Atomic Physics

This section explores the fascinating world of X-rays and nuclear energy, highlighting both theoretical and practical aspects. You will examine how X-rays are produced, their types (hard and soft), and their applications in medicine, industry, and security. The section also covers calculations involving energy, frequency, and wavelength of X-rays. Additionally, it introduces the principles of nuclear reactions, distinguishing between fission and fusion, and showing how nuclear energy is harnessed using reactors. Real-world implications, safety precautions, and biological effects of radiation are emphasised to connect concepts with everyday relevance.

KEY IDEAS

· X-rays are used in medical imaging (e.g., CT scans, mammography), industrial inspection (e.g., weld testing), and security scanning (e.g., airport luggage checks).

· X-rays are generated in an X-ray tube when fast-moving electrons strike a metal target, producing radiation with high energy, no mass or charge, and deep penetration power.

· X-rays are classified into hard and soft types based on energy and wavelength; this classification determines their penetrating ability and appropriate applications.

· Nuclear energy is released when mass is converted to energy in fission or fusion reactions, described by Einstein’s equation E=mc².

· Fission splits heavy nuclei (e.g., Uranium-235), while fusion joins light nuclei (e.g., Hydrogen isotopes), both processes influenced by nuclear binding energy and mass defect.

· Nuclear reactors control fission using fuel rods, moderators, and control rods to produce electricity, with strong safety protocols to manage radiation hazards and waste.

X-Rays Have you ever been to a hospital or a clinic where you needed to get an x-ray?

Maybe for a broken bone or a dental check-up? If so, you might have seen the x-ray machine or the room where the x-rays are taken.

Figure 4.1: A modern panoramic X-ray machine captures a detailed dental scan of a man X-rays are a type of electromagnetic wave; a special kind of non-visible light that doctors use to see inside your body without having to do surgery. They can help show broken bones, cavities, or other problems inside you.

You might wonder: how do these x-rays get made? Well, inside that x-ray machine is a device that shoots out very high-energy rays called x-rays. These rays come from speeding up tiny particles called electrons and stopping them suddenly inside what’s called an x-ray tube. So, by thinking about your experience visiting an x-ray unit, you’re already connected to the fascinating world of how these powerful rays are produced and used to help doctors look inside the body safely and quickly.

Nature and Production of X-rays

X-rays are a form of electromagnetic radiation. The spectrum of electromagnetic waves in order of increasing energy are radio waves, microwaves, infrared, visible light, ultraviolet light, x-rays and gamma waves. The key difference between all of these types of wave lies in their wavelength and energy. X-rays have very short wavelengths (generally ranging from 0.01 to 10 nanometres) with very high frequency and energy. This high energy is what allows them to penetrate materials including human body that visible light cannot.

Properties of X-rays

X-rays possess unique properties that make them incredibly useful

1. High Penetrating Power: This is their most well-known property. Due to their short wavelength and high energy, x-rays can pass through many materials that absorb or reflect visible light. The degree of penetration depends on the material’s density and atomic number. Denser materials with higher atomic numbers (like bone) absorb more X-rays, while less dense materials (like soft tissue) absorb less.

2. Ionising Radiation: X-rays have enough energy to remove electrons from atoms, a process called ionisation. This property is both useful (in medical imaging and treatment) and potentially harmful (requiring protective measures).

3. Travel in Straight Lines: Like all electromagnetic radiation, X-rays travel in straight lines unless they interact with matter. This property is crucial for creating clear images.

4. Invisible to the Human Eye: We cannot see X-rays directly. Special detectors or photographic films are needed to visualise them.

5. No Electric Charge or Mass: X-rays are photons, fundamental particles of light, and therefore have no charge or rest mass. This means they are not affected by electric or magnetic fields.

6. Produce Fluorescence: When X-rays strike certain materials (like those containing phosphor), they can cause these materials to emit visible light, a phenomenon called fluorescence. This property is utilised in intensifying screens in radiography.

7. Affect Photographic Film: X-rays can expose photographic film, leading to a visible image after processing. This was the original method of X-ray imaging.

Production of X-rays

How are these powerful rays generated? The production of x-rays relies on the principle of accelerating high-energy electrons and then suddenly stopping them.

This process commonly occurs within a specialised device called an x-ray tube.

The X-ray Tube

An X-ray tube is essentially a vacuum tube containing two main electrodes:

1. Cathode (Negative Electrode): This is typically a heated filament (like in an old light bulb). When heated, the filament undergoes thermionic emission, releasing a cloud of electrons.

2. Anode (Positive Electrode): This is a metal target, often made of tungsten or molybdenum, which has a high atomic number and high melting point.

Steps in X-ray Production

1. Electron Emission

The filament in the cathode is heated, causing electrons to “boil off” its surface.

2. Acceleration A high voltage (potential difference) is applied between the cathode and the anode. This voltage creates a strong electric field that accelerates the emitted electrons towards the positively charged anode with tremendous speed.

3. Collision and X-ray Generation

When these high-speed electrons strike the anode target, their kinetic energy is rapidly converted into other forms of energy. A small fraction (less than 1%) of this energy is converted into x-rays, while the vast majority is converted into heat (which is why x-ray tubes require cooling systems).

There are two primary mechanisms for x-ray production when electrons hit the target:

a. Bremsstrahlung (Braking Radiation) This is the most common mechanism. As the high-speed electrons approach the positively charged nuclei in the anode material, they are suddenly decelerated or “braked” by the electric field of the nuclei. This deceleration causes the electrons to lose energy, which is emitted as x-ray photons with a range of energies.

b. Characteristic X-rays If an incident electron has enough energy, it can knock out an inner- shell electron from an atom in the anode material. When an outer-shell electron drops down to fill the vacant inner-shell, it releases a photon with a specific, discrete energy. These are called characteristic x-rays because their energies are characteristic of the target material’s atomic structure.

Figure 4.2: Diagram of the x – ray tube Functions of the parts of the X – ray tube

1. Filament (Cathode): Heats up to emit electrons by thermionic emission.

2. Focusing Cup: Concentrates the electron beam toward the anode.

3. Anode (Target): Usually tungsten, chosen for its high melting point and atomic number, converts electron kinetic energy into x-rays.

4. Glass Envelope: Maintains vacuum to allow free electron movement.

5. Cooling System: Often a rotating anode or cooling fins to dissipate heat generated.

6. High Voltage Supply: Accelerates electrons from cathode to anode The x-rays exit the tube through a thin window and are directed toward the object or patient for imaging or analysis.

Figure 4.3: Diagram showing how x-rays work When we consider different types of x-rays, we can categorise them in a couple of ways:

1. Based on their energy/wavelength (soft vs. hard x-rays): This refers to the characteristics of the X-ray photons themselves.

2. Based on their application/imaging technique: This refers to how x-rays are used in practical settings, especially in medicine.

Let us expand on the “types” as defined by their energy/wavelength.

Types of X-rays: Based on Energy and Wavelength

X-rays are part of a continuous spectrum of electromagnetic radiation. While all X-rays possess the fundamental properties discussed (penetrating power, ionising ability, no mass/charge), their specific energy and wavelength determine how they interact with matter and, therefore, their suitability for different applications. This leads to the classification of x-rays into two main types: soft x-rays and hard x-rays.

This distinction is crucial because it dictates the penetrating power and the type of information x-rays can reveal.

Soft X-rays Energy: Lower energy, typically less than 10 keV (kiloelectron volts).

Wavelength: Longer wavelength, generally ranging from about 0.1 to 10 nanometres.

Penetrating Power: Less penetrating. They are easily absorbed by air and thin materials.

Interaction with Matter: Due to their lower energy, they interact more readily with the outer electrons of atoms and are absorbed quickly by denser materials.

Uses of the soft x–rays

1. Surface Imaging: Useful for imaging surfaces or very thin objects because they do not penetrate deeply.

2. Mammography: A common medical application where lower energy x-rays are preferred to visualise soft breast tissue and detect subtle changes, minimising the dose to deeper structures.

3. X-ray Microscopy: Used in scientific research to image very small objects at high resolution, often in specialised vacuum environments because they are absorbed by air.

4. Spectroscopy: Used in materials science to study the chemical composition and electronic structure of surfaces.

Hard X-rays Energy: Higher energy, typically greater than 10 keV.

Wavelength: Shorter wavelength, generally below 0.1 nanometres.

Penetrating Power: More penetrating. They can pass through denser and thicker materials, including bones and metals, with less absorption.

Interaction with Matter: Their higher energy allows them to pass through many atoms without significant interaction, only being significantly absorbed or scattered by very dense or thick materials.

Uses of the hard x–rays

1. General Radiography: Standard medical x-rays for visualising bones, diagnosing fractures, and examining internal organs like the lungs (e.g., chest x-rays).

Figure 4.4: An X-ray Image of the chest

2. Computed Tomography (CT scans): Used to create detailed cross-sectional images of the body, requiring X-rays that can penetrate complex structures.

3. Industrial Inspection (Non-destructive Testing): Detecting flaws, cracks, or internal defects in metal components, welds, or other dense industrial materials without damaging the object.

4. Security Scanning: Used in airports and other security checkpoints to scan luggage, cargo, and sometimes people for hidden objects or threats.

5. Radiation Therapy (Radiotherapy): High-energy hard x-rays are precisely directed at cancerous tumours to destroy malignant cells.

6. X-ray Crystallography: Used in science to determine the atomic and molecular structure of crystalline materials, as their short wavelengths are comparable to atomic spacing.

Energy of X-rays

X-rays are a form of electromagnetic radiation, meaning they are composed of discrete packets of energy called photons. The energy of these individual photons is what defines the “energy of the x-ray.”

Fundamental Relationship (Planck’s Equation)

In a previous topic, you learnt that the energy of an x-ray photon is directly related to its frequency (f) and inversely related to its wavelength (λ). This relationship is described by Planck’s equation:

E = hf And since for all electromagnetic waves, the speed of light (c) is equal to frequency times wavelength (c=fλ), we can also write the equation as:

E = hc__ λ Where:

E is the photon energy (typically measured in Joules (J) or, more commonly for x-rays, in electron volts (eV) or kiloelectron volts (keV)).

h is Planck’s constant (6.626×10⁻³⁴Js or 4.136×10⁻¹⁵eVs).

f is the frequency of the X-ray (in Hertz, H_(z)).

c is the speed of light in a vacuum (3.00×10⁸m/s).

λ is the wavelength of the X-ray (in metres, m).

Hazards of x-rays

1. Radiation burns (skin erythema, hair loss).

2. Genetic effects on reproductive cells.

3. DNA damage leading to mutations or cancer.

4. Acute radiation sickness (at high doses).

5. Effects on developing foetus.

Figure 4.5: Diagram showing effect of X-rays radiation on human body Safe Measures of Using X-Rays

1. Shielding: Lead aprons, thyroid collars, and barriers protect patients and staff.

2. Distance: Operators keep a safe distance or stay behind protective screens.

3. Time: Minimise exposure duration.

4. Controlled Areas: X-ray rooms are clearly marked and access limited during use.

5. Monitoring: Personnel wear dosimeters to track exposure.

6. Proper Training: Only qualified personnel operate x-ray equipment.

7. Equipment Maintenance: Regular checks ensure safety features work correctly.

Further Detail on the Applications of X-rays

The diverse properties of x-rays have led to their widespread application in numerous fields:

1. Medical Applications

a. Diagnostic Imaging: This is the most common application.

i. Radiography (X-ray Imaging): Used to visualise bones, teeth, and certain internal organs. For example, diagnosing fractures, pneumonia, or dental cavities.

Figure 4.6: Image of full-mouth dental X-ray

ii. Fluoroscopy: Provides real-time x-ray images, allowing doctors to observe the movement of organs (e.g., in angiography to visualise blood vessels).

iii. Computed Tomography (CT) Scans: Uses multiple x-ray images taken from different angles to create detailed cross-sectional images of the body, providing more comprehensive information than traditional x-rays.

iv. Mammography: Specialised x-ray imaging for breast cancer screening.

b. Radiation Therapy (Radiotherapy): High-energy x-rays are used to destroy cancerous cells while minimising damage to surrounding healthy tissue.

2. Industrial Application

a. Non-Destructive Testing (NDT) X-rays are used to inspect materials and products for flaws, cracks, or defects without damaging them.

i. Weld Inspection: Checking the integrity of welded joints in pipelines, aircraft, and other structures.

ii. Casting Inspection: Identifying voids or inclusions in metal castings.

iii. Security Screening: Used in airports to scan luggage for hidden objects.

b. Material Analysis

i. X-ray Diffraction (XRD): Used to determine the atomic and molecular structure of crystalline materials.

ii. X-ray Fluorescence (XRF): Used to identify the elemental composition of materials.

3. Security Applications

a. Airport Security: As mentioned, x-ray scanners are a staple in baggage screening.

b. Mail and Package Screening: Used to inspect suspicious packages for dangerous contents.

c. Border Control: Used to scan vehicles and cargo for contraband.

4. Scientific Research

a. Astronomy: X-ray telescopes are used to study high-energy phenomena in space, such as black holes, neutron stars, and galaxy clusters.

b. Materials Science: Researching new materials and understanding their properties at an atomic level.

c. Art and Archaeology: Used to examine the internal structure of artifacts, authenticate artworks, and reveal hidden details in paintings.

Activity 4.1 X-rays; Importance, Biological Effects & Safety Precautions Objective: To build foundational understanding of X-rays by engaging in a collaborative discussion that connects personal experiences to scientific concepts.

What you need

1. Notebook or paper for each group member

2. Pen or pencil

3. Optional: Device with internet access for quick research

4. Whiteboard or large paper for group notes (if available) What to do

1. Form small groups of 3-4 people Sit together comfortably, ideally facing one another, to facilitate a conversation.

2. Begin by asking each group member:

a. Have you ever heard of an x-ray before?

b. Have you or someone you know ever taken an x-ray?

3. Take turns sharing your experiences or stories related to x-rays, such as medical x-rays, dental x-rays, or other encounters. Discuss how these experiences made you feel or what you remember about the process.

4. Discuss what x-rays are and why they are important

a. Together, define x-rays in your own words.

b. Talk about why x-rays are useful in fields like medicine, security, and industry.

c. List specific examples of x-ray uses that group members know.

d. Write a brief group summary of your ideas.

5. Discuss the Biological Effects of Excessive X-ray Exposure

a. Discuss what you have heard can happen to the human body if exposed to too much x-ray radiation.

b. Note effects on sensitive parts of the body such as eyes and reproductive organs.

c. Write down agreed-upon key points.

6. Brainstorm protective measures against harmful x-ray exposure. Discuss why shielding and reducing exposure time are important safeguards. Write a short paragraph explaining these safety practices.

7. Combine your notes into one clear summary covering:

a. What x-rays are and their purpose

b. Biological effects of radiation exposure

c. Important safety precautions, especially shielding and exposure time

8. Prepare to share this summary verbally with another group or display it if possible.

Activity 4.2 Observing and Presenting X-ray Production in an X-ray Tube Objective: In groups, observe an x-ray tube operation through an interactive simulation or educational video.

What you need

1. Device with internet access (computer, tablet, or smartphone)

2. Access to the link below:

Educational Video on X-ray Production

https://www.youtube.com/watch?v=0vUQgKNpy2Y

3. Notebook or paper and pens/pencils

4. Chart paper or poster board / computer with presentation software (PowerPoint, Google Slides)

5. Coloured markers, pencils, or drawing tools

6. Presentation/display area (wall or digital projector) What to do

1. Form Your Group: Work with 3 to 5 classmates.

2. Open the video link above.

3. Watch or interact as a group, pausing frequently to discuss important parts:

a. How are electrons are emitted at the cathode?

b. How does the accelerating voltage speed up electrons toward the anode?

c. What occurs at the anode to produce x-rays?

Make sure everyone understands each component’s role.

4. Use devices to search online for another video or animation that explains x-ray production in an x-ray tube. Watch it together and compare with your initial resource. Add any new insights or clarifications to your notes.

5. Take Notes and Sketch

a. Write down each step of the x-ray production process in your own words.

b. Draw a labelled diagram of the x-ray tube showing cathode, anode, electron path, and X-ray emission.

6. Create a Poster or Slide Presentation: Include in your presentation:

a. A clear, labelled diagram.

b. A step-by-step explanation of the production process.

c. Key properties of x-rays (e.g., penetrating power, invisibility, effect on photographic film).

d. Real-life applications such as medical imaging, security screening, and material testing.

e. Safety precautions which should be carried out when exposure to x-rays is likely, including the importance of shielding an minimising exposure time.

Make your work visually appealing and easy to understand with colours, arrows, and bullet points.

7. Display and Share

a. Put your poster up on a wall or present your slides to other groups or classmates.

b. Explain the x-ray production process clearly and answer any questions.

c. View and discuss other groups’ presentations to learn more.

Activity 4.3 Researching and Presenting Sector-Specific Applications of

X-rays Objective: To develop an understanding of the diverse, real-world applications of X-rays across various sectors (medicine, security, and industry) by engaging in collaborative research.

What you need

1. Device with internet access (computer, tablet, or smartphone) for research

2. Notebook or paper and pens/pencils for note-taking

3. Poster materials (chart paper, markers, coloured pencils) or computer with presentation software (PowerPoint, Google Slides)

4. Presentation area (classroom wall, screen, or shared online space) What to do

1. Join 3–5 classmates to form a group.

2. Decide which sector your group will focus on

a. Medicine

b. Security

c. Industry

3. Search online or use textbooks to find specific ways x-rays are used in your sector.

4. Identify which type of x-rays (hard or soft) are involved in each application.

a. Hard x-rays are high-energy, deeply penetrating (often used in medicine and industrial inspection).

b. Soft x-rays are lower-energy, less penetrating (used in some medical imaging, surface studies, or research).

5. Take notes on

a. How x-rays help in your sector (e.g., diagnosis, security screening, quality control).

b. Examples of applications and how they work.

c. The benefits and importance of these x-ray applications.

6. Create a poster or slide presentation including

a. A title with your sector’s name.

b. Clear explanations of at least 3 specific x-ray applications in your sector.

c. Identification of the type(s) of x-rays used (hard or soft).

d. Illustrations, labelled diagrams, or images showing x-ray equipment or processes.

e. Bullet points highlighting key properties and benefits of the x-rays in this context.

7. Present and Share

a. Present your poster or slides to other groups or classmates.

b. Explain the applications clearly, emphasising how x-rays contribute to the sector.

c. Answer any questions the audience might have about your findings.

8. Learn from Others

a. View presentations from other groups focusing on different sectors.

b. Discuss similarities and differences in how x-rays are applied and the types used.

Activity 4.4 Comparing Hard and Soft X-rays

Objective: To develop a clear conceptual understanding of the differences between hard and soft x-rays by comparing their physical properties and relating these differences to real-world applications.

What you need

1. Table of x-ray properties (see example below)

2. Worksheet with matching tasks (check below)

3. Pens or pencils

4. Notebook or paper for notes and discussion

5. Calculator (optional) What to do

1. Form Small Groups (3–5 learners): Work together to read and understand the table of x-ray properties.

2. Review the key properties of hard and soft X-rays, including their energy ranges, penetration abilities, wavelengths, and typical characteristics.

3. As a group, discuss how hard and soft x-rays differ in

a. Energy levels (photon energy in keV)

b. Ability to penetrate materials (hard x-rays penetrate deeper)

c. Use cases suggested by their penetration and energy

4. Read the list of x-ray applications below

5. Match each application to the appropriate X-ray type (hard or soft) based on the properties in the table.

6. Justify each match with a brief explanation referencing energy and penetration.

7. Write a short group summary stating the main differences between hard and soft x-rays and why these differences matter for their uses.

8. Be ready to present your matched pairs and reasoning if asked in a group sharing session.

Example Properties Table

Property Hard X-rays Soft X-rays

Energy Range

(photon energy) Above ~5–10 keV Below ~5 keV Wavelength Short (0.01–0.2 nm) Longer (>0.2 nm) Penetration Ability High (penetrate thick materials) Low (absorbed easily by air or tissue) Typical Uses Medical radiography, airport security, industrial inspection, crystallography Surface studies, dental imaging, material science research Interaction with Matter Primarily via Compton scattering and photoelectric effect Mainly photoelectric absorption Worksheet Sample Questions (Matching Exercises)

1. Match the x-ray type used for airport luggage scanning.

2. Which x-ray type is used in studying thin surface layers of materials?

3. Identify the x-ray type that can penetrate bones and tissue for medical imaging.

4. Which x-rays are less penetrating and often absorbed by air?

5. Match the application of x-rays used in crystallography.

Activity 4.5 Calculating Energy of an X-ray photon Study the worked example below carefully before attempting the sample questions that follow.

Worked Example 1

A medical x-ray machine is designed to produce x-ray photons with a frequency of 2.5×10¹⁵Hz for general radiography. Calculate the energy of a single x-ray photon from this machine in Joules. (h = 6.6 × 10⁻³⁴Js ) Step by step Solution

Step 1 - Identify known values h = 6.6 × 10⁻³⁴Js f = 2.5 × 10¹⁵Hz

Step 2 - Introduce the formula for energy of a photon E = hf

Step 3 - Substitute known values and calculate E = 6.6 × 10⁻³⁴× 2.5 × 10¹⁵E = 16.5 × 10⁻¹⁹J

Worked Example 2

A security scanner at Kotoka International Airport (Accra, Ghana) uses x-ray photons with an energy of 95 keV to inspect checked luggage. Calculate the wavelength of these x-ray photons in metres. (h = 6.6 × 10⁻³⁴Js, c= 3.00×10⁸ m/s, 1 eV=1.6×10⁻¹⁹J) Step by step Solution

Step 1 - Identify known values E = energy = 95 keV= 95×10³×1.6×10⁻¹⁹J=1.52×10⁻¹⁴J h = Planck’s constant = 6.6×10⁻³⁴J s c = speed of light = 3.00×10⁸m/s

Step 2 - Introduce the formula for energy of a photon in terms of wavelength E = hc_ λ

Step 3 - Rearrange the formula to solve for λ λ = h c/E

Step 4 - Substitute known values and calculate λ = 6.6 × 10⁻³⁴3.00 × 10⁸___________ 1.5219 × 10⁻¹⁴λ = 1.30×10⁻¹¹m.

Practice Problem

Now, using the worked example as a guide, solve the following problem.

An x-ray machine at Tamale Teaching Hospital uses photons with an energy of 120 keV for diagnostic imaging. Calculate the wavelength of these x-ray photons in metres. (h = 6.6 × 10⁻³⁴Js , c= 3.00×10⁸m/s, 1 eV=1.602×10⁻¹⁹J)

Review Questions 4.1

1. A medical diagnostic centre in Accra is considering purchasing a new x-ray unit. They are evaluating two potential units based on the properties of the x-rays they produce:

Unit A: Produces x-rays with a wavelength of 0.05×10⁻⁹metres.

Unit B: Produces x-rays with a frequency of 2.0×10¹⁸Hz.

a. Calculate the energy (in keV) of a single x-ray photon produced by Unit A.

b. Calculate the energy (in keV) of a single x-ray photon produced by Unit B.

c. Based on your calculations and the document’s information on “soft x-rays” and “hard x-rays,” recommend which unit (A or B) would be more suitable for detailed bone imaging in fracture diagnosis, and justify your recommendation by explaining how the energy of the x-rays relates to their penetrating power in the human body.

2. An x-ray machine used in a dental clinic produces photons with a wavelength of 0.025 nm.

a. Calculate the energy of a single photon in Joules.

b. Calculate the frequency of these x-ray photons.

c. If the accelerating voltage in the x-ray tube determines the maximum photon energy, what minimum accelerating voltage (in kilovolts) would be required to produce these x-rays?

3. In an x-ray tube, electrons are accelerated towards a tungsten target. The electrons impact the target, and x-rays are produced.

a. Explain the two primary mechanisms by which x-rays are produced when accelerated electrons strike a target.

b. If the x-ray tube operates with an accelerating voltage of 80 kV, what is the shortest wavelength (cutoff wavelength) of the x-rays produced?

Review Questions 4.2

Investigate why many African countries are hesitant to adopt nuclear power despite energy shortages, then create a balanced argument for whether Ghana should invest in nuclear technology or focus on renewable alternatives.