Atomic Physics

In this section, we will explore some exciting ideas in modern physics. First, we’ll talk about the photoelectric effect, which shows how light can ‘knock’ electrons out of materials, proving that light behaves like tiny particles in certain situations.

We’ll also learn about Einstein’s law, which helps explain this effect. Next, we’ll discuss wave-particle duality, an idea that tells us that tiny things like electrons can act both like waves and particles. Finally, we’ll look at radioactivity, which is when unstable atoms release energy and particles. This process is important for things like medical treatments and power generation. Together, these areas help us understand how light, matter, and energy work in our world!

KEY IDEAS

• The photoelectric effect is the emission of electrons from the surface of a metal when exposed to radiation which meets or exceeds the threshold frequency for that metal.

• Wave-particle duality is the concept that quantum objects, such as light and electrons, can exhibit both wave-like and particle-like properties, depending on the experimental context.

• Einstein’s equation of photoelectric effect states that E = Wₒ + KEₘₐₓ

• Radioactivity is the spontaneous disintegration or decay of an unstable nucleus with the emission of radiation (α-particles, β-particles, γ-rays) and the release of energy to form a more stable nucleus.

• The decay law states that the activity of a given nuclide at any time is directly proportional to the number of nuclei N of the nuclide present A ∝ N

Wave-Particle Duality

Wave-particle duality is a fundamental concept in quantum mechanics that describes how every particle or quantum entity, such as light and electrons, exhibit both wave-like and particle-like properties. This duality challenges classical physics, which traditionally categorised light as a wave and matter as particles.

Key Concepts

Wave Properties: Particles can exhibit behaviours typical of waves, such as diffraction and interference. For instance, when electrons are passed through a thin sheet of graphite, they are diffracted by the lattice of ions and create an interference pattern similar to light waves, indicating their wave-like nature.

Particle Properties: Conversely, waves can exhibit particle-like behaviour when they interact with matter. The photoelectric effect shows that light can be quantised into photons, each carrying a specific amount of energy related to its frequency.

Complementarity Principle: Niels Bohr proposed that wave and particle descriptions are complementary aspects of quantum entities. Depending on the experimental setup, one aspect may become more apparent than the other, but both are necessary for a complete understanding of quantum phenomena.

Historical Background

The concept of wave-particle duality emerged from several key experiments and theories:

Thomas Young’s Double-Slit Experiment (1801): This experiment demonstrated that light behaves like a wave. When light passes through two closely spaced slits, it creates an interference pattern on a screen, indicative of wave behaviour. This phenomenon occurs because waves can overlap and interfere with each other, producing regions of constructive and destructive interference.

Figure 4.1: The pattern of bright and dark spots which appear on a screen due to wave diffraction interference Photoelectric Effect (1905): Albert Einstein’s explanation of the photoelectric effect provided evidence for the particle nature of light. He proposed that light consists of discrete packets of energy called photons. When light shines on a metal surface, it can eject electrons if the photons have sufficient energy, which is dependent on their frequency rather than intensity. This observation could not be explained solely by wave theory.

Figure 4.2: Image showing Photoelectric effect De Broglie’s Hypothesis (1923): Louis de Broglie extended the idea of wave- particle duality to matter, suggesting that particles such as electrons also exhibit wave-like behaviour. Electrons can be diffracted by thin sheets of graphite to produce a diffraction pattern; a behaviour attributed to waves rather than particles.

Figure 4.3: The circular diffraction pattern produce when electrons are diffracted through a sheet of graphite

Activity 4.1 Wave-particle duality Video Watch the following video explaining wave-particle duality: click here

Figure 4.4: Link to wave-particle duality video Photoelectric effect The photoelectric effect is a special phenomenon that happens when light hits certain materials, like metals. It suggests that light can ‘knock’ tiny particles called electrons out of those materials. Let’s break it down!

Activity 4.2 Solar panel investigation Conduct the following experiment to verify that light (photons) can create electricity by the liberation of electrons:

Figure 4.5: Experimental set up Materials needed

• Table lamp

• Connecting wires

• Crocodile clips

• Small (1.5V) bulb

• Small solar panel / photovoltaic cell Procedure

1. Connect up the solar panel, wires and bulb as shown in the image above.

2. Shine the table lamp light at the solar panel.

3. Observe the behaviour of the bulb.

4. If the bulb does not light, try moving the table lamp closer to the solar panel or using sunlight to illuminate the solar panel instead.

Conclusion: What are your observations? Did the brightness or type of light affect the behaviour of the bulb? Why are solar panels a preferred method for generating electricity?

Key points of the photoelectric effect include:

1. Photon energy: Einstein proposed that light consists of discrete packets of energy called photons, and each photon has an energy E proportional to its frequency f. The energy of the emitted electrons depends on the frequency of the incident light, with higher-frequency (or shorter wavelength) light causing the emission of more energetic electrons.

Energy of the photon (E) is given as E = hf or E = h c__ λ Where;

E is the energy of the photon in Joules h is Planck’s constant (6.63 × 10-³⁴J·s) c is the speed of light (3.0 × 10⁸m/s) f is the frequency of the incident light in Hertz λ is the wavelength of the incident light in metres

2. Threshold frequency: There is a minimum frequency of light required for the ejection of electrons. If the frequency is below this threshold, no electrons are emitted, regardless of the intensity of the light.

Threshold frequency f₀ is the minimum frequency of an electromagnetic radiation which must be exceeded to be able to eject electrons from the surface of a given metal.

Work function of a metal w₀ is the minimum amount of energy needed to just liberate an electron from a metal surface.

a. If the photon’s energy is less than the work function (E < Wₒ), no electrons are ejected.

Wₒ = h fₒ = h c_ λₒ where λₒ is also known as the threshold wavelength.

b. If the photon’s energy exceeds the work function (E > Wₒ), the excess energy is converted into the kinetic energy of the ejected electron.

3. Instantaneous emission: The emission of electrons happens instantaneously when light of the correct frequency strikes the material, indicating that the energy transfer occurs at the moment of photon absorption.

4. Intensity Effect: Increasing intensity of the light increases the number of photons, hence more electrons are emitted, but it does not affect the kinetic energy of the emitted electrons. The kinetic energy depends solely on the frequency of the light.

Figure 4.6: Image showing that the intensity of light affects the number of electrons emitted This phenomenon was explained by Albert Einstein in 1905, which helped solidify the concept of light behaving as both a wave and a particle.

Activity 4.3 Photoelectric effect Video Watch the following video explaining the photoelectric effect:

https://www.youtube.com/watch?v=jWbwDTPju-M

Figure 4.7: Link to video on the photoelectric effect Einstein’s equation of photoelectric effect Albert Einstein’s equation for the photoelectric effect explains how light energy is transferred to electrons during this phenomenon. The equation is expressed as:

E=Wₒ+ KEₘₐₓ Where:

E is the energy of the photon, Wₒ (or ϕ) is the work function of the metal, i.e., the minimum energy required to eject an electron from the surface, KEₘₐₓ is the maximum kinetic energy of the ejected electron.

Activity 4.4 Computer Simulation of the Photoelectric Effect

Objective: To explore the photoelectric effect by using computer simulations, allowing you to adjust variables such as light frequency, intensity, and metal type, predict outcomes, and confirm your predictions through experimentation.

Materials Needed

1. A computer or tablet with internet access

2. Access to a photoelectric effect simulation (e.g., PhET Simulation:

Photoelectric Effect or similar)

3. Notebook or digital document for recording predictions and observations

4. Calculator (optional for calculations) What to do

1. Open a web browser and navigate to a photoelectric effect simulation site, such as the PhET Interactive Simulations website. Look for the simulation specifically designed for the photoelectric effect. You can also use the link below.

Figure 4.8: PhET Interactive Simulation on Photoelectric effect

2. Spend a few minutes exploring the interface of the simulation. Understand how to adjust parameters such as:

a. Light Frequency: This controls the colour of light used in the experiment.

b. Light Intensity: This determines how much light is shining on the metal surface.

c. Metal Type: Different metals have different threshold frequencies and work functions.

3. Before adjusting any parameters, make predictions about what you think will happen when you change each variable:

a. Light Frequency: Predict how changing the frequency will affect electron ejection. Consider what you know about threshold frequency.

b. Light Intensity: Predict how increasing or decreasing intensity will impact the number of electrons emitted.

c. Metal Type: Predict how changing the metal will affect the results based on its work function.

4. Start by adjusting one parameter at a time. For example:

a. Set a specific metal and adjust the light frequency to see if it exceeds the threshold frequency.

b. Change the intensity of light while keeping other variables constant.

5. After each adjustment, run the simulation to observe what happens. Take

note of whether electrons are emitted and any changes in current or kinetic energy.

6. Use your notebook or digital document to record your predictions and actual outcomes for each trial. Note any discrepancies between your predictions and what you observed in the simulation.

7. After completing several trials with different combinations of parameters, analyse your results:

a. Did your predictions match the outcomes?

b. What patterns did you notice regarding light frequency, intensity, and metal type?

c. How does each parameter influence electron emission?

8. If you’re working with classmates, discuss your findings together. Share your predictions and outcomes, and explore any differences in results based on varying parameters.

Activity 4.5 Experiment to find the threshold frequency Read the following information and then write your own method for the experiment. Afterwards, use the data provided below to plot a graph of the results and use the graph to find the threshold frequency.

With the correct equipment, it would be possible to vary the frequency of the light incident on a solar panel. We would slowly increase the frequency of the light so that it appears red, then yellow, then blue, and finally ultraviolet.

The device needed to produce a variable frequency output of light is very specialist; if you have access to one, you could perform an experiment to find the threshold frequency of a metal.

If not (as is probably the case!) you should still write your own method for how this experiment could be carried out. Include an equipment list and a diagram to support your method.

Next, plot a graph of the following data (y axis = current, x axis = frequency) and use it to find the threshold frequency.

Table 4.1

Frequency (x10¹⁵Hz) Current (A)

0.5 0.0 0.7 0.0 0.9 0.0 1.1 0.2 1.3 0.2 1.5 0.2 1.7 0.2 Finally, plot this alternative data (y axis = kinetic energy of ejected electrons, x axis = frequency) and use it to find the threshold frequency.

Table 4.2

Frequency (x10¹⁵Hz) Kinetic energy of photoelectrons (x 10⁻¹⁹J) 2.00 5.90 2.50 9.21 3.00 12.52 3.50 15.84 4.00 19.15 Extension: you can also use the second graph to find the value of Planck’s constant. Can you work out how?

Activity 4.6 Calculating threshold frequency and wavelength, kinetic energy of ejected electrons.

Study the worked examples carefully below before attempting the example questions that follow

Worked Example 1

Calculate the energy of a photon with a wavelength of 500 nm.

h = 6.63 × 10-³⁴Js, c = 3.0 × 10⁸m/s

Step 1: Convert the wavelength to metres Since the wavelength is given in nanometres (1 nm = 10⁻⁹m):

λ = 500 nm = 500 × 10⁻⁹m = 5.0 × 10⁻⁷m

Step 2: Introduce the formula relating energy to wavelength E = h c_ λ

Step 3: Substitute the values E = 6.63 × 10-³⁴× 3.0 × 10⁸__________________ 5.0 × 10⁻⁷Step 4: Calculate to obtain the answer E = 3.978 × 10-¹⁹J

Worked Example 2

Calculate the threshold wavelength and threshold frequency of a metal with a work function of 3.4 eV.

h = 6.63 × 10-³⁴Js, c = 3.0 × 10⁸m/s, 1 eV = 1.6 × 10-¹⁹J

Step 1: Convert the work function to joules The work function (Wₒ) is given in electron volts (eV). Convert it to joules (J) using:

Wₒ(in J) = Wₒ(in eV) × 1.6 × 10-¹⁹ Substitute Wₒ= 3.4 eV:

Wₒ= 3.4 × 1.6 × 10-¹⁹= 5.44 × 10-¹⁹J

Step 2: Calculate the threshold frequency

a. Introduce the relationship between the work function and threshold frequency Wₒ= h × fₒ

b. Rearrange to find the threshold frequency:

fₒ = Wₒ_ h

c. Substitute Wₒ= 5.44 × 10-¹⁹J and h = 6.63 × 10-³⁴J·s:

fₒ = 5.44 × 10-¹⁹_________ 6.63 × 10-³⁴d. Calculate to obtain the answer fₒ= 8.20 × 10¹⁴Hz

Step 3: Calculate the threshold wavelength

a. Introduce the relationship between frequency and wavelength λₒ = C/fₒ

b. Substitute c = 3.0 × 10⁸m/s and fₒ = 8.20 × 10¹⁴Hz:

λₒ = 3.0 × 10⁸________ 8.20 × 10¹⁴c. Calculate to obtain the answer λₒ = 3.66 × 10⁻⁷m

Worked Example 3

A metal surface has a work function of 2.2 eV. When it is exposed to light with a wavelength of 300 nm, electrons are ejected from the surface. Calculate the maximum kinetic energy of the ejected electrons.

h = 6.63 × 10-³⁴Js, c = 3.0 × 10⁸m/s, 1 eV = 1.6 × 10-¹⁹J Step-by-Step Solution:

Step 1: Calculate the energy of the incoming photon (E):

a. Introduce the formula E = h c_ λ

b. Substitute the values:

E = ((6.63 × 10-³⁴) × (3.0 × 10⁸)___________________ (300 × 10⁻⁹)

c. Calculate to obtain the value of the energy of the incoming photon E = 6.63 × 10-¹⁹J.

Step 2. Convert the work function (Wₒ) from eV to joules:

The work function is Wₒ= 2.2 eV. Using the conversion 1 eV = 1.6 × 10-¹⁹J:

Wₒ= 2.2 × 1.6 × 10-¹⁹J Wₒ= 3.52 × 10-¹⁹J.

Step 3. Introduce the photoelectric equation to find the maximum kinetic energy KEₘₐₓ= E – Wₒ

Step 4: Substitute the values of the energy of the incoming photon and the work function KEₘₐₓ= 6.63 × 10-¹⁹- 3.52 × 10-¹⁹Calculate to obtain the answer KEₘₐₓ= 3.11 × 10-¹⁹J Practice Problems Now, using the worked example as a guide, solve the following problems individually or in groups.

h = 6.63 × 10-³⁴Js, speed of light c = 3.0 × 10⁸m/s, and 1 eV = 1.6 × 10-¹⁹J

1. Calculate the energy of a photon with a wavelength of 500 nm.

2. Calculate the threshold wavelength and threshold frequency of a metal with a work function of 2.5 eV.

3. A metal has a work function of 3.0 eV. When light of wavelength 400 nm is incident on the surface, electrons are emitted. Calculate the maximum kinetic energy of the ejected electrons in Joules.

Applications of photoelectric effect

Figure 4.9: Application of photoelectric effect The photoelectric effect is used in many daily applications, including:

1. Solar panels: They convert sunlight into electricity using a metal that releases energy when light hits it

2. Digital cameras: They use photoelectric sensors to detect and record light

3. Smartphone lighting sensors: They automatically adjust brightness based on lighting

4. Electric eye door openers: They use photoelectric sensors to detect when someone approaches, triggering the doors to open automatically

5. Light meters: These are used in photography to measure light intensity and ensure proper exposure

6. Photostatic copying: a process that uses the photoelectric effect to transfer images onto paper

7. Imaging technology: Used in television camera tubes and image intensifiers to enhance low-light images

8. Scientific research: Used to study nuclear phenomena and chemically analyse materials

9. Photomultiplier tubes: Convert light intensity into electrical currents

10. Scintillators: Emit light when they attract radiation λ = h/p

Activity 4.7 Research Project on the Photoelectric Effect

Objective: Investigate an application of the photoelectric effect, such as its role in solar panels or medical imaging devices, and present your findings in a research paper and class presentation.

Materials Needed

1. Access to the internet for research

2. Notebook or digital document for recording your findings

3. Presentation software (e.g., PowerPoint, Google Slides) for your presentation

4. Research paper format guidelines (if provided by your teacher) What to do

1. Select an application of the photoelectric effect to research from the list above.

2. Conduct your research by using reliable sources to gather information about your chosen topic. Look for:

a. How the photoelectric effect operates in your selected application.

b. Different materials used and their properties.

c. Efficiency ratings, advantages, and limitations of these materials or technologies.

d. Recent advancements or research findings related to your topic.

3. Create an outline for your research paper. Include sections such as:

a. Introduction to the photoelectric effect.

b. Detailed explanation of your chosen application.

c. Discussion on materials and their efficiencies or roles.

d. Conclusion summarising key points and future implications.

4. Write a comprehensive research paper based on your outline. Ensure to include citations for all sources used. Follow any specific formatting guidelines provided.

5. Create a presentation summarising your research findings. Include:

a. Key points from each section of your paper.

b. Visual aids such as graphs, images, or charts to illustrate concepts.

c. A clear explanation of how the photoelectric effect is applied in your topic.

6. Share your research with the class through your presentation. Be prepared to answer questions and discuss your findings with your classmates.

7. After completing the project, reflect on what you learned about the photoelectric effect and its applications. Consider how this knowledge could apply to future studies or real-world scenarios.

λₒ

Activity 4.8 Flashcard Matching Challenge

Objective: To reinforce your understanding of atomic physics terms by matching terms with their definitions using provided flashcards.

Materials Needed

1. Flashcards

a. Set A: Flashcards with key terms

b. Set B: Flashcards with corresponding definitions

2. Pen or Pencil

SET A

Figure 4.10: Flashcards on atomic physics terms SET B

Figure 4.11: Flashcards of some definitions on atomic physics terms What to do

1. Take a few minutes to read through both sets of flashcards. Familiarise yourself with the terms in Set A and their corresponding definitions in Set B.

2. To test your memory, close your eyes or turn away from the learner material to avoid looking at the definitions. This will help you recall the definitions based on the terms.

3. Start with the first term in Set A. Think about its meaning and try to recall which definition in Set B matches it.

4. Write down your answer.

5. Proceed through all the terms in Set A, matching each one to its definition in Set B. Take your time and think carefully about each match.

6. Once you have matched all the terms, go back through the flashcards to check your answers. Look at each term and its corresponding definition to see if they align correctly.

7. For any incorrect matches that are incorrect, review the definitions again to understand why they do not match. Take notes on any challenging terms.

1. Giancoli, D. C. (2008). Physics for Scientists and Engineers with Modern Physics (4th ed., pp. 582-585). Prentice Hall.

2. Serway, R. A., & Jewett, J. W. (2014). Physics for Scientists and Engineers (9th ed., pp. 1292-1295). Brooks/Cole.

3. Knight, R. D. (2016). Physics for Scientists and Engineers: A Strategic Approach (4th ed., pp. 1125-1127). Pearson.

4. OpenStax College. (2019). College Physics (2nd ed., pp. 975-978).

OpenStax.

Review Questions 4.1

1. Define Photoelectric effect.

2. State four laws of photoelectric effect.

3. State Einstein’s equation of photoelectric effect.

4. The surface of a metal is illuminated with light of wavelength 450 nm. The work function of the metal is 2.5 eV. Calculate the kinetic energy of the emitted electrons. (h = 6.63 × 10-³⁴Js, speed of light c = 3.0 × 10⁸m/s, and 1 eV = 1.6 × 10-¹⁹J)

5. Light of energy 6.2 eV strikes a metal surface, causing the emission of electrons. The maximum kinetic energy of the emitted electrons 1.5 eV.

Calculate the threshold wavelength of the metal in nanometres. (h = 6.63 × 10-³⁴Js, speed of light c = 3.0 × 10⁸m/s, and 1 eV = 1.6 × 10-¹⁹J)

6. A scientist wants to design a device that uses the photoelectric effect to detect light intensity. The device uses a metal with a known work function of 2.2 eV. During an experiment, light of wavelength 400 nm is shone onto the metal surface.

a. Explain why or why not electrons are emitted from the metal surface when the light is incident.

b. Predict how the kinetic energy of emitted electrons, if any, would change if light with a wavelength of 300 nm is used.

If the intensity of light at 400 nm is doubled, what will happen to the number of emitted electrons and their kinetic energy?

Review Questions 4.2

1. Name the three subatomic radiations emitted during radioactivity.

2. A radioactive sample of mass 30 grams has a half-life of 6 months. State and explain whether any of it will be left in 12 months.

3. The half-life of a certain isotope is 3 years. If 25% of the original sample remains, how many years have passed?

4. A radioactive substance has a half-life of 10 hours. How much of a 200 g sample remains after 30 hours?

5. A team managing a nuclear power plant needs to safely store a radioactive waste material with a half-life of 10 years. To reduce the material’s radioactivity to less than 1% of its original level, how long must the waste be stored?