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Physics / 09

Modern Physics

Explore the ideas that changed classical physics: relativity, quantum behaviour, photons, atomic structure, nuclear physics, and radioactivity.

From classical to modern physics

Classical physics successfully describes many everyday phenomena, but experiments involving very high speeds, extremely small scales, and electromagnetic radiation revealed important limitations.

Modern physics developed new frameworks to describe these situations, including relativity and quantum mechanics.

Special relativity

Special relativity describes how space, time, and motion behave for observers moving at constant relative velocities. It is based on the principle that the laws of physics are the same in inertial reference frames and that the speed of light in vacuum is invariant.

Time dilation Moving clocks can be measured to run more slowly relative to an observer in another inertial frame.
Length contraction Lengths measured along the direction of motion can differ between reference frames.

Mass and energy

Relativity reveals a deep connection between mass and energy.

Mass-energy equivalence

E = mc²

E is energy, m is mass, and c is the speed of light in vacuum.

This relationship is especially important in nuclear physics, where relatively small changes in mass can correspond to substantial amounts of energy.

Quantum physics

Quantum physics describes matter and radiation at microscopic scales. At this level, many physical quantities behave in ways that differ fundamentally from classical expectations.

Quantisation Some physical quantities can take only particular allowed values rather than every possible value.
Probability Quantum theory generally predicts probabilities for measurement outcomes rather than definite classical trajectories.
Wave-particle duality Quantum objects can display both wave-like and particle-like behaviour depending on the experiment.

Photons

Light can behave as though it consists of discrete packets of electromagnetic energy called photons.

Photon energy

E = hf

h is Planck's constant and f is the frequency of the electromagnetic radiation.

Photoelectric effect

The photoelectric effect occurs when light causes electrons to be emitted from a material.

The phenomenon helped establish that electromagnetic radiation can transfer energy in discrete amounts.

Einstein's photoelectric equation

hf = φ + Kmax

φ is the work function of the material and Kmax is the maximum kinetic energy of an emitted electron.

Matter waves

The wave-particle idea applies not only to light. Moving particles can also exhibit wave-like behaviour.

de Broglie wavelength

λ = h/p

λ is wavelength, h is Planck's constant, and p is momentum.

Atomic physics

Atoms consist of a compact nucleus surrounded by electrons. Modern atomic physics explains how electrons occupy allowed energy states.

Energy levels Electrons in atoms can occupy specific allowed energy states.
Emission An atom can emit electromagnetic radiation when an electron moves from a higher energy state to a lower one.
Absorption An atom can absorb energy when an electron moves to a higher allowed state.

Nuclear physics

Nuclear physics studies atomic nuclei and the interactions that determine their stability.

Protons Positively charged particles found within the nucleus.
Neutrons Electrically neutral particles found within the nucleus.
Isotopes Atoms of the same element with different numbers of neutrons.

Radioactivity

Some unstable nuclei spontaneously transform into other nuclear states while emitting radiation.

Alpha radiation Consists of helium nuclei and has relatively low penetrating ability.
Beta radiation Consists of high-speed electrons or positrons produced during certain nuclear transformations.
Gamma radiation High-energy electromagnetic radiation emitted by nuclei.

Half-life

The half-life of a radioactive substance is the time required for half of a given population of unstable nuclei to decay.

Radioactive decay

N = N₀(1/2)t/T₁/₂

N is the remaining quantity, N₀ is the initial quantity, t is elapsed time, and T₁/₂ is the half-life.

Fission and fusion

Nuclear fission A heavy nucleus splits into smaller nuclei and can release a large amount of energy.
Nuclear fusion Light nuclei combine to form a heavier nucleus while releasing energy under suitable conditions.

Quick example

Apply the idea

A radioactive sample has a half-life of 4 hours. If its initial amount is 80 units, how much remains after 8 hours?

After one half-life:

80 → 40

After two half-lives:

40 → 20

Answer: 20 units remain after 8 hours.