times931.5

E=13.059 MeV

Therefore to remove a neutron from the _{13}^{27}\textrm{Al} nucleus 13.059 MeV of energy is required 

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Sayak

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