Special Relativity
State Einstein's two postulates of special relativity
(1) The laws of physics are the same in all inertial frames.
(2) The speed of light in vacuum is constant (c) for all inertial observers, independent of the motion of source/observer
Light of wavelength 500 nm strikes a surface. Determine the photon energy in joules and electronvolts?
E= 3.98 x 10^-19 J
E = 2.48 eV
List six quarks
Up
Down
Charm
Strange
Top
Bottom
What are my children's names?
Jasper and Amelia
How many years have I been a teacher?
8
Define "proper time" and "proper length"
Proper time is the time measured by an observer at rest relative to the events (time between events occurring at the same place in that frame).
Proper length is the length measured in the object’s rest frame.
A metal has work function Φ=3.5 eV.
Monochromatic light of frequency 8.0×10^14Hz is incident. Will electrons be emitted? If so what is Ek?
Photon energy = 3.31 eV
3.31<3.5 - no electrons
Name six leptons
Electron
Electron neutrino
Muon
Muon neutrino
Tau
Tau neutrino
State the conservation laws that must hold in particle interactions.
Conservation of lepton number and baryon number
What university does Mr Munro attend
QUT
A spaceship measures a journey time of 5.0 yr onboard. If it travels at 0.60c relative to Earth, determine the time that elapses according to Earth observers.
t=6.25 years
- Discrete spectral lines
- Stability of the atom and why electrons don't radiate energy and spiral into nucleus.
List the four gauge bosons and which force they mediate
Photon - electromagnetic
Gluon - strong force
W+/W- and Z^0 - weak force
Explain the twin paradox briefly and its resolution
Twins: one travels at relativistic speed then returns younger. Resolution: traveling twin experiences acceleration/non-inertial frame during turnaround, so symmetry is broken; proper time along worldlines differs.
Calculate frequency for a photon of energy 2.0×10^−19J.
f = 3.02×10^14 Hz
A rod has proper length 10.0 m. Determine its length measured by an observer if the rod moves at 0.80c.
L = 6.0 m
A photon of energy 4.0 eV strikes a metal of work function 2.2 eV. What is maximum kinetic energy of emitted electrons in joules?
J = 2.884 x 10^-19 J
Differentiate between a baryon and meson. Give an example of each.
Baryons are composite particles of three quarks (e.g. proton uud, neutron udd). Mesons are quark–antiquark pairs (e.g. pion π⁺ = u anti-d).
A spectral line corresponds to energy difference 3.4×10^−19J between levels. What is the wavelength of emitted photon?
wavelength ≈5.844×10^−7 m ≈ 584 nm.
A spacecraft is 4.0 light-years from Earth in Earth frame. It travels at 0.80c. How long does the trip take according to (a) Earth observers and (b) onboard crew?
Earth time = 5 years
Onboard time = 3 years
Explain the relativity of simultaneity with a short example
Events simultaneous in one inertial frame need not be simultaneous in another moving frame.
Example: lightning strikes at two ends of a moving train can be simultaneous in ground frame but not for a passenger on the train.
Describe one experiment or observation that demonstrates wave–particle duality.
Young’s double-slit shows interference (wave), while the photoelectric effect shows quantised photon behaviour (particle). Also single-electron double-slit experiments show interference pattern builds up one electron at a time.
Explain an antiparticle and give two examples
Antiparticle has same mass and opposite charges (quantum numbers) as particle. Examples: positron (e⁺) is antiparticle of electron (same mass, +1e charge). Antineutrino is antiparticle of neutrino (opposite lepton number).
Using conservation laws, show whether the decay p → e++π0 allowed.
Violates baryon number (proton = baryon number of 1, products have baryon number of 0)
Proton decay not allowed in Standard Model
A collection of mesons was observed by a detector to move an average distance of 11.0 m when travelling at 95% of the speed of light. However, based on their properties, the mesons were expected to travel an average distance of 3.4 m.
Explain the difference between the observed and expected average distances.
The expected distance (3.4 m) is based on the mesons’ proper lifetime — the lifetime measured in their own rest frame (Stationary).
In the detector’s frame, the mesons are moving at 0.95 c, and due to time dilation, their internal processes — including decay — appear to occur more slowly.