A Uranium-235 nucleus undergoes nuclear fission after absorbing a thermal neutron accordin… — JAMB UTME

A Uranium-235 nucleus undergoes nuclear fission after absorbing a thermal neutron according to the reaction equation:

{^{235}_{92}\text{U}} + {^{1}_{0}\text{n}} \rightarrow {^{140}_{54}\text{Xe}} + {^{94}_{38}\text{Sr}} + x\ {^{1}_{0}\text{n}}

Given the rest masses:
- Mass of

{^{235}_{92}\text{U}} = 235.0439\text{ u}

- Mass of

{^{140}_{54}\text{Xe}} = 139.9216\text{ u}

- Mass of

{^{94}_{38}\text{Sr}} = 93.9154\text{ u}

- Mass of

{^{1}_{0}\text{n}} = 1.0087\text{ u}

1\text{ u} = 931.5\text{ MeV}

Calculate the total energy released during this fission process in MeV.

Answer: 184.62 MeV

184.62 MeV

The total energy released is calculated by first balancing the nuclear equation to determine that 2 neutrons are emitted (

x = 2

). The total mass of reactants is

236.0526\text{ u}

and the products is

235.8544\text{ u}

. The mass defect of

0.1982\text{ u}

multiplied by

931.5\text{ MeV/u}

yields

184.62\text{ MeV}

Balance the mass numbers in the nuclear equation to find the number of emitted neutrons (

x

)

x = 2

neutrons

Conservation of mass number requires

235 + 1 = 140 + 94 + x

, giving

236 = 234 + x

, so

x = 2

Calculate the total mass of the reactants before fission

236.0526\text{ u}

Summing the mass of U-235 (

235.0439\text{ u}

) and the incident neutron (

1.0087\text{ u}

Calculate the total mass of the products after fission

235.8544\text{ u}

Summing masses of Xe-140 (

139.9216\text{ u}

), Sr-94 (

93.9154\text{ u}

), and 2 neutrons (

2 \times 1.0087\text{ u} = 2.0174\text{ u}

Determine the mass defect (mass difference)

\Delta m = 0.1982\text{ u}

Mass defect

\Delta m = m_{\text{reactants}} - m_{\text{products}} = 236.0526 - 235.8544 = 0.1982\text{ u}

Convert mass defect to energy using

1\text{ u} = 931.5\text{ MeV}

184.62\text{ MeV}

Multiplying mass defect

0.1982\text{ u}

931.5\text{ MeV/u}

gives

184.6233\text{ MeV}

, which rounds to

184.62\text{ MeV}

Mass defect and mass-energy equivalence in nuclear fission reactions

Estimated Time:2m 30s

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