Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Modern Physics → Radioactivity ↓


Half-life and radioactive decay


Radioactive decay is a natural process by which unstable atomic nuclei lose energy by emitting radiation. This process is fundamental to the concept of radioactivity, first discovered by Henri Becquerel in 1896. Since then, the study of radioactive decay has provided valuable information about the nature of atoms and has become the basis of modern physics.

Understanding radioactive decay

Atoms are made up of protons, neutrons and electrons. The nucleus of an atom contains the protons and neutrons, while electrons orbit the nucleus. In some elements, the nucleus is unstable and can break down in on itself, releasing particles and energy. This phenomenon is known as radioactive decay.

There are several types of radioactive decay, the most common being alpha decay, beta decay, and gamma decay. Each type involves the emission of different particles or energy:

  • Alpha decay: An alpha particle is released from the nucleus, which contains two protons and two neutrons. This reduces the atomic number by 2 and the mass number by 4.
  • Beta decay: A beta particle, which is a high-energy electron or positron, is emitted. This process turns a neutron into a proton or vice versa, changing the atomic number by 1 but leaving the mass number unchanged.
  • Gamma decay: After alpha or beta decay, the nucleus may still be in an excited state. To release this extra energy, the nucleus emits a gamma ray, a form of electromagnetic radiation.

Concept of half-life

One of the most important concepts related to radioactive decay is the half-life. The half-life is the time it takes for half of the radioactive nuclei in a sample to decay. It provides a measure of how quickly or slowly a radioactive substance decays.

For example, imagine you have a sample of a radioactive isotope with a half-life of 10 years. If you start with 100 grams of this isotope, after 10 years, you will have 50 grams of the initial isotope left. After another 10 years (20 years total), you will have 25 grams left, and so on.

The half-life is a fixed property for each radioactive isotope, meaning it does not change over time. This makes it a valuable tool for predicting the behavior of radioactive materials.

Mathematical representation

The amount of radioactive material remaining after a certain period of time can be calculated using the following formula:

N(t) = N0 * (1/2)^(t/T)

Where:

  • N(t) is the amount of substance remaining after time t.
  • N0 is the initial amount of the substance.
  • t is the elapsed time.
  • T is the half-life of the substance.

This formula shows how the amount of a radioactive substance decreases over time through a constant halving. Let's look at a visual example:

Time amount of substance

This graph shows the decay of a radioactive substance over time. Each point on the graph represents a half-life interval, which shows half the amount of the substance remaining.

Practical applications of half-life

The concept of half-life is important in various fields such as archaeology, medicine and environmental science. Let's take a look at some of the applications:

  • Carbon dating: Carbon-14 dating is a technique used to determine the age of ancient artifacts. The ratio of carbon-14 and carbon-12 remains constant in living organisms. When an organism dies, it stops absorbing carbon, and the carbon-14 decays. By measuring the remaining carbon-14, scientists can estimate the age of the artifact. C = C0 * (1/2)^(t/5730), where 5730 years is the half-life of carbon-14.
  • Medical treatment: In nuclear medicine, short-lived isotopes with known half-lives are used to diagnose and treat diseases. For example, iodine-131 with a half-life of 8 days is used to treat thyroid cancer. Doctors can calculate how much radioactive material will remain in the body after a certain time, ensuring the safety and effectiveness of the treatment.
  • Environmental monitoring: Scientists use half-life to understand how long radioactive contaminants will persist in the environment after an event such as a nuclear accident. This helps in planning cleanup and safety measures.

Example calculation

Let's look at some examples to understand the use of the half-life formula:

Example 1

The half-life of a 100 gram sample of isotope X is 5 years. How much of the isotope will remain after 15 years?

N(t) = N0 * (1/2)^(t/T)
N0 = 100g
t = 15 years
T = 5 years
N(15) = 100 * (1/2)^(15/5) = 100 * (1/2)^3 = 100 * 1/8 = 12.5g

Thus, after 15 years the amount of isotope will remain 12.5 grams.

Example 2

How long will it take for a sample of isotope Y to decay to 1/4 of its original amount when its half-life is 10 years?

N(t) = N0 * (1/2)^(t/T)
When N(t) = 1/4 * N0, the equation becomes:
1/4 = (1/2)^(t/10)
To find t, recognize that 1/4 is (1/2)^2, so:
(1/2)^(t/10) = (1/2)^2
Therefore, t/10 = 2 or t = 20 years

It will take 20 years for the sample to decompose to 1/4 of its original volume.

Conclusion

The concepts of radioactive decay and half-life are fundamental to the study of radioactivity in modern physics. Understanding how radioactive substances change over time is important in many scientific and practical applications. Half-life allows scientists and researchers to predict the future behavior of these substances and use their properties in a variety of fields. Through examples, calculations, and visualizations, we can better understand the effects of this natural phenomenon on our world.


Grade 10 → 6.2.2


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Half-life and radioactive decay

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