Lecture 1 - Nuclear Composition

Electromagnetic Materials Group Information

Prof. Euan Hendry is part of the Electromagnetic materials group, located in Office 602 on the 6th floor of the physics department. For any queries, he can be reached at Phone: 01392 725654 (internal 5654) or through email at e.hendry@exeter.ac.uk. Students can access e-learning resources related to the course through the link: https://ele.exeter.ac.uk/course/view.php?id=26043.

Lecture Structure

PHY3052 – Nuclear and High Energy Physics

The course includes two live lectures each week, where students will have the opportunity for self-assessment and feedback on their progress. Attendance is encouraged as one tutorial session will occur approximately every two weeks, with details available on the ELE platform.

Lecture Content Overview

Lectures will cover two main areas:

Nuclear Physics: Understanding the formation of nuclei from protons and neutrons, which are composite particles.
Particle Physics: Focusing on the fundamental constituents of composite particles.

Topics to be Covered

Characteristics of the nuclear force and nuclear models.
Nuclear decay and reactions, specifically alpha (α) and beta (β) decay, as well as fission and fusion processes.
Fundamental constituents of matter, including quarks, electrons, and neutrinos.
The three fundamental forces and their functionalities.
Applications and limitations of the Standard Model of physics.

Expectations for Students

Knowledge Requirements

The course focuses on understanding concepts rather than memorizing equations. Here are the key expectations:

Students should grasp the fundamental physics principles without needing complex equations.
Remember only basic equations and derivations.
Recognize components of more complex equations and demonstrate an ability to apply them.
Familiarity with experimental ideas and techniques is vital.
While the history of nuclear and particle physics, including notable figures and Nobel prizes, will add context, such information is not exam-relevant.

Resources and Study Aids

Lecture notes, recordings, and video lectures are available on ELE and are anticipated to be comprehensive. If material isn't covered in these resources or self-study packages, it will not be exam-required.
Engaging in background reading is encouraged to enhance comprehension of lecture content.
Self-study components will constitute roughly 5 credits (about one-third of the examination weight).

Historical Context and Key Figures

Noteworthy Contributions

Enrico Fermi remarked, “Had I foreseen this I would have gone into botany.” This highlights the unexpected developments in nuclear physics, which is about 100 years old, and particle physics, only about 50 years old. Key figures in this field include:
- Marie Curie: The first woman to receive a Nobel Prize and the first individual to earn two Nobel Prizes, she coined the term "radioactivity." Curie passed away from aplastic anemia, likely due to radon exposure. She discovered radium (Radium-226) and realized that the emissions from radium remained radioactive for weeks. Radon, the daughter product, is a significant health concern, contributing to lung cancer.

Understanding Radioactivity

A safe dose of radioactivity is determined by factors including the type and absorption of radiation. Key metrics include:
- Number of radiation events per second.
- Absorbed energy per unit mass, which incorporates biological weighting, termed the "Quality factor" (approximately 1 for gamma radiation, 20 for alpha radiation).
The average yearly radiation dose is about 2600 micro-Sieverts, with 85% being naturally occurring. This dose can be substantially higher for populations in proximity to granite areas.

Applications of Nuclear Physics

Nuclear technology has broad applications:

Sterilization of medical instruments and food.
Utilization in nuclear reactors for electricity generation.
Imaging and testing of materials in manufacturing, utilizing techniques such as carbon dating.

Technetium and Medical Imaging

Technetium (99Tc) is the lightest radioactive element used in medical imaging, with a short half-life of 6 hours. In medical applications, it is incorporated into materials that preferentially accumulate in specific body parts (e.g., iodine for thyroid imaging). 99Tc emits gamma rays (140 keV) during decay, which are captured using single crystal scintillators that convert gamma rays into visible light.
99Tc is sourced from molybdenum (99Mo), which undergoes beta decay from the heavier isotope. 99Mo is produced through neutron activation from 98Mo, typically in hospital settings.

The Concept of the Atomic Nucleus

Classical Models and Their Limitations

The nucleus exhibits a positively charged structure composed of protons, with negatively charged electrons orbiting in a fashion analogous to planets around a sun. The size of the nucleus is significantly smaller than the size of the atom, with a classical planetary model proposing orbital paths which fail due to the prediction that accelerating charges emit electromagnetic radiation (according to Maxwell's equations). This led to the quantization of electron angular momentum as a solution.
In Hydrogen, for example, the Bohr radius is calculated to be approximately $5.3 imes 10^{-11} ext{ m}$ . Experimental evidence indicates the nucleus measures less than $10^{-14} ext{ m}$ .

Introduction of Isotopes

Isotopes require the postulation of a neutral particle within the nucleus; this was proposed by Rutherford in 1920s. He established that atomic variance in elements lies in differing numbers of positive charges (protons) balanced with negative electrons. Understanding the mass distribution between protons and neutrons led to discoveries of specific isotopes; for instance, natural chlorine consists of approximately 76% $^{35} ext{Cl}$ and 24% $^{37} ext{Cl}$ , providing a mean atomic mass of 35.5.

Discoveries in Nuclear Physics

The Search for the Neutron

The quest for a neutral particle resulted in multiple breakthroughs and ultimately the discovery of the neutron by James Chadwick in 1932, who received the Nobel Prize in 1935 for this discovery. Other notable figures included Ettore Majorana, whose genius was recognized by Enrico Fermi. Although Majorana formulated the concept of the neutron, he chose not to publish his findings, which allowed Chadwick to receive the acclaim.

Majorana's Mysterious Disappearance

Majorana, a prodigious talent in physics who recognized the need for a massive neutral particle, mysteriously vanished in 1938 at the age of 31 during a boat trip. Various theories surrounding his disappearance include suicide or voluntary disappearance; however, his contributions were largely forgotten until recent years, when investigations into his disappearance were reopened in 2011.

Nuclear Composition

Structure of Nuclei

Nuclear structure consists of protons and neutrons, with the following definitions:
- Number of protons (atomic number): Z.
- Number of neutrons: N.
- Total number of nucleons (atomic weight): A = Z + N.

Relationships of Nuclei

Nuclides that share the same atomic weight A are referred to as isobars. Nuclides with the same neutron count N are isotones, and those with the same proton count Z are isotopes.
The charge of a nucleus is simply the total of its proton charges, calculated as charge = +Ze (where e = $1.602 imes 10^{-19} ext{ C}$ ). In neutral atoms, this charge is balanced precisely by the electron charge, leading to the example of hydrogen which is electrically neutral.

Neutron Properties

Neutrons are indeed neutral but they possess a magnetic moment due to the dynamics of charge within them, confirming that they are composite particles despite having a zero charge sum.

Techniques for Nuclear Composition Measurement

Mass spectroscopy is the method employed for accurate measurement of mass and charge for elements and isotopes. The first chamber of the mass spectrometer utilizes crossed electric and magnetic fields to measure velocity, where the forces balance, allowing ions to pass through when speed is defined as $v = rac{E}{B}$ .
The second chamber facilitates separation based on mass using the equation $F_{B2} = qvB2 = rac{mv^2}{r}$ , leading to the determination of the ratio of mass to charge using the relationship $m/q = rac{B^2}{E} imes r$ .

Example Calculations in Mass Spectrometry

To derive the mass of an iron-56 nucleus when provided with the specified conditions of a cyclotron radius of 9.07 cm, a charge of +2, magnetic field strength B = 0.4 T, and electric field strength E = 0.5 kV/cm, students would use:
1. First Chamber: Setting up the equations $qE = qvB$ .
2. Second Chamber: $(qvB = rac{mv^2}{r})$ to find mass.
3. Calculation Process: Inputting known values into the mass equation to arrive at results.

Looking Ahead

Next Lecture Focus

In the next lecture, the topic of scattering experiments will be explored to understand more about the nuclear structure, alongside a discussion on Ettore Majorana’s contributions and life.