ATOMS AND NUCLEI

 PHYSICS  |  Class XII

Chapter 12 & 13

ATOMS AND NUCLEI

Atomic Models  ◆  Bohr's Theory  ◆  Nuclear Structure  ◆  Radioactivity  ◆  Nuclear Energy

 

PART A: ATOMS

The story of atomic structure is one of the most fascinating journeys in the history of science. It spans several centuries and involved some of the greatest minds in physics. From the primitive notion of an indivisible 'atom' proposed by the ancient Greeks, to the sophisticated quantum mechanical model of today, our understanding has been revolutionised by a series of landmark experiments and bold theoretical insights.

This part covers the discovery of the nuclear atom through Rutherford's experiment, the explanation of atomic spectra through Bohr's quantised model, and the limitations that ultimately led to quantum mechanics.

 

1. Early Atomic Models

1.1 Thomson's 'Plum Pudding' Model (1904)

After the discovery of the electron in 1897, J.J. Thomson proposed the first modern atomic model. He visualised the atom as a sphere of uniformly distributed positive charge (like a pudding), with electrons embedded inside it like plums in a pudding. This model explained why atoms are electrically neutral — the total negative charge of electrons equals the total positive charge.

Failure: Thomson's model could not explain the results of Rutherford's scattering experiment. It predicted that alpha particles would pass through the atom with very minor deflections — it could not account for the large-angle scattering and back-scattering observed.

 

1.2 Rutherford's Nuclear Model (1911)

Ernest Rutherford, along with Hans Geiger and Ernest Marsden, performed the famous Gold Foil Experiment (1909–1911). They directed a beam of alpha particles (helium nuclei, charge +2e) at a very thin gold foil (about 1000 atoms thick) and observed the scattering pattern using a circular ZnS (zinc sulphide) detector screen that flashed when hit by an alpha particle.

Figure 1: Rutherford's Gold Foil Experiment — Most alphas pass straight through; a few deflect; very few backscatter, revealing a dense, tiny, positive nucleus.

1.3 Observations and Conclusions

◆        Most alpha particles (> 99%) passed straight through the gold foil without any deflection → Most of the atom is empty space.

◆        Some alpha particles were deflected through small angles → The positive charge is concentrated in a tiny central region.

◆        A very few alpha particles (about 1 in 8000) were deflected by very large angles, even bouncing back (180°) → There must be a tiny, extremely dense, positively charged nucleus at the centre.

◆        The nucleus has a radius of order 10⁻¹⁵ m (femtometre or fermi), while the atomic radius is of order 10⁻¹⁰ m (Angstrom) → The nucleus is about 10,000 to 100,000 times smaller than the atom.

 

Distance of Closest Approach

r₀  =  k · (2e)(Ze) / KE  =  k · 2Ze² / ½mv²

 

Impact Parameter

b  =  (Ze²/4πε₀) · cot(θ/2) / KE

 

Failure of Rutherford's Model: According to classical electrodynamics, a charged particle moving in a curved path (like an electron orbiting the nucleus) must continuously emit electromagnetic radiation and lose energy. This would cause the electron to spiral inward and collapse into the nucleus within about 10⁻⁸ seconds. Also, the model could not explain the discrete spectral lines of hydrogen. A new model was urgently needed.

 

2. Bohr's Model of the Hydrogen Atom (1913)

Niels Bohr (1913) proposed a revolutionary new model of the atom by combining Rutherford's nuclear model with Planck's quantum hypothesis and Einstein's photon concept. His model, though later superseded by quantum mechanics, brilliantly explained the hydrogen spectrum and introduced the concept of quantisation of angular momentum.

Figure 2: Bohr's Atomic Model — Electrons orbit in fixed, quantised shells. Photons are emitted or absorbed during transitions between energy levels.

2.1 Bohr's Postulates

Bohr's Three Postulates

Postulate 1 (Stable Orbits): Electrons revolve around the nucleus in certain allowed circular orbits called stationary states or energy levels. While in these orbits, electrons do NOT emit radiation — they are stable. Postulate 2 (Quantisation of Angular Momentum): The angular momentum of an electron in an allowed orbit is an integral multiple of h/2π. That is:  L = mvr = nh/2π, where n = 1, 2, 3, ... is the principal quantum number. Postulate 3 (Quantum Jumps): An electron can make a transition from one stationary state to another. When it jumps from a higher energy level E2 to a lower level E1, it emits a photon of energy E2 − E1 = hν. When it absorbs a photon of the right energy, it jumps to a higher level.

 

2.2 Bohr's Formulae for Hydrogen-like Atoms

Quantisation of Angular Momentum

mvr  =  n h / 2π  =  n ℏ

 

Radius of nth Orbit

rₙ  =  n² a₀ / Z  =  n² × 0.529 Å / Z

 

Speed of Electron in nth Orbit

vₙ  =  Z e² / (2ε₀ h n)  =  2.18 × 10⁶ × (Z/n) m/s

 

Total Energy of nth Level

Eₙ  =  −13.6 × Z² / n²  eV

 

Frequency of Emitted Photon

hν  =  Eₙ₂  −  Eₙ₁  =  13.6 Z² (1/n₁² − 1/n₂²) eV

 

Rydberg Formula (wavenumber)

1/λ  =  R∞ Z² (1/n₁² − 1/n₂²)

 

Key Values: Bohr radius a₀ = 0.529 Å = 0.529 × 10⁻¹⁰ m.  Rydberg constant R∞ = 1.097 × 10⁷ m⁻¹.  Ground state energy of hydrogen = −13.6 eV.  Ionisation energy = +13.6 eV.

 

For hydrogen (Z=1): E₁ = −13.6 eV, E₂ = −3.4 eV, E₃ = −1.51 eV, E₄ = −0.85 eV, E∞ = 0 (ionised). The negative sign indicates that the electron is bound to the nucleus — energy must be supplied to free it.

2.3 Hydrogen Spectral Series

Figure 3: Hydrogen Energy Level Diagram — All spectral series shown. Transitions to n=1 form Lyman (UV); to n=2 form Balmer (visible); to n=3 form Paschen (IR).

Spectral Series	Transition to n=	Spectral Region	First Line (n₂→n₁)	Wavelength Range
Lyman Series	n₁ = 1	Ultraviolet (UV)	n=2 → n=1	91.2 nm – 121.6 nm
Balmer Series	n₁ = 2	Visible Light	n=3 → n=2 (656.3 nm, Red)	364.6 nm – 656.3 nm
Paschen Series	n₁ = 3	Near Infrared (IR)	n=4 → n=3	820.4 nm – 1875 nm
Brackett Series	n₁ = 4	Infrared (IR)	n=5 → n=4	1458 nm – 4051 nm
Pfund Series	n₁ = 5	Far Infrared	n=6 → n=5	2278 nm and above

 

2.4 Limitations of Bohr's Model

◆        Bohr's model works only for hydrogen and hydrogen-like ions (He⁺, Li²⁺). It fails for multi-electron atoms.

◆        It cannot explain the fine structure of spectral lines (splitting due to spin-orbit coupling observed under high resolution).

◆        It cannot explain the relative intensities of different spectral lines.

◆        It does not explain the Zeeman effect (splitting of spectral lines in a magnetic field) or the Stark effect (splitting in an electric field).

◆        It contradicts de Broglie's wave nature of electrons and is inconsistent with Heisenberg's Uncertainty Principle.

 

 

3. de Broglie's Explanation of Bohr's Quantisation

Louis de Broglie (1924) provided a beautiful physical interpretation of Bohr's seemingly arbitrary quantisation condition. He proposed that electrons have wave nature with wavelength λ = h/mv. For an electron to have a stable orbit, the de Broglie wave must form a standing wave around the orbit — meaning the circumference of the orbit must be an integral multiple of the wavelength.

de Broglie Condition for Stable Orbit

2πr  =  nλ  =  n(h/mv)

 

Rearranging: mvr = nh/2π — which is exactly Bohr's quantisation condition! This gave Bohr's postulate a firm physical foundation: electrons exist in orbits where their matter waves form closed, non-destructively-interfering standing waves.

 

 

PART B: NUCLEI

The nucleus is the dense core at the centre of every atom. Despite occupying only about 10⁻¹⁵ of the atomic volume, the nucleus contains about 99.97% of the atom's mass. The study of nuclear structure, radioactivity, and nuclear energy is not only of profound scientific importance but also has life-changing practical applications — from nuclear power plants and medical imaging to cancer radiotherapy and carbon dating.

 

4. Nuclear Structure and Properties

4.1 Constituents of the Nucleus

Proton: Positively charged particle in the nucleus. Charge = +1.6 × 10⁻¹⁹ C. Mass = 1.00728 u = 1.673 × 10⁻²⁷ kg. Atomic number Z = number of protons.

Neutron: Electrically neutral particle in the nucleus. Mass = 1.00866 u = 1.675 × 10⁻²⁷ kg. N = number of neutrons = A − Z.

Nucleon: Common name for protons and neutrons. Mass number A = Z + N = total number of nucleons.

 

Nuclear Notation

ᴬZ X   where A = mass number, Z = atomic number, X = element symbol

 

Nuclear Radius

R  =  R₀ × A^(1/3)   where R₀ = 1.2 × 10⁻¹⁵ m = 1.2 fm

 

Nuclear Density

ρ  ≈  2.3 × 10¹⁷  kg/m³   (constant for all nuclei — independent of A)

 

Nuclear density is the same for all nuclei regardless of size — this is because both the mass and volume of a nucleus are proportional to A. The density of nuclear matter is about 10¹⁴ times the density of water — a teaspoon of nuclear matter would weigh about 100 million tonnes!

Figure 4: Nuclear Structure — Tightly packed protons (red) and neutrons (blue) in the nucleus. Nuclear radius R = R₀A^(1/3), density constant ~2.3×10¹⁷ kg/m³.

4.2 Isotopes, Isobars, and Isotones

Term	Definition	Same	Different	Example
Isotopes	Same element, different mass numbers	Z (atomic number)	A and N	¹H, ²H (deuterium), ³H (tritium)
Isobars	Different elements, same mass number	A (mass number)	Z and N	¹⁴C and ¹⁴N (both A=14)
Isotones	Different elements, same neutron number	N (neutrons)	Z and A	³He and ⁴H (N=1 each; rare)

 

4.3 Atomic Mass Unit (u)

The atomic mass unit (u) is defined as 1/12th of the mass of a carbon-12 (¹²C) atom.

1 atomic mass unit

1 u  =  1.66054 × 10⁻²⁷ kg  =  931.5 MeV/c²

 

This last equivalence (1 u = 931.5 MeV/c²) comes directly from Einstein's mass-energy relation E = mc² and is extremely important in nuclear physics calculations.

 

5. Mass Defect and Binding Energy

One of the most important discoveries in nuclear physics is that the mass of a nucleus is always less than the sum of the masses of its constituent protons and neutrons. This difference is called the Mass Defect (Δm). According to Einstein's mass-energy equivalence (E = mc²), this missing mass has been converted into the energy that holds the nucleus together — called the Binding Energy.

Mass Defect

Δm  =  Z·mₚ  +  N·mₙ  −  M_nucleus

 

Binding Energy

BE  =  Δm · c²  =  Δm × 931.5 MeV  (if Δm in u)

 

Binding Energy per Nucleon

BE/A  =  (Δm · c²) / A   [MeV/nucleon]

 

The binding energy per nucleon (BE/A) is the most useful quantity — it measures the average stability of each nucleon in the nucleus. Plotting BE/A vs mass number A gives the famous Binding Energy Curve:

Key Features of the Binding Energy Curve

* BE/A rises sharply for light nuclei (H, He, Li) then increases more slowly. * BE/A reaches a maximum of about 8.8 MeV/nucleon near iron-56 (Fe-56) — the MOST STABLE nucleus. * Beyond Fe-56, BE/A decreases gradually for heavier nuclei (uranium etc.). * Light nuclei (A < 20) can release energy by FUSION (combining) — they move up the curve toward Fe. * Heavy nuclei (A > 100) can release energy by FISSION (splitting) — they also move toward Fe on the curve. * This curve explains why both nuclear fission and nuclear fusion release enormous amounts of energy.

 

 

6. Nuclear Forces

The nucleus contains protons that are positively charged and therefore repel each other with enormous electrostatic (Coulomb) force. Yet the nucleus is stable — the protons and neutrons are held together. This requires a much stronger attractive force called the Strong Nuclear Force (or simply the Nuclear Force).

Properties of the Nuclear Force

1. Strongest force in nature: The nuclear force is about 100 times stronger than the electromagnetic force and 10³⁸ times stronger than gravity. 2. Short range: The nuclear force is effective only at very short ranges — less than about 1 fm (10⁻¹⁵ m). Beyond 2–3 fm, it rapidly falls to zero. 3. Charge-independent: The nuclear force is the same between p-p, n-n, and p-n pairs (ignoring Coulomb repulsion between protons). 4. Saturating: Each nucleon interacts only with its nearest neighbours — hence nuclear density is constant. 5. Spin-dependent: The nuclear force depends on the relative spin orientations of the interacting nucleons. 6. Non-central: Unlike gravity or Coulomb force, it is not a simple central force.

 

 

7. Radioactivity

Radioactivity is the spontaneous disintegration of unstable atomic nuclei with the emission of radiation. It was discovered by Henri Becquerel in 1896, while studying uranium salts. Marie Curie and Pierre Curie subsequently discovered the radioactive elements polonium and radium, and Marie Curie coined the term 'radioactivity'. Rutherford identified and named the three types of radiation.

Radioactive decay is: Spontaneous (occurs on its own, without external trigger), Random (we cannot predict which specific nucleus will decay next), and Independent of physical/chemical conditions (temperature, pressure, chemical bonding do not affect the decay rate).

 

Figure 5: Three Types of Radioactive Decay — Alpha emits He-4 nucleus; Beta emits electron or positron; Gamma emits high-energy photon. Each has different penetrating power.

7.1 Alpha (α) Decay

In alpha decay, an unstable heavy nucleus emits an alpha particle — which is a helium-4 nucleus consisting of 2 protons and 2 neutrons (²⁴He). Alpha particles have high ionising power but low penetrating power (stopped by a sheet of paper or a few centimetres of air).

Alpha Decay

ᴬ_Z X  →  ᴬ⁻⁴_(Z-2) Y  +  ⁴₂He  +  Q

 

Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He + 4.27 MeV.  The Q-value represents the energy released. For alpha decay to occur spontaneously, Q > 0 (i.e., the mass of parent > mass of daughter + mass of alpha particle).

 

7.2 Beta (β) Decay

Beta decay occurs in two forms. In β⁻ decay, a neutron in the nucleus converts to a proton with the emission of an electron (β⁻ particle) and an anti-neutrino. In β⁺ decay, a proton converts to a neutron with emission of a positron and a neutrino. Beta particles have moderate penetrating power (stopped by a few mm of aluminium).

Beta-minus (β⁻) Decay

ᴬ_Z X  →  ᴬ_(Z+1) Y  +  e⁻  +  ν̄_e

 

Beta-plus (β⁺) Decay

ᴬ_Z X  →  ᴬ_(Z-1) Y  +  e⁺  +  ν_e

 

Neutrino: The existence of the neutrino (ν) was postulated by Pauli in 1930 to explain the continuous energy spectrum of beta particles (conservation of energy and momentum required a third particle). The neutrino has near-zero mass and very weak interaction with matter — making it extremely difficult to detect.

 

7.3 Gamma (γ) Decay

Gamma decay is the emission of high-energy electromagnetic photons (gamma rays, λ ~ 10⁻¹² to 10⁻¹⁰ m) from an excited nucleus. It usually accompanies alpha or beta decay when the daughter nucleus is left in an excited energy state. Gamma rays do not change the mass number or atomic number — they only carry away the excess energy. Gamma rays have the highest penetrating power (require several centimetres of lead or concrete to be stopped).

Gamma Decay

ᴬ_Z X*  →  ᴬ_Z X  +  γ      (X* = excited nucleus)

 

 

7.4 Comparison of α, β, γ Radiations

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium-4 nucleus (⁴₂He)	Electron (β⁻) or Positron (β⁺)	Electromagnetic photon
Charge	+2e	−e or +e	Zero (neutral)
Mass	4 u (≈ 6.64×10⁻²⁷ kg)	9.11×10⁻³¹ kg	Zero (massless)
Speed	~ 5–7% of c	Up to 99% of c	c (speed of light)
Ionising Power	Very High (strongest)	Moderate	Low (weakest)
Penetrating Power	Very Low (paper stops it)	Moderate (Al sheet stops it)	Very High (Pb stops it)
Deflected by E/B	Yes (positively)	Yes (negatively)	No

 

 

8. Radioactive Decay Law

The number of radioactive nuclei decaying per unit time is proportional to the number of radioactive nuclei present at that instant. This is an empirical law discovered by Rutherford and Soddy. Since decay is random and spontaneous, it follows a statistical law.

Radioactive Decay Law

dN/dt  =  −λN   →   N(t)  =  N₀ e^(−λt)

 

Activity

A  =  |dN/dt|  =  λN  =  λN₀ e^(−λt)  =  A₀ e^(−λt)

 

Half-Life (T₁/₂)

T₁/₂  =  0.693 / λ  =  ln2 / λ

 

Mean Life (τ)

τ  =  1 / λ  =  T₁/₂ / ln2  =  T₁/₂ / 0.693

 

Remaining nuclei after n half-lives

N  =  N₀ / 2ⁿ   where n = t / T₁/₂

 

Activity Unit

1 Becquerel (Bq) = 1 decay/second;  1 Curie (Ci) = 3.7 × 10¹⁰ Bq

 

Figure 6: Radioactive Decay Curve — N(t) = N₀ e^(−λt). Every half-life T₁/₂, the number of nuclei (and activity) reduces by exactly half.

At t = T₁/₂: N = N₀/2.  At t = 2T₁/₂: N = N₀/4.  At t = 3T₁/₂: N = N₀/8.  At t = nT₁/₂: N = N₀/2ⁿ. Note: The decay constant λ is the probability of decay per nucleus per unit time. Mean life τ is always greater than half-life T₁/₂ (τ = 1.44 T₁/₂).

Carbon Dating: Radioactive ¹⁴C (T₁/₂ = 5730 years) is continuously produced in the atmosphere by cosmic ray interactions and absorbed by living organisms. After death, ¹⁴C decays without replenishment. By measuring the ratio of ¹⁴C to ¹²C in a sample, the age of organic material up to ~50,000 years can be determined.

 

9. Nuclear Energy

9.1 Nuclear Fission

Nuclear fission is the process in which a heavy nucleus (like ²³⁵U or ²³⁹Pu) absorbs a slow (thermal) neutron and splits into two lighter nuclei of comparable mass, called fission fragments, along with the release of 2–3 fast neutrons and a large amount of energy (~200 MeV per fission event).

Uranium-235 Fission (typical)

²³⁵₉₂U + ¹₀n  →  ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + ~200 MeV

 

The energy released per fission (200 MeV) is about 50 million times more than the energy released in burning one carbon atom (4 eV). This immense energy release is due to the conversion of mass defect into energy via E = mc².

Chain Reaction: The 2–3 neutrons released in each fission event can trigger further fissions in nearby ²³⁵U nuclei, leading to a self-sustaining chain reaction. In a nuclear reactor, this chain reaction is controlled by inserting neutron-absorbing control rods (boron or cadmium) and using a moderator (heavy water or graphite) to slow down fast neutrons. In a nuclear bomb, the chain reaction is uncontrolled and explosive.

 

Critical Mass Condition

Multiplication factor k = 1 (controlled), k > 1 (bomb), k < 1 (subcritical)

 

9.2 Nuclear Fusion

Nuclear fusion is the process in which two light nuclei combine (fuse) to form a heavier nucleus, releasing enormous energy. Fusion powers the Sun and stars and is the most energy-dense process known in nature. Per kilogram of fuel, fusion releases about 4 times more energy than fission, and millions of times more than chemical reactions.

Proton-Proton Chain (in Sun)

4 ¹₁H  →  ⁴₂He + 2e⁺ + 2νₑ + 2γ + 26.7 MeV

 

Deuterium-Tritium Fusion (experimental)

²₁H + ³₁H  →  ⁴₂He + ¹₀n + 17.6 MeV

 

Fusion requires overcoming the enormous electrostatic repulsion between positively charged nuclei. This requires extremely high temperatures (10⁷ to 10⁸ K) and pressures — conditions that exist naturally at the core of stars. On Earth, achieving controlled fusion has been the goal of research for decades (ITER project in France). The main challenges are achieving and sustaining such extreme temperatures (plasma confinement using magnetic fields in Tokamak reactors).

Fission vs Fusion — Comparison

Fission: Heavy nucleus splits into lighter ones.  Fusion: Light nuclei combine to form heavier ones. Fission: Triggered by slow neutrons.  Fusion: Requires extremely high temperature (~10⁸ K). Fission: Releases ~200 MeV per event.  Fusion: Releases ~17.6 MeV per D-T event (but much more per kg of fuel). Fission: Used in nuclear power plants and atomic bombs.  Fusion: Powers stars; being researched for clean energy (ITER). Fission: Produces radioactive waste.  Fusion: Produces mainly helium (safe) — much cleaner. Both reactions release energy because the products have higher binding energy per nucleon than the reactants.

 

 

10. Master Formula Table — Atoms and Nuclei

Formula/Law	Expression	Key Points
Bohr Radius (n=1)	a₀ = 0.529 Å	Radius of hydrogen ground state orbit
nth Orbit Radius	rₙ = n²a₀/Z	Grows as n², shrinks with Z
Energy of nth Level	Eₙ = −13.6Z²/n² eV	Ground state (n=1) = −13.6 eV for H
Photon Frequency	hν = E₂ − E₁	Emitted when electron falls from E₂ to E₁
Rydberg Formula	1/λ = R∞Z²(1/n₁² − 1/n₂²)	R∞ = 1.097 × 10⁷ m⁻¹
Angular Momentum	L = nh/2π = nℏ	Quantised; n = 1,2,3,...
Nuclear Radius	R = R₀A^(1/3)	R₀ = 1.2 fm = 1.2×10⁻¹⁵ m
Mass Defect	Δm = Zmₚ + Nmₙ − M	M = actual nuclear mass
Binding Energy	BE = Δm × 931.5 MeV	Δm in atomic mass units (u)
Decay Law	N = N₀ e^(−λt)	λ = decay constant (s⁻¹)
Half-Life	T₁/₂ = 0.693/λ	Time for N to halve
Mean Life	τ = 1/λ = 1.44 T₁/₂	Average lifetime of a nucleus
Activity	A = λN = A₀ e^(−λt)	Unit: Becquerel (Bq)
n Half-Lives	N = N₀ / 2ⁿ	n = t/T₁/₂
1 atomic mass unit	1 u = 931.5 MeV/c²	From E = mc²
Distance of Approach	r₀ = kZe²/KE × 2	k = 9×10⁹ Nm²C⁻²

 

 

11. Quick Revision — Key Points

Atoms — Must Know

* Thomson model: electrons embedded in positive sphere. Failed to explain Rutherford's scattering. * Rutherford's experiment: most alpha pass straight; few back-scatter → tiny, dense, positive nucleus. * Distance of closest approach: r₀ = k·2Ze²/KE (kinetic energy of alpha particle). * Bohr's 3 postulates: (1) stable orbits, (2) L = nh/2π, (3) photon emitted on de-excitation. * Energy of nth level: Eₙ = −13.6Z²/n² eV. For H(Z=1): E₁=−13.6, E₂=−3.4, E₃=−1.51 eV. * Rydberg formula: 1/λ = R∞Z²(1/n₁² − 1/n₂²). Lyman→n₁=1(UV), Balmer→n₁=2(Visible), Paschen→n₁=3(IR). * de Broglie explains Bohr: 2πr = nλ → mvr = nh/2π (standing matter waves in orbit).

 

Nuclei — Must Know

* Nucleus: Z protons + N neutrons. R = R₀A^(1/3), R₀=1.2 fm. Nuclear density is constant ~2.3×10¹⁷ kg/m³. * 1 u = 1.66×10⁻²⁷ kg = 931.5 MeV/c². Mass defect Δm → Binding Energy BE = Δm × 931.5 MeV. * BE/A max at Fe-56 (~8.8 MeV/nucleon) → most stable. Fusion of light + Fission of heavy → both go toward Fe. * Alpha decay: A decreases by 4, Z decreases by 2. Beta(-): Z increases by 1. Beta(+): Z decreases by 1. Gamma: A,Z unchanged. * Decay law: N = N₀e^(−λt). Half-life T₁/₂ = 0.693/λ. Mean life τ = 1/λ = 1.44 T₁/₂. * After n half-lives: N = N₀/2ⁿ. Activity A = λN (unit: Becquerel; 1 Ci = 3.7×10¹⁰ Bq). * Fission: ²³⁵U + n → Ba + Kr + 3n + 200 MeV. Chain reaction — controlled in reactor, uncontrolled in bomb. * Fusion: 4H → He + 26.7 MeV (in Sun). Requires T ~ 10⁸ K. Cleaner than fission, being developed (ITER).

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