Nuclear Chemistry — Fission, Fusion, and Radioactivity

Nuclear chemistry deals with changes in atomic nuclei — the tiny, dense core that makes up nearly all the mass of an atom. Unlike ordinary chemical reactions (which involve electrons and bonds), nuclear reactions involve protons, neutrons, and the forces that hold the nucleus together.

The energy scales are completely different: nuclear reactions release millions of times more energy per atom than chemical reactions. This is why nuclear power plants can run cities on a few kilograms of uranium, while coal plants need trainloads of fuel for the same output.

Key Terms & Definitions

Radioactivity: The spontaneous emission of particles or energy from unstable nuclei. Discovered by Henri Becquerel (1896); Marie Curie coined the term and isolated radium and polonium.

Nuclide notation: A nuclide is written as $^A_Z X$ , where $A$ = mass number (protons + neutrons), $Z$ = atomic number (protons), $X$ = element symbol.

Isotopes: Atoms of the same element with the same atomic number but different mass numbers (different neutron counts). Example: $^{12}$ C and $^{14}$ C are carbon isotopes.

Binding energy: Energy required to completely separate all nucleons in a nucleus. High binding energy → more stable nucleus. The binding energy per nucleon peaks around iron-56 — the most stable nucleus.

Q-value: Energy released (Q > 0) or absorbed (Q < 0) in a nuclear reaction. $Q = \Delta mc^2$ where $\Delta m$ is the mass defect.

Mass defect: The difference between the sum of masses of free nucleons and the actual nuclear mass. This “missing mass” has been converted to binding energy.

Half-life ( $T_{1/2}$ ): Time for exactly half the nuclei in a sample to decay.

Activity: Rate of decay of a radioactive sample. $A = -dN/dt = \lambda N$ . Unit: Becquerel (Bq) = 1 decay/second. Older unit: Curie (Ci) = $3.7 \times 10^{10}$ Bq.

Types of Radioactive Decay

Alpha (α) Decay

Emission of an alpha particle ( $^4_2\text{He}$ nucleus — 2 protons, 2 neutrons).

^A_Z X \rightarrow ^{A-4}_{Z-2}Y + ^4_2\text{He}

Properties of α particles:

Charge: +2e
Heaviest, slowest type of radiation
Penetrating power: very low (stopped by a sheet of paper, a few cm of air)
Most ionising (highest ionisation density)
Dangerous if ingested/inhaled (polonium-210 poisoning)

Example: $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\text{He}$

Beta (β) Decay

β⁻ decay: Emission of an electron ( $^0_{-1}e$ or $\beta^-$ ) and an antineutrino. A neutron converts to a proton:

n \rightarrow p + e^- + \bar{\nu}_e

^A_Z X \rightarrow ^A_{Z+1}Y + ^0_{-1}e + \bar{\nu}_e

β⁺ decay (positron emission): Emission of a positron ( $^0_{+1}e$ ). A proton converts to a neutron:

^A_Z X \rightarrow ^A_{Z-1}Y + ^0_{+1}e + \nu_e

Properties of β particles:

Charge: –1e (β⁻) or +1e (β⁺)
Intermediate penetrating power (stopped by a few mm of aluminium)
Intermediate ionising power

Gamma (γ) Radiation

Emission of high-energy photons from excited nuclei. No change in atomic number or mass number — only energy state changes.

^A_Z X^* \rightarrow ^A_Z X + \gamma

Properties of γ radiation:

No charge, no mass
Highest penetrating power (requires thick lead or concrete)
Lowest ionising power per unit path length
Often accompanies α and β decay

In nuclear equations, two conservation laws must be satisfied: (1) Conservation of mass number (A): total A on left = total A on right. (2) Conservation of atomic number (Z): total Z on left = total Z on right. These two rules are sufficient to complete any nuclear equation.

Radioactive Decay Laws

Number of nuclei remaining:

N(t) = N_0 e^{-\lambda t} = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}}

Decay constant and half-life:

T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}

Activity:

A = \lambda N = A_0 e^{-\lambda t}

Mean life ( $\tau$ ):

\tau = \frac{1}{\lambda} = \frac{T_{1/2}}{\ln 2} = 1.443 \times T_{1/2}

Nuclear Fission

Fission: A heavy nucleus splits into two or more lighter nuclei upon absorbing a neutron, releasing enormous energy plus additional neutrons.

Classic fission reaction:

^{235}_{92}\text{U} + ^1_0n \rightarrow ^{141}_{56}\text{Ba} + ^{92}_{36}\text{Kr} + 3^1_0n + \text{energy}

Energy released per fission: ~200 MeV ( $3.2 \times 10^{-11}$ J) — compare this to burning carbon: ~4 eV per reaction.

Chain reaction: The neutrons released by one fission event trigger further fissions. If on average >1 neutron per fission causes another fission, the chain reaction is supercritical (exponentially growing — nuclear bomb). If exactly 1 neutron sustains further fissions, it’s critical (steady power — nuclear reactor).

Critical mass: The minimum mass of fissile material required to sustain a chain reaction.

Nuclear reactor components:

Fuel: Enriched uranium ( $^{235}$ U) or plutonium ( $^{239}$ Pu)
Moderator: Slows down fast neutrons to increase fission probability. Heavy water (D₂O) or graphite.
Control rods: Cadmium or boron rods that absorb neutrons, controlling reaction rate. Inserted to slow down or shut down the reactor.
Coolant: Water, heavy water, or CO₂ — carries heat from reactor to steam turbines.

Nuclear Fusion

Fusion: Light nuclei combine to form a heavier nucleus, releasing energy. Requires extreme temperatures (~10⁷–10⁸ K) to overcome electrostatic repulsion between positive nuclei.

Key fusion reaction (Sun and H-bomb):

^2_1\text{H} + ^3_1\text{H} \rightarrow ^4_2\text{He} + ^1_0n + 17.6\text{ MeV}

(Deuterium + Tritium → Helium + neutron)

Why fusion releases more energy per unit mass than fission: Fusion products are on the steeply rising part of the binding energy curve (near helium, binding energy per nucleon increases rapidly). Fission products are closer to iron (binding energy per nucleon is high but the change is smaller).

Fusion vs Fission:

Feature	Fission	Fusion
Reaction type	Heavy nucleus splits	Light nuclei combine
Fuel	$^{235}$ U, $^{239}$ Pu	Deuterium, Tritium
Energy per unit mass	High	Higher (~4× more than fission)
Radioactive waste	Significant	Minimal (helium is inert)
Trigger	Slow neutron	Extreme temperature (~10⁸ K)
Current use	Nuclear power plants	H-bombs, experimental reactors (ITER)

Solved Examples

Example 1 — CBSE Level: Complete the nuclear equation

Q: Fill in the missing particle: $^{214}_{82}\text{Pb} \rightarrow ^{214}_{83}\text{Bi} + ?$

Solution: Conservation of mass number: 214 = 214 + A → A = 0. Conservation of atomic number: 82 = 83 + Z → Z = –1.

The missing particle has A = 0, Z = –1 → beta particle ( $^0_{-1}e$ or $\beta^-$ ).

Example 2 — JEE Main Level: Half-life calculation

Q: A radioactive sample initially has 800 nuclei. If the half-life is 2 hours, how many nuclei remain after 6 hours?

Solution: Number of half-lives = 6/2 = 3.

$N = N_0 \times (1/2)^3 = 800 \times (1/8) = 100$ nuclei remain.

Example 3 — JEE Main Level: Mass defect and binding energy

Q: The atomic mass of $^4_2$ He is 4.0026 u. Mass of proton = 1.0073 u; mass of neutron = 1.0087 u. Find the mass defect and binding energy. (1 u = 931.5 MeV)

Solution:

Mass of 2 protons + 2 neutrons = $2(1.0073) + 2(1.0087) = 2.0146 + 2.0174 = 4.0320$ u

Mass defect: $\Delta m = 4.0320 - 4.0026 = 0.0294$ u

Binding energy: $BE = 0.0294 \times 931.5 = 27.39$ MeV

Binding energy per nucleon: $27.39/4 = 6.85$ MeV/nucleon.

Exam-Specific Tips

CBSE Class 12 Physics: Nuclear reactions completion (using conservation laws), half-life numericals, binding energy calculation, comparison of fission and fusion. These topics contribute 5–8 marks to the board exam.

JEE Main: Numericals on decay constant, activity, mean life, Q-value calculations, and nuclear equation completion. Know the conversion 1 u = 931.5 MeV for mass-energy calculations.

NEET: More conceptual — type of radiation, properties of α/β/γ, half-life meaning, differences between fission and fusion, applications (nuclear power, radiocarbon dating, medical uses of radioisotopes).

Common Mistakes to Avoid

Mistake 1: In β⁻ decay, writing that the atomic number decreases. In β⁻ decay, a neutron converts to a proton — the atomic number increases by 1 (not decreases). Students confuse this because they think “electron is emitted, so we lost negative charge, so Z decreases.” Wrong — the new proton increases Z.

Mistake 2: Using atomic masses instead of nuclear masses in binding energy calculations. When using atomic masses (as given in most tables), you should include the electron masses. Most problems are set up so this cancels out, but be careful in problems that mix nuclear and atomic masses.

Mistake 3: Thinking that nuclear reactions conserve the number of protons and neutrons separately. Only the total number of nucleons (mass number A) is conserved, not protons and neutrons separately. In β decay, a neutron converts to a proton (or vice versa).

Mistake 4: Saying fusion is used in nuclear power plants. Current nuclear power plants use fission (controlled chain reaction of uranium/plutonium). Fusion power is still experimental (ITER, NIF). Fusion is used in hydrogen bombs (thermonuclear weapons).

Practice Questions

Q1. $^{60}_{27}$ Co undergoes β⁻ decay. Write the nuclear equation.

$^{60}_{27}\text{Co} \rightarrow ^{60}_{28}\text{Ni} + ^0_{-1}e + \bar{\nu}_e$ . (Atomic number increases by 1: 27 → 28, which is nickel.)

Q2. If the half-life of $^{131}$ I is 8 days, after how many days will only 12.5% of a sample remain?

12.5% = 1/8 of original = $(1/2)^3$ . So 3 half-lives needed. Time = $3 \times 8 = 24$ days.

Q3. What is the binding energy per nucleon for $^{56}$ Fe? (Given: mass of $^{56}$ Fe = 55.9349 u, proton = 1.0073 u, neutron = 1.0087 u)

$^{56}$ Fe has 26 protons and 30 neutrons. Mass of constituents = $26(1.0073) + 30(1.0087) = 26.1898 + 30.261 = 56.4508$ u. Mass defect = $56.4508 - 55.9349 = 0.5159$ u. BE = $0.5159 \times 931.5 = 480.6$ MeV. BE/nucleon = $480.6/56 = 8.58$ MeV/nucleon (one of the highest values — iron is very stable).

FAQs

Why does uranium fission but not hydrogen?

Fission releases energy for very heavy nuclei (A > ~120) because splitting them moves toward the peak of the binding energy curve (iron, A ≈ 56). For light nuclei like hydrogen, splitting would require energy input, not release it. Fusion releases energy for light nuclei because combining them also moves toward the binding energy peak.

How is radiocarbon dating used?

Living organisms continuously exchange carbon with the environment, maintaining a constant ratio of $^{14}$ C to $^{12}$ C (about 1:10¹²). When an organism dies, it stops incorporating new carbon, and the $^{14}$ C (half-life = 5730 years) decays. By measuring the remaining $^{14}$ C fraction and comparing to the living-organism ratio, scientists can calculate when death occurred (up to ~50,000 years back).

What is the difference between nuclear power and nuclear weapons?

Both use the same fission reactions. The difference is the reaction rate: nuclear reactors maintain a controlled, steady chain reaction (exactly critical — one fission produces one more). Nuclear weapons have a supercritical design where the chain reaction grows exponentially in microseconds (energy released in an uncontrolled explosion).