Further Physics: From Atoms to the Universe
Unit 5 brings together thermal physics, nuclear physics, oscillations and the physics of stars and the universe. Many of the ideas are connected by energy, motion and fundamental physical laws.
Energy transfer → microscopic behaviour → oscillatory motion → stars → galaxies → universe.
- Thermodynamics and thermal energy
- Nuclear decay and radioactive processes
- Simple harmonic motion
- Springs and oscillations
- Simple pendulums
- Gravitational fields and orbital motion
- Astrophysics and stellar evolution
- Luminosity and intensity
- Stellar spectra and temperature
- Redshift and cosmology
Thermodynamics
Thermodynamics describes energy transfers involving temperature, internal energy and changes of state.
Internal Energy
The internal energy of a system is the sum of the microscopic kinetic and potential energies of its particles.
where ΔE is the change in internal energy, m is mass, c is specific heat capacity and Δθ is the temperature change.
Specific Latent Heat
During a change of state, energy can be transferred without changing the temperature of the substance.
Here l is the specific latent heat.
Ideal Gas Equation
This relates pressure, volume, amount of gas and absolute temperature for an ideal gas.
A substance of mass 0.50 kg has a specific heat capacity of 4200 J kg⁻¹ K⁻¹. Its temperature rises by 10 K.
ΔE = 0.50 × 4200 × 10
ΔE = 21 000 J
Nuclear Decay
Radioactive decay is a spontaneous and random process in which unstable nuclei transform into more stable configurations.
Activity
Activity is the number of nuclear decays per second.
Exponential Decay
Half-life
Radioactive decay is random for an individual nucleus, but the behaviour of a very large number of nuclei follows a predictable statistical pattern.
Decay Constant
The decay constant λ represents the probability per unit time that a particular unstable nucleus will decay.
Oscillations and Simple Harmonic Motion
Oscillations occur when an object repeatedly moves around an equilibrium position.
Simple Harmonic Motion
In simple harmonic motion, acceleration is proportional to displacement from equilibrium and directed towards equilibrium.
Angular Frequency
Maximum Speed
Energy in SHM
The acceleration must always act towards the equilibrium position and have magnitude proportional to displacement.
Springs and Oscillations
Springs provide a useful physical system for studying oscillatory motion and elastic potential energy.
Hooke's Law
The relationship applies while the spring remains within its limit of proportionality.
Elastic Potential Energy
Period of a Mass-Spring System
Increasing the mass attached to a spring increases the period of oscillation.
From T = 2π√(m/k), the period is proportional to the square root of the mass.
Simple Pendulum
For small oscillations, the period of a simple pendulum depends on its length and the gravitational field strength.
The mass of the pendulum bob does not affect the period in the ideal model.
A graph of T² against l should produce a straight line through the origin for an ideal simple pendulum.
Gravitational Fields and Orbits
Gravitational fields describe the influence of a mass on another mass.
Gravitational Field Strength
Gravitational Potential
Orbital Speed
The orbital speed of a circular orbit depends on the mass of the central object and the orbital radius.
Astrophysics
Astrophysics applies physics to stars, galaxies and other astronomical objects.
Stellar Evolution
A star's evolution depends strongly on its initial mass. Stars spend much of their lives on the main sequence, where nuclear fusion provides the energy that balances gravitational collapse.
- Nebula
- Protostar
- Main sequence
- Red giant or supergiant
- Final stellar remnant
The greater the initial mass of a star, the more rapidly it generally consumes its nuclear fuel.
Luminosity and Intensity
Luminosity is the total power radiated by a star. Intensity describes the power received per unit area.
This is the Stefan-Boltzmann relationship for a star approximated as a black body.
Intensity
As distance increases, the intensity received from a source decreases according to the inverse-square relationship.
Stellar Spectra and Temperature
The spectrum of a star contains information about its temperature, composition and motion.
Wien's Law
Hotter stars have shorter peak wavelengths, while cooler stars have longer peak wavelengths.
Spectral Lines
Absorption and emission lines can be used to identify elements present in astronomical objects.
Spectral evidence allows astronomers to determine physical properties of objects that cannot be directly sampled.
Cosmology and the Expanding Universe
Cosmology studies the origin, evolution and large-scale structure of the universe.
Redshift
When light from a distant object is shifted towards longer wavelengths, the object is described as redshifted.
Hubble's Law
The approximate proportionality between recession velocity and distance provides evidence that the universe is expanding.
Density of the Universe
The average density of the universe is important when considering its large-scale evolution.
Observations such as galactic redshift provide evidence for an expanding universe.
Unit 5 Equation Vault
Click a formula to reveal what each relationship is used for.
Experimental Physics
Unit 5 practical work develops the ability to connect theoretical relationships with real measurements.
- Plan suitable investigations.
- Identify independent and dependent variables.
- Control relevant variables.
- Repeat measurements.
- Calculate uncertainties.
- Plot and interpret graphs.
- Determine gradients.
- Identify anomalous results.
- Evaluate limitations.
- Suggest realistic improvements.
An improvement should directly address a specific limitation of the method rather than simply saying "use better equipment."
Unit 5 Challenge
Test your understanding. Select an answer for each question.
Unit 5 in One Screen
Understand the physics first. Then choose the equation, substitute carefully, track units and interpret the answer in physical terms.