Lesson Notes By Weeks and Term v3 - Senior Secondary 3
Nucleus
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Nucleus
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Subject: Physics
Class: Senior Secondary 3
Term: 1st Term
Week: 1
Theme: Energy Quantization And Duality Of Matter
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Students should be able:Identify the radiation from radioactive substances using the ir characteristics Solve simple problems in volving half-life of radioactive substances State some uses of radioactive substances Use the concept of nuclear fission and fusion for the development of nuclear energy programme for Nigeria
Radioactivity is the spontaneous disintegration of unstable atomic nuclei, accompanied by the emission of radiation (alpha, beta, or gamma particles/waves) and the release of energy, transforming the unstable nucleus into a more stable one.
Natural Radioactivity: Occurs spontaneously in nature from naturally occurring unstable isotopes (e.g., Uranium-238, Thorium-232, Radium-226). Artificial Radioactivity (Induced Radioactivity): Occurs when stable nuclei are bombarded with high-energy particles (e.g., neutrons, protons, alpha particles) in a laboratory setting, making them unstable and radioactive. This was first discovered by Irene and Frederic Joliot-Curie. The three main types of radiation emitted during radioactive decay are Alpha ($\alpha$) particles, Beta ($\beta$) particles, and Gamma ($\gamma$) rays. | Characteristic | Alpha ($\alpha$) Particle | Beta ($\beta$) Particle (electron) | Gamma ($\gamma$) Ray | | :------------------ | :-------------------------------------------------------------- | :--------------------------------------------------------------- | :---------------------------------------------------------- | | Nature | Helium nucleus ($^4_2$He) | Fast-moving electron ($^0_{-1}e$) or positron ($^0_{+1}e$) | Electromagnetic wave (high-energy photon) | | Charge | +2e (positive) | -1e (negative for electron, +1e for positron) | 0 (neutral) | | Mass | Relatively large (approx. 4 amu) | Very small (approx. 1/1836 amu) | Zero (massless) | | Penetrating Power | Very low (stopped by paper, a few cm of air, skin) | Moderate (stopped by a few mm of aluminium) | Very high (reduced by several cm of lead or metres of concrete) | | Ionizing Power | Very high (causes significant ionization in matter due to large charge and mass) | Moderate (less than alpha, more than gamma) | Very low (causes minimal ionization) | | Deflection in E-field | Deflected towards the negative plate | Deflected strongly towards the positive plate (for electrons) | No deflection | | Deflection in B-field | Deflected according to Fleming's Left-Hand Rule (less than beta due to larger mass) | Deflected strongly according to Fleming's Left-Hand Rule (more than alpha) | No deflection | | Speed | ~0.1c (10% speed of light) | ~0.9c (90% speed of light) | c (speed of light) | | Biological Effect | Highly damaging if ingested/inhaled | Significant internal and external damage | Significant internal and external damage | Radioactive decay is a random and spontaneous process. The rate of decay is proportional to the number of undecayed nuclei present. Decay Constant ($\lambda$): The probability per unit time that a nucleus will decay. Its unit is s−
1. Half-Life ($T_{1/2}$): The time it takes for half of the initial number of radioactive nuclei in a sample to decay. It is a characteristic constant for each radioactive isotope. Relationship between Half-Life and Decay Constant: $T_{1/2} = \frac{\ln(2)}{\lambda} = \frac{0.693}{\lambda}$ Mathematical Formulas for Radioactive Decay: Number of remaining nuclei/mass after 'n' half-lives: $N_t = N_0 \left(\frac{1}{2}\right)^n$ Where: $N_t$ = number of radioactive nuclei (or mass) remaining after time 't' $N_0$ = initial number of radioactive nuclei (or mass) $n$ = number of half-lives that have passed ($n = \frac{t}{T_{1/2}}$) $t$ = total time elapsed $T_{1/2}$ = half-life Exponential Decay Formula: $N_t = N_0 e^{-\lambda t}$ Where 'e' is the base of the natural logarithm (approximately 2.718).
Activity (A): The rate of decay of a radioactive sample. $A = \lambda N$ The unit of activity is Becquerel (Bq), where 1 Bq = 1 decay per second. Another unit is Curie (Ci), where 1 Ci = $3.7 \times 10^{10}$ Bq. Radioactive isotopes (radioisotopes) have numerous beneficial applications across various sectors in Nigeria and globally: Medicine: Diagnosis: Tracers like Iodine-131 (thyroid function), Technetium-99m (bone scans, imaging organs). These help identify abnormalities without invasive surgery.
Therapy: Cobalt-60 or I-131 (for thyroid cancer) used in radiotherapy to destroy cancerous cells. Radium-226 in brachytherapy.
Sterilization: Gamma radiation (from Cobalt-60) sterilizes medical instruments, bandages, and drugs, ensuring they are germ-free for use in hospitals.
Industry: Gauging and Control: Beta or gamma sources are used to measure the thickness of materials (e.g., paper, plastic sheets, metal foils) and liquid levels in containers.
Tracing Leaks: Radioisotopes mixed with fluids can detect leaks in underground pipelines (water, oil, gas) by monitoring radioactivity changes along the pipe.
Non-Destructive Testing: Gamma rays (from Iridium-192 or Cobalt-60) are used to detect flaws (cracks, voids) in metal castings, welds, and structures without damaging them.
Smoke Detectors: Americium-241 is used in smoke detectors, ionizing air to detect smoke particles.
Agriculture: Pest Control: Sterilization of male insects using radiation (sterile insect technique) to reduce insect populations, e.g., tsetse flies in parts of Nigeria.
Crop Improvement: Inducing mutations in seeds using radiation to develop new crop varieties with improved yields, disease resistance, or faster maturity.
Food Preservation: Gamma irradiation is used to kill bacteria, molds, and pests in food products (e.g., spices, grains, fruits), extending shelf life and reducing spoilage. This is relevant for Nigeria's food security efforts.
Fertilizer Uptake Studies: Tracers (e.g., Phosphorus-32) help researchers study how plants absorb fertilizers, optimizing application for better yields.
Dating: Carbon-14 Dating: Used to determine the age of archaeological artifacts, fossils, and ancient organic materials (up to ~60,000 years old). This is crucial for understanding Nigeria's rich history and pre-history.
Uranium-Lead Dating: Used for dating geological formations and very old rocks, providing insights into Earth's history.
Example 1 (Half-life calculation): A radioactive isotope has a half-life of 10 days. If an initial sample contains 200g of the isotope, how much will remain after 30 days?
Solution: Given: $N_0 = 200g$, $T_{1/2} = 10 \text{ days}$, $t = 30 \text{ days}$ Number of half-lives, $n = \frac{t}{T_{1/2}} = \frac{30 \text{ days}}{10 \text{ days}} = 3$ Using the formula $N_t = N_0 \left(\frac{1}{2}\right)^n$: $N_t = 200g \left(\frac{1}{2}\right)^3$ $N_t = 200g \left(\frac{1}{8}\right)$ $N_t = 25g$ Therefore, 25g of the isotope will remain after 30 days.
Example 2 (Decay constant and activity): A radioactive sample contains $6.0 \times 10^{23}$ atoms and has a half-life of 2 years. (a) Calculate its decay constant. (b) Calculate its initial activity.
Solution: Given: $N_0 = 6.0 \times 10^{23}$ atoms, $T_{1/2} = 2 \text{ years}$ (a) Decay Constant ($\lambda$): First, convert half-life to seconds (or use years, but activity is usually in Bq/s). Let's use years for $\lambda$, then convert for activity. $T_{1/2} = 2 \text{ years} = 2 \times 365.25 \times 24 \times 60 \times 60 \text{ seconds} = 6.307 \times 10^7 \text{ s}$ $\lambda = \frac{0.693}{T_{1/2}}$ If $T_{1/2}$ is in years: $\lambda = \frac{0.693}{2 \text{ years}} = 0.3465 \text{ years}^{-1}$ If $T_{1/2}$ is in seconds: $\lambda = \frac{0.693}{6.307 \times 10^7 \text{ s}} \approx 1.099 \times 10^{-8} \text{ s}^{-1}$ (b)
Initial Activity (A0): $A_0 = \lambda N_0$ Using $\lambda$ in s−1: $A_0 = (1.099 \times 10^{-8} \text{ s}^{-1}) \times (6.0 \times 10^{23} \text{ atoms})$ $A_0 \approx 6.594 \times 10^{15} \text{ Bq}$ Example 3 (Time elapsed): A sample of a radioactive material initially contains $8.0 \times 10^{10}$ atoms. After 60 minutes, the number of atoms reduces to $1.0 \times 10^{10}$. What is the half-life of the material?
Solution: Given: $N_0 = 8.0 \times 10^{10}$ atoms, $N_t = 1.0 \times 10^{10}$ atoms, $t = 60 \text{ minutes}$ Using $N_t = N_0 \left(\frac{1}{2}\right)^n$: $1.0 \times 10^{10} = 8.0 \times 10^{10} \left(\frac{1}{2}\right)^n$ $\frac{1.0 \times 10^{10}}{8.0 \times 10^{10}} = \left(\frac{1}{2}\right)^n$ $\frac{1}{8} = \left(\frac{1}{2}\right)^n$ Since $\frac{1}{8} = \left(\frac{1}{2}\right)^3$, then $n = 3$. We know $n = \frac{t}{T_{1/2}}$: $3 = \frac{60 \text{ minutes}}{T_{1/2}}$ $T_{1/2} = \frac{60 \text{ minutes}}{3} = 20 \text{ minutes}$ The half-life of the material is 20 minutes.
Electricity Generation in Nigeria (Nuclear Fission): Nigeria faces significant challenges in electricity supply. The knowledge of nuclear fission is directly applicable to understanding how nuclear power plants could provide a stable, large-scale, and low-carbon electricity source. The Nigeria Atomic Energy Commission (NAEC) has plans for building nuclear power plants (e.g., the proposed plant in Akwa Ibom State). This topic allows students to critically evaluate the benefits (reliable power, reduced reliance on fossil fuels) and risks (safety, waste management, high costs) associated with such a national energy strategy. Healthcare and Medical Diagnostics/Treatment: Radioactive isotopes are routinely used in Nigerian hospitals for diagnostic imaging (e.g., detecting bone fractures or organ malfunctions using Technetium-99m) and cancer therapy (e.g., using Cobalt-60 or Iodine-131 in oncology centers across major cities like Lagos, Abuja, Ibadan). Students can relate this to improved healthcare outcomes, early disease detection, and advanced medical treatments available locally. Agricultural Advancement and Food Security: Radioisotopes are crucial tools in agricultural research carried out by institutes like the International Institute of Tropical Agriculture (IITA) in Ibadan or the National Cereals Research Institute. They are used to improve crop varieties (e.g., developing drought-resistant or high-yielding strains through mutation breeding), control pests (e.g., sterile insect technique to combat tsetse flies affecting livestock), and extend the shelf life of food products through irradiation, thereby contributing to Nigeria's food security and economic development.