Quantum and Nuclear Physics is a fascinating branch of physics that deals with the smallest scales of energy levels of atoms and subatomic particles. This study note will cover key concepts from the International Baccalaureate (IB) syllabus, including the interaction of matter with radiation, the photoelectric effect, matter waves, the uncertainty principle, quantum tunneling, and nuclear physics fundamentals.
Photons are fundamental particles that make up all forms of electromagnetic radiation. A photon is a massless "packet" or "quantum" of electromagnetic energy.
The energy of a photon can be calculated using the formula: $$ E = hf $$ where:
Using the wave equation, energy can also be expressed as: $$ E = \frac{hc}{\lambda} $$ where:
Tip:
Remember, the higher the frequency of EM radiation, the higher the energy of the photon.
The photoelectric effect occurs when light shines on a metal surface and ejects electrons from that surface.
$$ E_{photon} = \phi + KE_{max} $$ where:
Example:
Consider a metal with a work function (\phi = 2 , \text{eV}). If light with a frequency of (1 \times 10^{15} , \text{Hz}) shines on it, calculate the maximum kinetic energy of the ejected electrons.
Experiments to observe the photoelectric effect typically involve shining UV light on a metal surface and measuring the emitted electrons' kinetic energy.
To solve photoelectric problems, use the photoelectric equation and ensure units are consistent (e.g., converting eV to Joules if necessary).
De Broglie hypothesized that particles, like electrons, have wave properties. This is described by the de Broglie wavelength: $$ \lambda = \frac{h}{p} $$ where:
Pair production occurs when a photon creates a particle-antiparticle pair, such as an electron and a positron. Annihilation occurs when a particle and its antiparticle collide and convert their mass into energy.
Bohr's model of the hydrogen atom introduced the idea that the angular momentum of electrons is quantized: $$ L = n\hbar $$ where:
Schrodinger's equation describes how the quantum state of a physical system changes with time. The wave function, ( \psi ), provides information about the probability amplitude of a particle's position and momentum.
The Heisenberg Uncertainty Principle states that certain pairs of physical quantities, such as position and momentum, cannot be known precisely at the same time: $$ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} $$ where:
Similarly, for energy and time: $$ \Delta E \cdot \Delta t \geq \frac{h}{4\pi} $$
Note:
This principle highlights the fundamental limit to how precisely we can know the properties of a quantum system.
Quantum tunneling is a phenomenon where particles pass through a potential barrier that they classically shouldn't be able to pass.
Example:
A scanning tunneling microscope uses quantum tunneling to map the surface of a material at the atomic level by maintaining a constant tunneling current between its tip and the surface.
Rutherford's gold foil experiment demonstrated that atoms have a small, dense nucleus. The scattering of alpha particles provided insights into the size and charge of the nucleus.
When high-energy particles (like electrons or neutrons) are directed at a nucleus, they diffract around it, forming patterns that can be used to determine nuclear size.
Deviations occur due to nuclear forces and the finite size of the nucleus, which are not accounted for in the original Rutherford model.
Nuclei have quantized energy levels, similar to electrons in atoms. These levels can be observed through the emission or absorption of gamma rays.
Neutrinos are nearly massless particles that interact very weakly with matter. They were postulated to explain the missing energy in beta decay.
Radioactive decay follows first-order kinetics, described by: $$ N(t) = N_0 e^{-\lambda t} $$ where:
The half-life (( T_{1/2} )) is the time required for half of the radioactive nuclei to decay: $$ T_{1/2} = \frac{\ln 2}{\lambda} $$
Alpha decay can be explained by quantum tunneling, where an alpha particle tunnels through the potential barrier of the nucleus.
Example:
Consider an alpha particle in a nucleus with a potential barrier. The probability of tunneling through the barrier can be calculated using the Schrödinger equation and the concept of wavefunctions.
Quantum and Nuclear Physics explores the fundamental nature of particles and their interactions. Understanding these principles is crucial for advancements in technology, such as semiconductors, medical imaging, and nuclear energy.