Physics · Nuclei

Nuclear Fission

Nuclear fission is the neutron-induced splitting of a heavy nucleus such as $^{235}_{\,92}\mathrm{U}$ into two intermediate-mass fragments, releasing additional neutrons and an energy of the order of 200 MeV per event. NCERT develops this in §13.7 Nuclear Energy and §13.7.1 Fission, tracing the energy to the rise in binding energy per nucleon; NIOS Chapter 27 adds the mechanism, the chain reaction and the controlled-fission reactor. For NEET this subtopic is reliably examined through the fission equation, the ~200 MeV estimate, and the gain-in-binding-energy calculation.

What Is Nuclear Fission

Beyond the natural radioactive decays, new possibilities emerge when nuclei are bombarded with other nuclear particles such as protons, neutrons or $\alpha$-particles. The most important neutron-induced nuclear reaction of this kind is fission: a heavy nucleus, after capturing a neutron, breaks into two intermediate-mass nuclear fragments together with the emission of further neutrons and a large release of energy. Lise Meitner and Otto Frisch named the process in 1938, drawing an analogy with the division of a biological cell.

The phenomenon was discovered when Otto Hahn and Fritz Strassmann found barium — an element of intermediate mass — among the products of slow-neutron bombardment of uranium, accompanied by the release of nearly 200 MeV of energy. This was wholly unexpected, since the prevailing expectation had been the production of heavier transuranic elements.

Fission matters because it converts a small mass defect into an enormous energy yield. NCERT states that nuclear sources produce about a million times more energy than chemical sources for the same quantity of matter, the energy per event being of the order of MeV rather than eV. It is the source of energy in nuclear reactors and, in its uncontrolled form, in an atom bomb.

FeatureChemical reactionNuclear fission
What interactsValence electronsThe nucleus
Energy per eventOrder of eV (e.g. 4.08 eV for CO₂)Order of MeV (~200 MeV)
Energy from 1 kg~$10^{7}$ J (coal)~$10^{14}$ J (uranium)
Mass change~$10^{-35}$ kg, undetectableMeasurable mass defect
ResultNew moleculeNew elements (transmutation)

The U-235 Fission Reaction

A representative example of fission is the uranium isotope $^{235}_{\,92}\mathrm{U}$ capturing a neutron and splitting. NCERT writes one such mode as a barium–krypton split:

$$ {}^{235}_{\,92}\mathrm{U} + {}^{1}_{0}n \;\rightarrow\; {}^{236}_{\,92}\mathrm{U} \;\rightarrow\; {}^{144}_{\,56}\mathrm{Ba} + {}^{89}_{\,36}\mathrm{Kr} + 3\,{}^{1}_{0}n $$

The same reaction can produce other pairs of intermediate-mass fragments. NCERT lists, among others, an antimony–niobium split with four neutrons, and a xenon–strontium split with two neutrons:

$$ {}^{235}_{\,92}\mathrm{U} + {}^{1}_{0}n \;\rightarrow\; {}^{133}_{\,51}\mathrm{Sb} + {}^{99}_{\,41}\mathrm{Nb} + 4\,{}^{1}_{0}n $$

A single $^{235}\mathrm{U}$ nucleus can fission in more than 40 different modes, producing about 80 different intermediate-mass nuclei. The fragments are characteristically of unequal mass — one being roughly 1.5 to 2 times heavier than the other, with heavier fragments around mass 140 and lighter ones around mass 95. The number of neutrons emitted is two or three, the average per fission of $^{235}\mathrm{U}$ being about 2.5. The fragment products are themselves radioactive and reach stable end products by emitting $\beta$ particles in succession.

n U-235 + n Ba 144 Kr 89 n n n + ~200 MeV
A thermal neutron is captured by $^{235}\mathrm{U}$, forming an excited $^{236}\mathrm{U}$ that splits into two unequal fragments (here Ba and Kr), releasing about 3 neutrons and ~200 MeV.

Energy Released — The ~200 MeV Estimate

The energy released — the Q value — in the fission of a uranium-like nucleus is of the order of 200 MeV per fissioning nucleus. NCERT estimates this directly from the binding-energy-per-nucleon curve. Take a nucleus of mass number $A = 240$ breaking into two fragments each of $A = 120$:

QuantityValue
$E_{bn}$ for the $A = 240$ nucleusabout 7.6 MeV
$E_{bn}$ for each $A = 120$ fragmentabout 8.5 MeV
Gain in binding energy per nucleonabout 0.9 MeV
Total gain ($240 \times 0.9$)about 216 MeV

The deeper reason is the shape of the $E_{bn}$ versus $A$ curve. The binding energy per nucleon is highest (about 8.75 MeV near $A = 56$) for intermediate-mass nuclei and falls to about 7.6 MeV for $A = 238$. When a heavy nucleus splits into intermediate-mass fragments, the nucleons become more tightly bound; the increase in total binding energy is liberated. This disintegration energy first appears as the kinetic energy of the fragments and neutrons, and is eventually transferred to the surrounding matter as heat.

NEET Trap

Where the fission energy comes from — and which side of the BE/A curve

The energy is released because the fragments have a higher binding energy per nucleon than the original heavy nucleus — the products are more tightly bound, so energy is given out. A common error is to say energy is released because the products are "less bound." It is the reverse. Equally, do not memorise "200 MeV" as a fixed law: it is an order-of-magnitude estimate (the NCERT worked figure is about 216 MeV; NIOS quotes ~200 MeV from a mass-defect of about 0.2154 u).

Fission releases energy because heavy → intermediate-mass means a rise in $E_{bn}$ (a positive mass defect for the reaction). Magnitude ≈ 200 MeV per fission.

The contrast with chemical fuel is dramatic. NCERT notes that fission of 1 kg of uranium generates about $10^{14}$ J, whereas burning 1 kg of coal yields only about $10^{7}$ J — a factor of roughly a million, exactly the ratio between MeV-scale nuclear energies and eV-scale chemical energies.

Worked Example

Estimate the energy released in the fission shown in NIOS Table 27.1, where $^{235}\mathrm{U} + n$ (total mass 236.052565 u) yields $^{141}\mathrm{Ba} + ^{92}\mathrm{Kr} + 3n$ (total mass 235.837195 u).

Mass defect $\Delta m = 236.052565 - 235.837195 = 0.21537\ \text{u}$.

Using $1\ \text{u} \approx 931\ \text{MeV}/c^2$, the energy released is

$$E = 0.21537 \times 931 \approx 200\ \text{MeV}.$$

This confirms the order-of-magnitude estimate obtained from the binding-energy curve.

Build the foundation first

The whole fission energy argument rests on the shape of the binding-energy curve. Revise it in Nuclear Binding Energy before attempting Q-value problems.

Mechanism of Fission

Why is a slow neutron such an effective trigger? Because a neutron is neutral, it experiences no Coulomb barrier and can penetrate a nucleus even at very low energy. Even thermal neutrons — with energy of about 0.0253 eV — are readily captured by $^{235}\mathrm{U}$. Charged projectiles such as protons must instead overcome a Coulomb barrier of several MeV.

The accepted picture is the liquid-drop model of Bohr and Wheeler. When the nucleus captures a thermal neutron, the binding energy of that neutron is released and excites the nucleus, distorting its shape. Surface tension tries to restore the spherical shape while the Coulomb force tends to distort it further; the nucleus oscillates between spherical and dumb-bell shapes. When the excitation is large enough, the dumb-bell elongates until the two charge centres are separated beyond a critical distance, at which point electrostatic repulsion overcomes the nuclear surface tension and tears the nucleus into two fragments.

U capture n excited, deformed dumb-bell shape scission
Liquid-drop mechanism: neutron capture excites and deforms the nucleus, which oscillates into a dumb-bell shape; when the charge centres separate past a critical distance, Coulomb repulsion overcomes surface tension and the nucleus splits.

A substance such as $^{235}\mathrm{U}$ that undergoes fission by thermal neutrons is called a fissile material. NIOS lists the principal fissile nuclides as $^{233}\mathrm{Th}$, $^{233}\mathrm{U}$, $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$ — all of which have odd mass number and even atomic number. A fission event itself occurs within about $10^{-17}$ s of neutron capture, and the fission neutrons are emitted within about $10^{-14}$ s.

The Chain Reaction and Critical Mass

The neutrons released in each fission are the key to a sustained reaction. Since one captured neutron produces two or three new neutrons, each fission event can in principle remove one neutron and replace it with more than two. These secondary neutrons can be captured by further $^{235}\mathrm{U}$ nuclei, causing further fissions, which release still more neutrons. This self-multiplying process is the nuclear chain reaction.

U U U U U U U leakage leakage gen 0 gen 1
A branching chain reaction. Each fission releases 2–3 neutrons; some induce further fissions (purple), some escape through the surface (red, dashed). Self-sustained operation requires neutron production to balance neutron loss.

Not every chain reaction sustains itself. Some neutrons escape through the surface of the material before being captured, and the smaller the sample, the larger its surface-to-volume ratio and the greater the fractional leakage. The reaction becomes self-sustained only when the rate of production of neutrons equals the rate of loss of neutrons. This requires a minimum amount of fissile material, the critical mass: below it, too many neutrons leak out and the chain dies; at or above it, the reaction can sustain itself.

NEET Trap

Controlled vs uncontrolled — and the role of critical mass

A controlled chain reaction (each fission triggers, on average, exactly one further fission) is the basis of a nuclear reactor producing electricity. An uncontrolled chain reaction (each fission triggers more than one) multiplies explosively — this is the atom bomb. The chain reaction cannot become self-sustained at all unless the fissile mass reaches the critical mass; a sub-critical sample simply loses too many neutrons to its surface.

Reactor = controlled (multiplication factor ≈ 1). Bomb = uncontrolled. Either way, a self-sustained chain needs at least the critical mass.

The Nuclear Reactor

A nuclear reactor is the device designed to maintain a self-sustained and controlled chain reaction. Its operating principle is simple: the heat liberated in fission is used to produce high-pressure, high-temperature steam by circulating a coolant around the fuel, and the steam drives a turbine–generator system to produce electricity — just as a coal-fired plant burns coal to raise steam, except that one fission event releases roughly $7 \times 10^{5}$ times more energy than burning one carbon atom.

Two components require special care in NEET questions: the moderator and the control rods. The neutrons released in fission are fast (a few MeV), but $^{235}\mathrm{U}$ fissions most efficiently with slow neutrons. A moderator — ordinary water or heavy water — slows these fast neutrons down to thermal energies through repeated collisions. Separately, control rods of cadmium or boron absorb neutrons; inserting or withdrawing them adjusts the neutron population to hold the chain reaction at the desired steady level.

ComponentTypical materialFunction
Fuel$^{235}\mathrm{U}$ (or $^{239}\mathrm{Pu}$)Undergoes fission, releasing energy and neutrons
ModeratorOrdinary water / heavy waterSlows fast neutrons to thermal speeds
Control rodsCadmium or boronAbsorb neutrons to control the reaction rate
CoolantWater / heavy waterRemoves heat from the core
ReflectorReduces neutron leakage from the core
ShieldThick concreteProtects personnel from radiation
Reactor core fuel + moderator control rods hot coolant cool coolant heat exchanger steam turbine generator
Schematic of a nuclear power reactor. Fission heat in the core (with fuel, moderator and neutron-absorbing control rods) is carried by a coolant to a heat exchanger; the steam produced drives a turbine–generator to produce electricity.

The heat generated in the core is removed by circulating a coolant, which transfers its heat to a secondary fluid (usually water) in a heat exchanger, generating the steam that runs the turbine–generator. In India, thermal power reactors operate at sites such as Tarapur, Narora, Kota and Kaiga, and a fast breeder research reactor is being developed at Kalpakkam.

Quick Recap

Nuclear Fission in one screen

  • Definition: a heavy nucleus (e.g. $^{235}\mathrm{U}$) captures a neutron and splits into two intermediate-mass fragments plus 2–3 neutrons.
  • Sample reaction: $^{235}_{\,92}\mathrm{U} + n \rightarrow ^{144}_{\,56}\mathrm{Ba} + ^{89}_{\,36}\mathrm{Kr} + 3n + \sim200\ \text{MeV}$.
  • Energy ≈ 200 MeV per fission, from the rise in $E_{bn}$ (≈7.6 → ≈8.5 MeV; total gain ≈ 216 MeV for $A=240 \to 2 \times A=120$).
  • Mechanism: liquid-drop model — neutron capture deforms the nucleus into a dumb-bell that splits when Coulomb repulsion beats surface tension.
  • Chain reaction sustains only at or above the critical mass; reactor = controlled, bomb = uncontrolled.
  • Reactor: moderator slows neutrons; control rods (Cd, B) absorb them; coolant carries heat to make steam.

NEET PYQ Snapshot — Nuclear Fission

Real NEET previous-year questions on the fission reaction and the gain in binding energy.

NEET 2021

A nucleus with mass number 240 breaks into two fragments each of mass number 120. The binding energy per nucleon of the unfragmented nucleus is 7.6 MeV while that of the fragments is 8.5 MeV. The total gain in binding energy in the process is

  • (1) 216 MeV
  • (2) 0.9 MeV
  • (3) 9.4 MeV
  • (4) 804 MeV
Answer: (1) 216 MeV

Total gain = (BE of products) − (BE of reactant) = $[120 + 120] \times 8.5 - 240 \times 7.6 = 2040 - 1824 = 216$ MeV. This is exactly the NCERT estimate of the energy released per fission.

NEET 2020

When a uranium isotope $^{235}_{\,92}\mathrm{U}$ is bombarded with a neutron, it generates $^{89}_{\,36}\mathrm{Kr}$, three neutrons and:

  • (1) $^{91}_{\,40}\mathrm{Zr}$
  • (2) $^{101}_{\,36}\mathrm{Kr}$
  • (3) $^{103}_{\,36}\mathrm{Kr}$
  • (4) $^{144}_{\,56}\mathrm{Ba}$
Answer: (4) $^{144}_{\,56}\mathrm{Ba}$

Conserve mass number: $235 + 1 = 89 + A + 3(1) \Rightarrow A = 144$. Conserve atomic number: $92 = 36 + Z \Rightarrow Z = 56$, i.e. barium. So $^{235}_{\,92}\mathrm{U} + n \rightarrow ^{144}_{\,56}\mathrm{Ba} + ^{89}_{\,36}\mathrm{Kr} + 3n$.

NEET 2022

A nucleus of mass number 189 splits into two nuclei having mass numbers 125 and 64. The ratio of the radii of the two daughter nuclei respectively is

  • (1) 4 : 5
  • (2) 5 : 4
  • (3) 25 : 16
  • (4) 1 : 1
Answer: (2) 5 : 4

Since $R = R_0 A^{1/3}$, the ratio of radii of the fission fragments is $\left(\dfrac{125}{64}\right)^{1/3} = \dfrac{5}{4}$, i.e. 5 : 4. This applies the nuclear-radius law directly to fission daughter nuclei.

FAQs — Nuclear Fission

Common NEET doubts on fission energy, the chain reaction and reactor components.

How much energy is released per fission of a uranium-235 nucleus?
About 200 MeV is released per fissioning uranium nucleus. NCERT estimates this from the binding-energy curve: a nucleus of A = 240 with Ebn ≈ 7.6 MeV splitting into two A = 120 fragments with Ebn ≈ 8.5 MeV gives a gain of about 0.9 MeV per nucleon, so the total gain is 240 × 0.9 ≈ 216 MeV. The energy first appears as kinetic energy of the fragments and neutrons, which becomes heat in the surrounding matter.
Why are slow (thermal) neutrons used to cause fission in U-235?
Neutrons are neutral, so they experience no Coulomb barrier and can enter the nucleus even at very low energy. Slow, thermal neutrons (about 0.0253 eV) are readily captured by U-235, exciting and distorting the nucleus until it splits. Fast neutrons released in fission are far less efficient at inducing further fission, which is why a reactor uses a moderator to slow them down.
What is a nuclear chain reaction and what is critical mass?
Each fission of U-235 releases 2 to 3 neutrons (average about 2.5), and these can trigger further fissions, so the number of fission events can multiply rapidly — this is a chain reaction. A self-sustained chain reaction needs a minimum amount of fissile material, the critical mass, so that enough neutrons are captured rather than escaping the surface. Below the critical mass too many neutrons leak out and the reaction dies.
What is the difference between a moderator and a control rod in a reactor?
A moderator (such as ordinary water or heavy water) slows fast fission neutrons down to thermal speeds so they can be captured efficiently by U-235 — it does not stop the reaction. Control rods (made of cadmium or boron) absorb neutrons and are inserted to reduce the neutron population, holding the chain reaction at a steady, controlled level. They serve opposite functions and must not be confused.
Where does the fission energy actually come from?
The energy comes from the increase in binding energy per nucleon when a heavy nucleus splits into intermediate-mass fragments. Heavy nuclei (A > 170) have Ebn below the peak; the fragments lie nearer the peak (A ≈ 56) and are more tightly bound. The released energy equals the difference in total binding energy, which by mass–energy equivalence shows up as the kinetic energy of the products and is equivalent to the small mass defect of the reaction.
How does fission energy compare with chemical (coal) energy?
Nuclear energies are about a million times larger than chemical energies for the same mass. NCERT notes that fission of 1 kg of uranium generates about 10^14 J, whereas burning 1 kg of coal gives only about 10^7 J. This is because nuclear reactions involve MeV-scale energies per event while chemical reactions involve only eV-scale energies.