Nuclear Physics

Welcome to the fascinating world of atomic structure! Today, we’re going to explore the nucleus, the tiny centre of the atom, and learn about radioactivity.

The Structure of The Nucleus

The nucleus consists of the following components:

1. Protons. Protons are particles with a positive charge. The number of protons in an atom’s nucleus determines its atomic number, which identifies the element (e.g., hydrogen has 1 proton, helium has 2 as shown in figure 1 and carbon has 6). Each proton carries a charge of +1 and has a mass of about 1.67 × 10–²⁷kg.

2. Neutrons. Neutrons are neutral particles, meaning they have no electric charge. Their mass is slightly greater than that of protons, also around 1.67×10⁻²⁷kg. Neutrons help stabilise the nucleus by reducing the repulsive forces between the positively charged protons.

3. Strong Nuclear Force. The strong nuclear force is responsible for holding protons and neutrons together. It operates over extremely short distances (about 10⁻¹⁵meters) and is much stronger than the electromagnetic force that causes repulsion between protons, ensuring nucleons remain bound within the nucleus.

The nucleus forms the core of an atom, comprising protons and neutrons, collectively referred to as nucleons. These nucleons are held together by the strong nuclear force, which is one of the fundamental forces of nature and significantly stronger than the electromagnetic force that causes repulsion between the positively charged protons. Here’s a summary of its structure:

Fig 8.12: A Structure of a Helium-4 atom Nuclear Stability Nuclear stability depends on the balance between protons and neutrons. If this balance is disrupted, with too many or too few neutrons relative to protons, the nucleus may become unstable and undergo radioactive decay to achieve a more stable state.

Identifying the number of protons and neutrons in different nuclei The atomic number (symbol Z) of an element refers to the number of protons in the nucleus of each atom of that element. In a neutral atom, the atomic number also equals the number of electrons. For example, in a neutral helium atom ₂ ⁴He as shown in figure 1, the atomic number is 2, indicating 2 protons and 2 electrons.

Note that in the case of an ion, for example the chloride ion ₁₇ ³⁵Cl-, the atomic number remains 17 (indicating 17 protons), but there are 18 electrons due to the additional negative charge.

The mass number (symbol A) represents the total number of protons and neutrons in the nucleus. It is also known as the nucleon number. For example, in a helium atom, the mass number is 4, indicating 4 nucleons in the nucleus.

The relationship between the mass number (A), atomic number (Z), and neutron number (N) is expressed as A = Z + N.

Activity 8.9: Identifying Protons and Neutrons in Atomic Nuclei From the mass and atomic numbers, identify the number of protons and neutrons in the following nuclei:

Isotopes: isotopes are atoms of the same element having the same atomic number but different mass numbers due to differences in the number of neutrons.

For example:

11 23Na and ₁₁ ²⁴Na are isotopes of sodium 1H, ₁ ²H and ₁ ³H are isotopes of hydrogen 6 12C and ₆ ¹³C are isotopes of carbon 8 16O, ₈ ¹⁷O, and ₈ ¹⁸O are isotopes of oxygen 17 35Cl and ₁₇ ³⁷Cl are isotopes of chlorine All elements have a number of isotopes. Hydrogen has the fewest number of isotopes with only three. The elements with the most isotopes are caesium and xenon, with 36 known isotopes

Table 8.2: Proton-Neutron Composition and Nuclide Notation of Sodium Isotopes Element No. of protons No. of Neutrons No. of Nucleons Nuclide notation Sodium-23 11 12 23 ₁₁ ²³Na Sodium-24 11 13 24 ₁₁ ²⁴Na

Activity 8.10: Modelling Atomic Nuclei and Isotopes

Objective: Understanding the structure of atomic nuclei and isotopes through a hands-on model-building activity.

Materials needed:

• Modelling clay or beads in two colours (e.g., red for protons, blue for neutrons)

• Magnets (optional for bonding)

• A periodic table for reference Instructions:

1. Assigning Colours:

• Red clay/beads represent protons.

• Blue clay/beads represent neutrons.

2. Choosing an Element: Select an element from the periodic table (e.g., carbon-12, oxygen-16).

3. Building the Nucleus:

• Use the correct number of protons (same as the atomic number) and neutrons (varies for different isotopes) to create a nucleus model.

• For Carbon-12, you will use 6 red beads (protons) and 6 blue beads (neutrons).

4. Creating Isotopes: Modify your model by adding or removing neutrons to represent different isotopes of the same element. For example, you can change Carbon-12 to Carbon-14 by adding two neutrons.

5. Discussion:

a. After building models, discuss how changing the number of neutrons affects the isotope but not the chemical element.

b. Explain why isotopes have different atomic masses but the same number of protons.

6. Presentation: Present your nucleus models and explain the element and isotope you have created.

Activity 8.11: Understanding Radioactivity Through Dialogue

Read the dialogue from Nana Poku, Okuapeman school and Khairy, Aburi Girls Nana Poku: Hey Khairy, have you heard about the Chernobyl accident?

Khairy Nhyira: Yes, I have! It’s a tragic event that happened in 1986 in Ukraine. What really struck me was how dangerous radioactivity can be.

Fig 8.13: An aerial view of the Chernobyl Disaster Nana Poku: Exactly! The explosion at the nuclear power plant released a massive amount of radioactive materials into the environment.

Khairy Nhyira: Right. So, what exactly is radioactivity?

Nana Poku: Radioactivity is when unstable atomic nuclei lose energy by emitting radiation. This can be in the form of alpha particles, beta particles, or gamma rays.

Khairy Nhyira: And that radiation can be harmful, right? Especially to living organisms?

Nana Poku: Yes, it can damage cells and even lead to cancer. That’s why the areas around Chernobyl are still largely uninhabited.

Radioactivity refers to the spontaneous or induced breakdown of unstable atomic nuclei, releasing energy in the form of particles like alpha (a), beta (b), and gamma radiation (g). Unstable isotopes undergo this process to become stable, a phenomenon called radioactive decay. Isotopes that exhibit radioactivity are termed radioisotopes or radionuclides, while those that don’t decay are called stable isotopes. For instance, Carbon-14 is radioactive, whereas Carbon-12 and Carbon-13 are stable. There are 339 naturally occurring nuclides, with 286 classified as primordial, existing since the formation of the Solar System.

Alpha, beta, and gamma radiation all originate from the atomic nucleus (hence the name, nuclear radiation).

When an alpha particle is emitted, the nucleus loses 2 protons and 2 neutrons, altering its composition and turning it into a different element entirely.

When a beta particle is emitted, a neutron has spontaneously turned into a proton and an electron inside the nucleus. The electron is emitted at high speed (this is the beta particle), but the proton remains. This also means that the nucleus has turned into that of a different element.

When a gamma particle is emitted, the nucleus loses energy, but its structure is unchanged.

Activity 8.12: Investigating the Properties of Alpha, Beta, and Gamma Radiation

1. Research and use the chart below to record information about alpha, beta, and gamma radiation.

2. Fill in each cell with the appropriate information regarding the particle’s nature, charge, mass, ionisation power, and penetrating power.

Table 8.3 Table to complete activity 8.12 α β γ Nature Charge Mass Penetration Electric and Magnetic Effect Ionisation Fluorescence Velocity Stopping Material Natural and Artificial Radioactivity Nuclear radiation is emitted by multiple sources, and there is always some level of background radiation, wherever you live or work.

Natural radioactivity is the spontaneous disintegration of unstable nuclei without an external source with an emission of particles or radiation.

Artificial radioactivity is the spontaneous disintegration of unstable nuclei produced by bombarding nuclei with another nucleus with an emission of particles or radiation.

Activity 8.13: Categorising Sources of Background Nuclear Radiation

Create a Venn diagram of sources of background nuclear radiation, sorting the following into ‘natural’ or ‘artificial’:

1. Radon gas

2. Rocks, buildings and materials

3. Medical (x-ray machines, radiotherapy machines, etc)

4. Food

5. Cosmic rays

6. Nuclear power plants

7. Any others that you research!

Activity 8.14: Exploration Through Simulations and Videos

Instructions:

1. Visit the following links to explore the ionisation and penetrating power of alpha, beta, and gamma radiation.

2. Take notes on the key differences in their properties and effects.

Resources:

PhET Interactive Simulations: [PhET Radioactive Dating Game] https://phet.colorado.edu/en/simulations/category/physics BBC Bitesize: [Types of Radiation] https://www.bbc.co.uk/bitesize/guides/z8j4mnb/revision/1 YouTube: Crash Course Physics: [Radiation and Radioactivity] https://www.youtube.com/watch?v=Z5x9eU4gWwM

Activity 8.15: Exploring Applications of Radioactivity

Research the use of radioactivity. Create a poster presentation about your chosen application, explaining whether an alpha, beta, or gamma source is chosen and why. You should also discuss the ‘half-life’ of the isotope used, defining this term.

Nuclear equations represent the reactants and products in radioactive decay, nuclear fission, or nuclear fusion. Instead of chemical equations, where we see that the number of atoms of a particular element is conserved in a reaction, in a nuclear reaction the atomic mass and proton numbers are conserved.

Nuclear reactions can be represented by equations. Such equations are known as nuclear equations. Two laws governing nuclear equations are

1. The law of conservation of mass numbers states that the total atomic numbers on both sides of the equation (left and right) must be the same or equal.

E.g. _(b) ᵃLi + _(d) ᶜCl = _(f) ᵉLiCl, then a + c = e

2. Law of conservation of atomic numbers states that the total atomic numbers on both sides of the equation must be the same.

For example, if _(b) ᵃLi + _(d) ᶜCl = _(f) ᵉLiCl then b + d = f We use the above laws to find out the missing or left-out values by equating the sum of the atomic or mass numbers at the left side of the equation to the right side of the equation.

Worked example

82 yPb → ₈₃ ²¹⁴Bi +ₓ ⁰e + energy Balancing the mass numbers left and right: y = 214 + 0 = 214 Balancing the atomic numbers left and right: 82 = 83 + x, therefore x = –1.

Activity 8.16: Balancing Nuclear Reactions

A nuclear reaction is found to be x 14N + ₂ ⁴He →₈ ʸO + ₁ ¹H Find the values of x and y in the nuclear equation given above.

Radioactive decay Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation.

This decay can occur in several forms, including:

Alpha particle decay (α) Alpha particle emission is an emission that has alpha particles involved at the product side of the nuclear equation to produce other nuclides. E.g., if an α particle is emitted, the process is described as α-decay. In that case, the parent nuclide loses atomic number by 2 and mass number by 4. This is demonstrated below:

Beta-decay (β) Beta emission is an emission that has beta particles involved at the product side of the nuclear equation to produce other nuclides. If a b particle is emitted, the process is described as b-decay. In such a case, the parent nuclide gains an atomic number of 1 while there is no change in mass number. Hence, a beta particle is described as an electron with high speed.

Gamma emission (γ) Gamma emission is an emission that has gamma particles involved at the product side of the nuclear equation to produce other nuclides. Also, if a γ photon is emitted, the process is described as γ-decay. In this case, there is no change in both mass number and atomic number of the parent nuclide.

Activity 8.17: Verifying Balanced and Unbalanced Nuclear Equations

Examine each nuclear reaction and determine whether it is balanced or unbalanced.

96 244Cm → ₉₇ ²⁴⁰Bk +₂ ⁴He 84 210Po → ₈₂ ²⁰⁶Pb +₂ ³He 88 226Ra → ₈₆ ²²²Rn +₂ ⁴He 27 60Co → ₂₈ ⁶⁰Ni +− 1 0e

Activity 8.18:Determining Missing Values in Nuclear Reactions

For each of the following examples, find the missing values.

92 238U → _(Z1) ᴬ¹Th +₂ ⁴He 6 14C → _(Z2) ᴬ²N +− 1 0e 27 60Co → _(Z3) ᴬ³Ni +− 1 0e

Activity 8.19: The Neutrino Hypothesis: Exploring Its existence through research Research the ‘neutrino’ and explain the reason(s) why it was postulated to exist.

ANNEXES Annex 8.1: Solutions to some activities (Atomic Physics)

Activity 8.3: Limitations of the J.J. Thompson’s model Thompson’s model of the atom faced limitations because it could not account for the results and observations of Rutherford’s alpha particle experiment.

Alpha particles (positive charges) were directed into a metal foil and detected on a screen afterwards.

The observations made by Rutherford that were limitations to Thompson’s model are:

i. Most of the alpha particles went through the thin metal foil without any change in path

ii. A few alpha particles were deflected through small angles

iii. Very few alpha particles were deflected backwards Thompson’s model had limited success because if the electrons, which were negatively charged, were uniformly positioned throughout the mass of positive charge, there would be no strong resultant force to deflect the heavy alpha particles backwards, as observed by Rutherford.

Activity 8.5

Note that your research may give slightly different values!

Wave Frequency range (Hz) Wavelength range Radio wave Less than 3.0x10¹¹Greater than 1 millimetre Microwave 3x10¹¹to 10¹³25 micrometres – 1 millimetre Infrared 10¹³to 4x10¹⁴750 nanometres to 25 micrometres Visible light 4x10¹⁴to 7.5x10¹⁴400 to 750 nanometres Ultraviolet 10¹⁵to 10¹⁷1 to 400 nanometres X-rays 10¹⁷to 10²⁰1 picometre to 1 nanometre Gamma rays 10²⁰to 10²⁴Less than 1 picometer

Activity 8.7

1. E = hf = 6.63 × 10⁻³⁴J s × 3.2 × 10¹⁰Hz = 2.1 × 10⁻²³J

2. λ = hc/E λ = 6.63 × 10⁻³⁴× 3.0 × 10⁸m s⁻¹______________________ 6.5 × 10⁻¹⁹J λ = 3.1 × 10⁻⁷m = 300 nm

3. E = hc__ λ E = 6.63 × 10⁻³⁴J s × 3.0 × 10⁸m s⁻¹________________________ 550 × 10⁻⁹m E = 3.6 × 10⁻¹⁹J

4. E = hf, Making ‘f’ the subject f = E/h E = 10.21eV = 10.21 × 1.6 ×10⁻¹⁹Substituting into the formula f = E/h = 10.21 × 1.6 × 10⁻¹⁹______________ 6.63 × 10⁻³⁴= 2.48×10¹⁵Hz

Activity 8.8

1. The ionisation energy is the energy needed to allow an electron to leave its ground a state and be freed from the electrostatic pull of the atom.

2. E₁ = - 13.6/1²= - 13.58 eV = - 13.6 eV E₂ = - 13.6/2²eV = -3.39 eV ∆ E = hf, ∆ E = E₂ − E₁ then hf = E₂ − E₁ Making ‘f’ the subject f = E₂ − E₁______ h E₂ − E₁ = -3.39 – (-13.6) = 10.21 eV E₂ − E₁= 10.21 × 1.6 ×10⁻¹⁹J Substituting into the formula f = E₂ − E₁______ h = 10 . 21 × 1 . 6 × 10⁻¹⁹_______________ 6 . 5 × 10⁻³⁴= 2.48×10¹⁵Hz

3. Given Eₙ = - 2.16 × 10⁻¹⁸_________ n²J, when n = 1 E₁ = 2.16 × 10⁻¹⁸_________ 1²= -2.16×10⁻¹⁸J When n = 2, the state has energy E₂ = − 2.16 × 10⁻¹⁸__________ 2²= - 0.54×10⁻¹⁸J When n = 3, the state has energy E₃ = − 2.16 × 10⁻¹⁸__________ 3²= -0.24 × 10⁻¹⁸J E₃ − E₂ = hf but f = c__ λ E₃ − E₂ = hc__ λ →λ = hc/E₃ − E₂ λ = 6.6 × 10⁻³⁴× 3.0 × 10⁸______________________ − 0.24 × 10⁻¹⁸− (− 0.54 × 10⁻¹⁸) = 6.6 × 10⁻⁷m Annex 8.2: Solutions to some activities (Nuclear Physics)

Activity 8.9

• Calcium (Ca) o Mass Number: 40 (most common isotope: Ca-40) o Atomic Number: 20 o Proton Number: 20 o Neutron Number: 20 (40 - 20 = 20)

• Chlorine (Cl) o Mass Number: 35 (most common isotope: Cl-35) o Atomic Number: 17 o Proton Number: 17 o Neutron Number: 18 (35 - 17 = 18)

• Oxygen (O) o Mass Number: 16 (most common isotope: O-16) o Atomic Number: 8 o Proton Number: 8 o Neutron Number: 8 (16 - 8 = 8)

• Helium (He) o Mass Number: 4 (most common isotope: He-4) o Atomic Number: 2 o Proton Number: 2 o Neutron Number: 2 (4 - 2 = 2)

Activity 8.12

α β γ Nature Helium nucleus Fast Moving electron Electromagnetic wave Charge Positive Negative Neutron Mass Heaviest Heavy No effect Penetration Least Great Greater Electric and Magnetic Effect Little High No effect Ionization High Moderate Least Fluorescence Large Small Nil Velocity Slow Fast Very slow Stopping Material Thin paper Aluminum Foil Thick lead Annex 8.3: Further Information on Nuclear Physics Important applications of nuclear radioactivity across different fields

1. Medical Applications

Radiotherapy: Used in cancer treatment to target and kill cancerous cells.

Diagnostic Imaging: Techniques like PET (Positron Emission Tomography) and SPECT (Single Photon Emission Computed Tomography) use radioactive tracers to visualize bodily functions.

Sterilisation: Radioactive sources are used to steriliSe medical equipment and pharmaceuticals by killing bacteria and other pathogens.

2. Industrial Applications

Radiographic Testing: Used for non-destructive testing of materials and welds to identify structural integrity.

Gauging Devices: Radioactive isotopes are used in devices for measuring the thickness of materials in manufacturing processes.

Tracer Studies: Radioisotopes are used as tracers in industrial processes to follow the movement of materials and diagnose leaks in systems like oil pipelines.

3. Energy Production

Nuclear Power: Nuclear reactors use controlled chain reactions of radioactive isotopes, primarily uranium-235 and plutonium-239, to generate electricity.

Nuclear Propulsion: Radioactivity is also used in submarines and spacecraft for power and propulsion systems.

4. Agriculture Food Irradiation: Radioactivity is used to preserve food by killing bacteria and parasites, extending shelf life.

Mutation Breeding: Inducing mutations in plants to develop new varieties with desirable traits and disease resistance.

Fertiliser Efficiency: Radioisotopes are used in tracer studies to optimize fertilizer usage by tracking the uptake of nutrients by plants.

5. Scientific Research

Radiometric Dating: Techniques like carbon dating use the decay of radioactive isotopes to determine the age of archaeological finds.

Environmental Tracing: Radioactive isotopes can help track pollution sources and study environmental changes.

Tracer Studies in Biology and Chemistry: Radioisotopes are used as tracers to study biological processes, chemical reactions, and drug metabolism.

Fundamental Research: Radioactive materials are used in experiments to study the properties of atoms, nuclear reactions, and subatomic particles.

Geological Dating: Other isotopes like Uranium-238 and Potassium-40 are used to date rocks and geological formations to determine the age of the Earth

6. Space Exploration

Radioisotope Thermoelectric Generators (RTGs): These are used in spacecraft to provide power for long-duration missions, utilizing the heat generated from radioactive decay.

7. Smoke Detectors

Some smoke detectors use americium-241, a weak radioactive source, to detect smoke particles.

In all these applications, the controlled use of radioactivity allows for significant advancements in technology, science, and medicine while emphasising safety to minimise radiation exposure.

Annex 8.4: Solutions to some activities (Nuclear decay equations)

Activity 8.16

From the law of conservation of mass numbers 14 + 4 = y + 1 → y = 18 – 1 = 17 From the law of conservation of atomic numbers x +2 = 8 + 1 → x = 9 – 2 = 7

Activity 8.17

Balanced or unbalanced 96 244Cm → ₉₇ ²⁴⁰Bk +₂ ⁴He UNBALANCED 84 210Po → ₈₂ ²⁰⁶Pb +₂ ³He UNBALANCED 88 226Ra → ₈₆ ²²²Rn +₂ ⁴He BALANCED 27 60Co → ₂₈ ⁶⁰Ni +− 1 0e BALANCED

Activity 8.18

92 238U → ₉₀ ²³⁸Th +₂ ⁴He 6 14C → ₇ ¹⁴N +− 1 0e 27 60Co → ₂₈ ⁶⁰Ni +− 1 0e