9 min readPathway sheet1-mark MCQ, 2-mark balanced reaction, 3-mark energy numericals, part of 5-mark answers; also a NEET favourite

Nuclear fission

A slow neutron splits a heavy nucleus such as ²³⁵U into two medium nuclei and two or three neutrons, releasing about 200 MeV per fission.

A typical fission¹₀n + ²³⁵₉₂U → ²³⁶₉₂U* → ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3 ¹₀n + energy

Energy per fissionAbout 200 MeV

DiscoveryOtto Hahn and Fritz Strassmann, 1938

Fission compared with coalFission of 1 kg of uranium gives about 10¹⁴ J; burning 1 kg of coal gives only about 10⁷ J

Fission of uranium-235, step by step

1
A slow (thermal) neutron is absorbed by a ²³⁵₉₂U nucleus.
2
This forms an unstable, excited compound nucleus ²³⁶₉₂U*.
3
The excited nucleus stretches and splits into two medium-mass fragments, for example barium and krypton.
4
Two or three neutrons are set free.
5
About 200 MeV is released, mostly as kinetic energy of the fragments, which becomes heat as they slow down.

Balanced fission equations

In every nuclear equation, the total mass number and the total charge (atomic number) are the same on both sides.

1
¹₀n + ²³⁵₉₂U → ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3 ¹₀n
Mass numbers: 1 + 235 = 144 + 89 + 3 = 236. Charges: 92 = 56 + 36.
2
¹₀n + ²³⁵₉₂U → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + 2 ¹₀n
Mass numbers: 236 = 140 + 94 + 2. Charges: 92 = 54 + 38.
3
¹₀n + ²³⁵₉₂U → ¹³³₅₁Sb + ⁹⁹₄₁Nb + 4 ¹₀n
Mass numbers: 236 = 133 + 99 + 4. Charges: 92 = 51 + 41.

Why fission gives so much energy

Uranium has a binding energy per nucleon of about 7.6 MeV. The fragments have about 8.5 MeV. So each of the roughly 236 nucleons becomes about 0.9 MeV more tightly bound, and about 200 MeV is released in all. Extra reading (not in your textbook): the 2 or 3 neutrons set free can split more uranium nuclei, which give more neutrons, and so on. This is a chain reaction. In a nuclear power station it is kept under control so that energy is released steadily.

Worked example: energy from 1 kg of uranium-235

Problem

Each fission of ²³⁵U releases 200 MeV. Find the energy released when 1 kg of ²³⁵U undergoes fission. (Avogadro number = 6.02 × 10²³ per mol, 1 MeV = 1.6 × 10⁻¹³ J)

Working

Moles in 1 kg = 1000 g ÷ 235 g/mol = 4.26 mol.
Number of nuclei = 4.26 × 6.02 × 10²³ = 2.56 × 10²⁴.
Energy = 2.56 × 10²⁴ × 200 MeV = 5.12 × 10²⁶ MeV.
In joules: 5.12 × 10²⁶ × 1.6 × 10⁻¹³ = 8.2 × 10¹³ J.
For comparison, burning 1 kg of coal gives only about 10⁷ J, millions of times less.

Answer

About 8.2 × 10¹³ J

Worked example: energy released from the masses

Problem

Find the energy released in ¹₀n + ²³⁵₉₂U → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + 2 ¹₀n. Take the masses as: ²³⁵U = 235.0439 u, ¹₀n = 1.0087 u, ¹⁴⁰Xe = 139.9216 u, ⁹⁴Sr = 93.9154 u; 1 u = 931.5 MeV.

Working

Mass before = 235.0439 + 1.0087 = 236.0526 u.
Mass after = 139.9216 + 93.9154 + 2 × 1.0087 = 235.8544 u.
Mass lost ΔM = 236.0526 − 235.8544 = 0.1982 u.
Energy released = 0.1982 × 931.5 MeV ≈ 184.6 MeV.

Answer

About 185 MeV

In real life

India's nuclear power stations, such as Tarapur in Maharashtra and Kudankulam in Tamil Nadu, use controlled fission chain reactions to boil water and spin turbines that make electricity.

Exam angle

2 marks: “What is nuclear fission? Write a balanced equation for the fission of ²³⁵U by a slow neutron.” Splitting of a heavy nucleus into two medium nuclei with release of energy. ¹₀n + ²³⁵₉₂U → ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3¹₀n + about 200 MeV.

3 marks: “Calculate the energy released in the fission ¹₀n + ²³⁵₉₂U → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + 2¹₀n, using the given masses.” ΔM = (235.0439 + 1.0087) − (139.9216 + 93.9154 + 2.0174) = 0.1982 u. Energy = 0.1982 × 931.5 ≈ 185 MeV.

2 marks: “How much energy is released by the fission of 1 g of ²³⁵U if each fission gives 200 MeV?” Nuclei = (1/235) × 6.02 × 10²³ = 2.56 × 10²¹. Energy = 2.56 × 10²¹ × 200 × 1.6 × 10⁻¹³ J ≈ 8.2 × 10¹⁰ J.

Remember it

One in, three out, 200 out: one slow neutron goes in; two or three neutrons and about 200 MeV come out.