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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 20^41ca and _13^27 Al from the Following Data: - CBSE (Science) Class 12 - Physics

ConceptMass-energy and Nuclear Binding Energy Nuclear Binding Energy

#### Question

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 ""_20^41Ca and ""_13^27 Al from the following data:

m(""_20^40Ca) = 39.962591 u

m(""_20^41Ca) = 40.962278 u

m(""_13^26Al) = 25.986895  u

m(""_13^27Al) = 26.981541 u

#### Solution

For ""_20^41 Ca: Separation energy  = 8.363007 MeV

For ""_13^27Al: Separation energy = 13.059 MeV

A neutron (""_0n^1) is removed from a ""_20^41 Ca nucleus. The corresponding nuclear reaction can be written as:

""_20^41Ca -> ""_20^40Ca + _0^1n

It is given that:

Mass m(""_20^40 Ca)= 39.962591 u

Mass m(""_20^41 Ca) = 40.962278 u

Mass m(""_0n^1) = 1.008665 u

The mass defect of this reaction is given as:

Δm = m(""_20^40Ca) + (""_0^1n) - m(""_20^41 Ca)

= 39.962591 + 1.008665 - 40.962278 = 0.008978 u

But 1 u = 931.5 "MeV/c^2"

∴Δm = 0.008978 × 931.5 MeV/c2

Hence, the energy required for neutron removal is calculated as:

E = trianglemc^2

= 0.008978 xx 931.5 = 8.363007 MeV

For ""_13^27 Al the neutron removal reaction can be written as:

""_13^27 Al -> _13^26 Al + _0^1 n

it us given that.

Mass m(""_13^27 Al) = 26.981541 u

Mass m(""_13^26 Al) = 25.986895 u

The mass defect of this reaction is given as:

trianglem = m(""13^26 Al) + m(""_0^1 n) - m(""_13^27 Al)

= 25.986895 + 1.008665 - 26.981541

= 0.014019 u

= 0.014019 xx 931.5 "MeV/c"^2

Hence, the energy required for neutron removal is calculated as:

E = trianglemc^2

= 0.014019 x 931.5 = 13.059 MeV

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Solution 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 20^41ca and _13^27 Al from the Following Data: Concept: Mass-energy and Nuclear Binding Energy - Nuclear Binding Energy.
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