Lesson Notes By Weeks and Term v3 - Senior Secondary 3
Energy quantization
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Energy quantization
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
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 to:- explain the concept of energy quantization. Use the photon concept to explain the effect of electrons in the photoelectric effect Describe x-ray production and state its characteristics, properties and uses.
Introduction: In classical physics, energy was thought to be continuous, meaning it could take any value.
However, experiments like blackbody radiation showed discrepancies. In 1900, Max Planck proposed a radical idea: energy is not continuous but is emitted or absorbed in discrete packets, or "quanta." Definition: Energy Quantization is the concept that energy can only exist in discrete amounts, rather than in a continuous range. Each discrete amount is called a "quantum" (plural: quanta).
Planck's Hypothesis: Planck proposed that the energy (E) of a quantum of electromagnetic radiation is directly proportional to its frequency (f).
The formula is given by: E = hf Where: E is the energy of a quantum (in Joules, J) h is Planck's constant (a fundamental physical constant) f is the frequency of the radiation (in Hertz, Hz)
Planck's Constant (h): The accepted value for Planck's constant is approximately 6.63 × 10−34 J s (Joule-seconds).
Relationship with Wavelength: Since the speed of light (c) is related to frequency (f) and wavelength (λ) by the equation c = fλ, we can also express the energy of a quantum in terms of wavelength: f = c / λ Substituting this into Planck's equation: E = hc / λ Photon: A photon is a quantum of electromagnetic radiation (light). It is a particle with zero rest mass and carries a discrete amount of energy determined by its frequency. Example 2.1: Calculate the energy of a photon of green light with a frequency of 6.00 × 1014 Hz. (Given h = 6.63 × 10−34 J s)
Solution: Using the formula E = hf: E = (6.63 × 10−34 J s) × (6.00 × 1014 Hz) E = 3.978 × 10−19 J The energy of the green light photon is 3.98 × 10−19 J (to 3 significant figures).
Definition: The photoelectric effect is the phenomenon in which electrons are emitted from the surface of a metal when light of a sufficiently high frequency (or short wavelength) shines on it. The emitted electrons are called photoelectrons.
Limitations of Classical Wave Theory: Classical wave theory predicted that: The energy of emitted electrons should depend on the intensity of light. Photoelectric emission should occur for any frequency of light, provided the intensity is high enough. There should be a time delay between the light striking the surface and the emission of electrons, for energy to accumulate.
However, experiments showed: The maximum kinetic energy of photoelectrons depends only on the frequency of light, not its intensity. There is a minimum frequency (threshold frequency) below which no electrons are emitted, regardless of light intensity. Electron emission is instantaneous, occurring almost immediately if the threshold frequency is met.
Einstein's Explanation (Photon Theory): Albert Einstein explained the photoelectric effect in 1905 by extending Planck's idea of quantization to light itself. He proposed that light consists of discrete energy packets called photons. When a photon strikes a metal surface, it transfers all its energy (E = hf) to a single electron. If the photon's energy is greater than the minimum energy required to liberate the electron from the metal surface, the electron is emitted. Any excess energy the electron receives becomes its kinetic energy.
Key Terms and Concepts: Work Function (Φ or W_o): The minimum amount of energy required to remove an electron from the surface of a particular metal. It is a characteristic property of the metal. If a photon's energy is less than the work function, no electron will be emitted. The work function can be expressed in Joules (J) or electron volts (eV). 1 eV = 1.602 × 10−19
J. Threshold Frequency (f_o): The minimum frequency of incident light required to cause photoelectric emission from a particular metal surface. At this frequency, the photon energy is just equal to the work function, and the emitted electrons have zero kinetic energy.
Relationship: Φ = hf_o Threshold Wavelength (λ_o): The maximum wavelength of incident light that can cause photoelectric emission. Wavelength is inversely proportional to frequency, so a maximum wavelength corresponds to a minimum frequency.
Relationship: Φ = hc / λ_o Maximum Kinetic Energy (K_max): The maximum kinetic energy of the emitted photoelectrons. This corresponds to electrons ejected from the very surface of the metal without losing energy to collisions inside the metal.
Einstein's Photoelectric Equation: When a photon of energy hf strikes a metal surface: A part of its energy, Φ, is used to overcome the binding forces and eject the electron (work function). The remaining energy is converted into the kinetic energy (K_max) of the emitted electron.
Therefore: hf = Φ + K_max Rearranging to find K_max: K_max = hf - Φ Substituting Φ = hf_o: K_max = hf - hf_o = h(f - f_o) Example 2.2: The work function of potassium is 2.29 eV. (a) Calculate the threshold frequency for potassium. (b) If light of frequency 7.00 × 1014 Hz falls on potassium, calculate the maximum kinetic energy of the emitted photoelectrons in Joules. (Given h = 6.63 × 10−34 J s, 1 eV = 1.60 × 10−19 J)
Solution: First, convert the work function from eV to Joules: Φ = 2.29 eV × (1.60 × 10−19 J/eV) = 3.664 × 10−19 J (a) Calculate the threshold frequency (f_o): Using Φ = hf_o f_o = Φ / h f_o = (3.664 × 10−19 J) / (6.63 × 10−34 J s) f_o = 5.526 × 1014 Hz The threshold frequency is 5.53 × 1014 Hz (to 3 significant figures). (b) Calculate the maximum kinetic energy (K_max): Given incident frequency (f) = 7.00 × 1014 Hz Using K_max = hf - Φ: K_max = (6.63 × 10−34 J s × 7.00 × 1014 Hz) - 3.664 × 10−19 J K_max = 4.641 × 10−19 J - 3.664 × 10−19 J K_max = 0.977 × 10−19 J K_max = 9.77 × 10−20 J (to 3 significant figures). X-rays for lung conditions).
Mammography: Screening for breast cancer.
Computed Tomography (CT) scans: Detailed 3D images of organs and tissues.
2. Medical Therapy: Radiotherapy: High-energy X-rays are used to destroy cancerous cells and shrink tumors.
3. Industrial Applications: Non-destructive Testing (NDT): Inspecting the internal structure of materials, detecting flaws, cracks, or air bubbles in castings, welds, and manufactured parts without damaging them. Used in aerospace, construction, and manufacturing.
Security Screening: Used in airport baggage scanners and other security checkpoints to detect concealed objects, weapons, or contraband.
Crystallography: X-ray Diffraction (XRD) is used to determine the atomic and molecular structure of crystals, crucial in material science and chemistry.
4. Art and Archaeology: Examining the internal structure of paintings or artifacts to reveal underlying layers, forgeries, or internal damage.
Definition: X-rays are a form of electromagnetic radiation with extremely short wavelengths (typically 0.01 to 10 nanometers) and high frequencies, ranging from approximately 3 × 1016 Hz to 3 × 1019 Hz. This places them between ultraviolet light and gamma rays in the electromagnetic spectrum. Production of X-rays (Coolidge Tube / X-ray Tube): X-rays are produced when fast-moving electrons collide with a metal target. The device used for this is typically called a Coolidge tube or an X-ray tube.
Components of an X-ray tube:
1. Evacuated Glass Tube: Contains a vacuum to prevent electrons from colliding with air molecules.
2. Cathode: A heated filament (usually tungsten) which, when heated by a low voltage current, undergoes thermionic emission, releasing electrons. This part is negatively charged.
3. Anode (Target): A heavy metal block (often tungsten or molybdenum due to their high melting points and atomic numbers) set at a high positive potential relative to the cathode. This part is positively charged. It is usually angled and often rotates to dissipate heat.
4. High Voltage Supply: Provides a large potential difference (typically 20 kV to 150 kV) between the cathode and anode, accelerating the electrons.
5. Cooling System: Often present to cool the anode, as a lot of heat is generated during X-ray production.
Process of X-ray Production:
1. Electron Emission: The filament (cathode) is heated to a high temperature, causing electrons to be emitted via thermionic emission.
2. Electron Acceleration: A high potential difference is applied between the cathode and anode, accelerating these emitted electrons towards the anode at very high speeds.
3. Collision and X-ray Generation: When these high-speed electrons strike the metal target (anode), they are rapidly decelerated. This deceleration causes them to lose kinetic energy, which is converted into two main types of X-rays: Bremsstrahlung (Braking Radiation): This occurs when the incoming electrons are decelerated by the electric fields of the target nuclei. The electrons lose varying amounts of energy, resulting in a continuous spectrum of X-ray wavelengths. Most X-rays produced are of this type.
Characteristic X-rays: If an incident electron has enough energy to knock an inner-shell electron out of a target atom, an outer-shell electron drops into the vacant inner shell to fill the gap. When this happens, a photon of specific energy (and thus specific wavelength) is emitted. These X-rays are "characteristic" of the target material.
Characteristics and Properties of X-rays:
1. Electromagnetic Nature: They are electromagnetic waves, similar to light, radio waves, and gamma rays.
2. High Penetrating Power: They can pass through many materials that absorb visible light, such as soft tissues of the body. Their penetration depth depends on their energy (shorter wavelength = higher energy = greater penetration).
3. No Electric or Magnetic Deflection: Being neutral (no charge), they are not deflected by electric or magnetic fields.
4. Travel at Speed of Light: In a vacuum, they travel at the speed of light (c = 3 × 108 m/s).
5. Affect Photographic Plates: They can expose photographic films, which is the basis for conventional X-ray imaging.
6. Ionization: They can ionize gases (remove electrons from atoms), making the gas electrically conductive.
7. Fluorescence: They can cause certain substances to glow (fluoresce), which is used in fluoroscopy and in detecting X-rays.
8. Harmful to Living Cells: X-rays are a form of ionizing radiation and can damage living cells, leading to mutations or cell death. This necessitates careful use and shielding.
9. Invisible: They are invisible to the human eye.
Uses of X-rays:
1. Medical Diagnostics: Radiography: Imaging bones (e.g., fractures), detecting dental problems (tooth decay), imaging internal organs (e.g., chest X-rays for lung conditions).
Mammography: Screening for breast cancer.
Computed Tomography (CT) scans: Detailed 3D images of organs and tissues.
2. Medical Therapy: Radiotherapy: High-energy X-rays are used to destroy cancerous cells and shrink tumors.
3. Industrial Applications: Non-destructive Testing (NDT): Inspecting the internal structure of materials, detecting flaws, cracks, or air bubbles in castings, welds, and manufactured parts without damaging them. Used in aerospace, construction, and manufacturing.
Security Screening: Used in airport baggage scanners and other security checkpoints to detect concealed objects, weapons, or contraband. *
Solar Power Generation (Photoelectric Effect): The photoelectric effect is the fundamental principle behind solar cells (photovoltaic cells). These cells convert sunlight directly into electrical energy. In Nigeria, solar panels are increasingly common, providing electricity to homes, businesses, and rural communities, especially where grid electricity is unreliable or unavailable. Students can appreciate how the energy of photons striking semiconductor materials like silicon (exhibiting the photoelectric effect) drives sustainable energy solutions across the country, from streetlights in Lagos to powering boreholes in remote villages. Medical Diagnostics in Nigerian Hospitals (X-rays): X-ray technology is indispensable in Nigerian healthcare. Hospitals, clinics, and diagnostic centers across the country use X-rays daily to diagnose bone fractures, dental issues, chest infections (like pneumonia or tuberculosis), and even detect foreign objects in the body. Students can connect their learning to real-world scenarios where X-ray scans provide crucial information for doctors, contributing to effective patient care and public health in Nigeria. Security and Industrial Inspection (X-rays): X-rays are vital for security screening at Nigerian airports (e.g., Murtala Muhammed International Airport in Lagos, Nnamdi Azikiwe International Airport in Abuja) and seaports, where baggage and cargo are scanned to detect contraband, weapons, or explosives. Industrially, X-rays are used in non-destructive testing (NDT) to inspect the quality of welds in pipelines (e.g., oil and gas pipelines in the Niger Delta), check for flaws in manufactured components, or assess the structural integrity of materials used in construction. This ensures safety and quality in critical national infrastructure.