Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Nuclear and particle physics ↓


Radioactivity


Radioactivity is a fascinating and important aspect of nuclear and particle physics. It refers to the spontaneous emission of particles or electromagnetic radiation from the nucleus of an unstable atom. This radioactive decay is a natural process that results in one element changing into another. Understanding radioactivity provides information about the forces that hold atomic nuclei together and has important implications in a variety of fields such as energy production, medicine, and archaeology.

The concept of the atom

Before diving into radioactivity, it is necessary to understand the structure of the atom. An atom consists of three main particles:

  • Proton: Positively charged particle located in the nucleus.
  • Neutrons: Neutral particles that are also found in the nucleus.
  • Electrons: Negatively charged particles that orbit the nucleus at different energy levels.

The nucleus, which contains both protons and neutrons, is held together by the strong nuclear force, which is strong enough to overcome the repulsive electrostatic force between the positively charged protons.

Types of radioactive decay

There are three main types of radioactive decay, each involving different particles and changes to the nucleus:

1. Alpha decay (α-decay)

In alpha decay, the nucleus emits an alpha particle, which consists of two protons and two neutrons (similar to a helium nucleus). This process decreases the atomic number by 2 and the mass number by 4.

^A_ZX -> ^{A-4}_{Z-2}Y + ^4_2He

Example: Uranium-238 undergoes alpha decay to become thorium-234.

^{238}_{92}U -> ^{234}_{90}Th + ^4_2He

2. Beta decay (β-decay)

Beta decay is a process in which the nucleus emits a beta particle. There are two types of beta decay:

  • β - decay: a neutron in the nucleus is converted into a proton, and a beta negative particle (electron) and an antineutrino are emitted. 
    ^A_ZX -> ^A_{Z+1}Y + e^- + bar{ν}_e

    Example: Disintegration of carbon-14 into nitrogen-14.

    ^{14}_{6}C -> ^{14}_{7}N + e^- + bar{ν}_e
  • β + decay: A proton decays into a neutron, releasing a beta-positive particle (positron) and a neutrino. 
    ^A_ZX -> ^A_{Z-1}Y + e^+ + ν_e

    Example: Disintegration of sodium-22 into neon-22.

    ^{22}_{11}Na -> ^{22}_{10}Ne + e^+ + ν_e

3. Gamma decay (γ-decay)

Gamma decay involves the emission of gamma rays, which are high-energy photons. This decay process usually occurs after alpha or beta decay, as the daughter nucleus transforms into a lower energy state.

^A_ZX^* -> ^A_ZX + γ

Gamma decay does not change the atomic number or mass number, but instead brings the nucleus to a lower energy equilibrium state.

Half-life and radioactive decay law

One of the fundamental concepts in radioactivity is the half-life of a radioactive element. The half-life is the time it takes for half of the radioactive nuclei in a sample to decay.

The decay rate is described by the exponential decay law:

N(t) = N_0 * e^{-λt}

Where:

  • N(t) is the number of undisintegrated nuclei at time t.
  • N_0 is the initial number of nuclei.
  • λ is the decay constant.
  • t is the elapsed time.

The relation between the half-life T_{1/2} and the decay constant is given by:

T_{1/2} = frac{ln(2)}{λ}

This equation shows that the half-life is inversely proportional to the decay constant.

Applications of radioactivity

Radioactivity has many applications in various fields:

1. Medicine

Radioactive isotopes are used in medical diagnosis and treatment. For example, iodine-131 is used in the treatment of thyroid disorders, and technetium-99m is used in advanced imaging techniques.

2. Energy production

Nuclear power plants use the process of controlled nuclear fission, often using uranium-235, to produce energy. This process is a direct application of radioactive decay principles.

3. Archaeology

Radiocarbon dating uses the radioactive decay of carbon-14 to determine the age of organic material. This method is essential in determining the age of ancient artifacts and fossils.

Visualization of radioactive decay

Let's visually represent a simplified model of radioactive decay using shapes and arrows:

Parent nucleus Alpha Particles Daughter nuclei

This simplified diagram shows how during alpha decay the parent nucleus reacts to form a daughter nucleus and an alpha particle.

Safety concerns and radioactive waste

Radioactivity sometimes releases energy for a short time, which can pose potential health risks. Handling radioactive materials requires following strict safety protocols to prevent exposure and contamination.

Radioactive waste is another serious concern, especially in nuclear power production. Safe storage and disposal of this waste is essential to protect the environment and public health. Scientists are constantly working on better ways to manage and reduce the hazards associated with radioactive waste.

Conclusion

Radioactivity plays a vital role in understanding the subatomic world and has many practical applications that benefit society. Harnessing the power of radioactive decay safely and effectively remains a dynamic area of research in nuclear and particle physics, presenting both challenges and opportunities for advances in technology and science.


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Radioactivity

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