Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Modern Physics → Atomic and Nuclear Physics ↓


Radioactive decay and half-life


Radioactive decay is a fundamental concept in nuclear physics, a branch of modern physics. It is the process by which an unstable atomic nucleus loses energy. It is an essential phenomenon that helps us understand the stability of elements and the changes they undergo over time. Also, we discuss half-life, which is important for measuring how quickly a radioactive substance decays.

Understanding radioactive decay

Basically, radioactive decay is a natural process whereby an unstable nucleus changes into a more stable nucleus, releasing particles or energy in the process. This can happen in several ways, including alpha decay, beta decay, and gamma decay.

Types of radioactive decay

  • Alpha decay: This involves the release of an alpha particle, which consists of two neutrons and two protons. This reduces the atomic number by 2 and the mass number by 4. For example, when uranium-238 undergoes alpha decay, it becomes thorium-234:
    Uranium-238 → Thorium-234 + Alpha particle
    Uranium-238 → Thorium-234 + Alpha particle
  • Beta decay: occurs when a neutron in the nucleus is transformed into a proton or vice versa, with a beta particle (electron or positron) emitted. If a neutron is transformed into a proton, a beta-minus particle (electron) is emitted:
    Neutron → Proton + Beta-minus particle
    Neutron → Proton + Beta-minus particle
  • Gamma decay: This involves the emission of gamma rays, which are high-energy photons. This usually occurs after alpha or beta decay, as the nucleus gives up the extra energy to become more stable without changing the number of protons or neutrons.
    Excited nucleus → Stable nucleus + Gamma rays
    Excited nucleus → Stable nucleus + Gamma rays

Visualization of radioactive decay

Radioactive decay can be understood with a simple visual diagram showing how an unstable nucleus changes over time.

Unstable nucleiinitial stateStable nucleiemission of particles or energy

Understanding half-life

The half-life is the time it takes for half of a sample of radioactive material to decay. This concept is important for evaluating the longevity and activity of radioactive materials.

Calculating the half-life

If you start with a certain number of radioactive atoms, in one half-life half of them will decay. This process continues, and with each half-life, the number of remaining radioactive atoms is halved.

The equation describing this process is:

N(t) = N0 * (1/2)^(t/T)
N(t) = N0 * (1/2)^(t/T)
  • N(t) is the number of radioactive atoms remaining at time t .
  • N0 is the initial number of radioactive atoms.
  • T is the half-life of the substance.

Visual example of half-life

The process of half-life can be made more easy to understand by visualizing it.

100% initial50% first half-life25% second half-lifestate of decayfor a longer period of time

Example of calculating half-life

Suppose we have a radioactive isotope with a half-life of 10 years. If we start with 100 grams of this isotope, we can calculate how much remains after various intervals:

  • 10 years later:
    N(10) = 100 * (1/2)^(10/10) = 50 grams
        N(10) = 100 * (1/2)^(10/10) = 50 grams
  • After 20 years:
    N(20) = 100 * (1/2)^(20/10) = 25 grams
        N(20) = 100 * (1/2)^(20/10) = 25 grams
  • After 30 years:
    N(30) = 100 * (1/2)^(30/10) = 12.5 grams
        N(30) = 100 * (1/2)^(30/10) = 12.5 grams

Importance of radioactive decay and half-life

Radioactive decay and half-life are not just academic concepts; they also have practical applications in various fields such as archaeology, medicine and nuclear energy.

Applications in various fields

  • Archaeology: Carbon dating relies on the principles of half-life to estimate the age of archaeological finds.
  • Medicine: Radioisotopes are used in medical diagnosis and treatment, and their half-lives provide information about dosage and safety.
  • Nuclear energy: Understanding decay is important for the management of nuclear fuel and waste.

Closing thoughts on radioactive decay and half-life

Understanding radioactive decay and half-life provides fundamental information about the nature of the atomic nucleus and the passage of time in nuclear processes. Whether considering the historical time scales involved in carbon dating or the life-saving properties of medical isotopes, these principles illuminate the microscopic and macroscopic worlds alike.


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Radioactive decay and half-life

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