Atomic and Nuclear Physics is a branch of physics that deals with the structure of atoms and the interactions and transformations of atomic nuclei. This study note will cover core concepts from the International Baccalaureate (IB) Physics syllabus, including mass-energy equivalence, isotopes, nuclear reactions, and the discovery of the nucleus. We will break down complex ideas into digestible sections, providing detailed explanations and examples to aid understanding.
Einstein's Theory of Relativity introduced the concept that matter can be considered a form of energy, encapsulated in the famous equation:
$$ E = mc^2 $$
Where:
This equation implies that:
Tip:
Remember that the speed of light ( c ) is a constant and has a very large value, which means even a small amount of mass can be converted into a significant amount of energy.
Experiments have shown that the total mass of a nucleus is less than the sum of the masses of its individual nucleons (protons and neutrons). This difference is known as the mass defect ((\Delta m)).
The mass defect (\Delta m) can be calculated using the formula:
$$ \Delta m = Zm_p + (A - Z)m_n - m_{\text{total}} $$
Where:
The mass defect corresponds to the nuclear binding energy ((E_b)), which is the energy required to disassemble a nucleus into its component protons and neutrons. This energy can be calculated using:
$$ E_b = \Delta m \cdot c^2 $$
Note:
The binding energy per nucleon is a measure of the stability of a nucleus. Higher binding energy per nucleon means a more stable nucleus.
A nuclide is a group of atoms with the same number of protons and neutrons. Atomic symbols are written in a specific notation called AZX notation:
$$ ^{A}_{Z}X $$
Where:
Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons.
Example:
Hydrogen has three isotopes:
Fusion is the process of combining two small nuclei to form a larger nucleus, releasing energy. For example, the fusion of deuterium (( ^{2}{1}H )) and tritium (( ^{3}{1}H )) produces helium (( ^{4}_{2}He )) and a neutron (( n )):
$$ ^{2}{1}H + ^{3}{1}H \rightarrow ^{4}_{2}He + n + \text{energy} $$
Note:
Fusion requires extremely high temperatures and pressures to overcome the electrostatic repulsion between positively charged nuclei.
Fission is the splitting of a large atomic nucleus into smaller nuclei, releasing energy. For example, the fission of uranium-235 (( ^{235}_{92}U )) when it absorbs a neutron:
$$ ^{235}{92}U + n \rightarrow ^{141}{56}Ba + ^{92}_{36}Kr + 3n + \text{energy} $$
Tip:
Fission reactions are used in nuclear power plants to generate electricity.
The structure of the atom was discovered through the Rutherford-Geiger-Marsden experiment, also known as the gold foil experiment. Alpha particles (( \alpha )-particles) were fired at thin gold foil, and their scattering was observed.
Common Mistake:
A common misconception is that electrons are part of the nucleus. In reality, electrons orbit the nucleus and contribute very little to the atom's mass.
Understanding atomic and nuclear physics is crucial for grasping the fundamental principles of matter and energy. From mass-energy equivalence to nuclear reactions, these concepts form the backbone of modern physics and various technological applications, such as nuclear power and medical imaging.