Key Defintions Flashcards
Precise
Multiple measurements with the same or very similar results.
Accurate
How close a measurement is to the true value.
Systematic Error (what is it)
An error of measurement due to readings that systematically differ from the actual value (follow a pattern, trend or bias)
Systematic Error (defining features)
Poor accuracy
Definite causes
Reproducable
Cannot be eliminated with a mean
Random Error (what is it)
An error of measurement due to readings that vary randomly (or have an outlier) with no recognisable pattern, trend or bias.
Random Error (defining features)
Poor precision
Nonspecific causes
Not reproducable
Can be reduced by calculating a mean.
Elastic Behaviour
Deforms when force is applied, returns to original shape when force removed
Plastic Behaviour
Deforms when force is applied, does not return to original shape when force removed
Brittle
Breaks through cracks/fracture propagation (little/none plastic deformation)
Ductile
Undergoes plastic deformation under tensile forces
Malleable
Undergoes plastic deformation under compressive forces
Tough
Can absorb a lot of energy (by plastic deformation) before breaking
Hard
Resistance to scratching
Stiff
Requires lots of force for a little amount of deformation
Strong
Requires large forces to break
Hooke’s Law
For a material behaving elastically, the extension/compression is proportional to the force applied
Ionic Bonds
Strong bonds formed by the transfer of electrons between atoms
Covalent Bonds
Bonds that hold atoms together in molecules, formed by the sharing of electrons.
Metallic Bonds
Some electrons loosely held and not tied to particular atoms.
A metal is effectively made up of +ve ions in a sea of -ve electrons.
Hydrogen Bonds
Weak bonds which hold together adjacent molecules (such as water) through electrostatic attraction between the slightly +ve oxygen and slightly -ve hydrogen of adjacent molecules
Crystalline
Atoms bonded w/ a regular arrangement extending in all three spatial directions
Polycrystalline
Made up of many interlocking crystals
Atoms bonded in a ‘regular’ structure
Boundaries between separate interlocking grains
Amorphus
Atoms bonded w/out irregular structure
Has regions of weakness, brittle
Toughness
Can be indicated by the energy absorbed before breaking, per unit cross-sectional area
1D defect
Point Defect
Types of defect (1D)
Vacancy
Interstatial Impurity
Substitution Impurity
2D defect
Line Deformity
Types of defect (2D)
Edge Dislocation
Line defects often ____ under stress due to _____. This leads to ___ and will continue until ___.
Migrate
Breaking and reforming of bonds
The plastic flow of deformations
The line defects reach the grain boundary and build up
Charge Carrier Density
The number of free conduction electrons per m^3 of material
m-^3
Charge Carrier Density of an Insulator
approx. 10^7 m^-3
Charge Carrier Density of a Conductor
approx. 10^28 m^-3
Semi-Conductor
materials who’s conductivity changes depending on outside conditions
Metal
Consists of a single element or a blend of elements (alloy)
Metal properties
Tend to be good conductors (heat + elec)
Tend to be strong, stiff and tough
Generally hard, malleable and ductile
Ceramic
Chemical compound (often oxides or nitrates)
Often formed by mixing a starting material with water, shaping and then firing to harden
Ceramic Properties
Generally inert with high melting points
Generally very strong and stiff
Usually hard and brittle
Polymer (Definition + general property)
Organic compound made of long chain molecules
Typically strong and flexible
Thermoplastics (Polymer)
Easily moulded into desired shape when warm (can be remelted and shaped)
Thermosets (Polymer)
Hard and brittle, difficult to shape after polymerisation (even if heated)
Composites
Combine desirable properties of different component materials
Limit of Proportionality
Up until this point a material behaves as a regular elastic solid
Yield Point
Denotes the onset of plastic deformation
Yield Strength
The stress at which an object starts to plastically deform. This is at the Yield Point
Wavelength of Gamma Radiation
Less than 1 pm
Less than 1*10^-12 m
Wavelength of X-Rays
Between 1 pm and 1 nm
Between 1 *10^-12 m and 1 *10^-9 m
Wavelength of UV
Between 1 nm and 400 nm
Between 1 *10^-9 m and 400 *10^-9 m
Wavelength of Visible
Between 400 nm (purple) and 750 nm (red)
Between 400 *10^-9 m and 750 *10^-9 m
Wavelength of Infrared
Between 750 nm and 2.5 μm
Between 750 *10^-9 m and 2.5 *10^-6 m
Wavelength of Near Infrared
Between 2.5 μm and 25 μm
Between 2.5 *10^-6 m and 25 *10^-6 m
Wavelength of Microwave
Between 25 μm and 1 mm
Between 25 *10^-6 m and 1 *10^-3 m
Wavelength of Radiowave
Greater than 1 mm
Greater than 1*10^-3 m
Wavefronts after focussing are ____.
Curved
n.b. lenses add constant curvature
Lens Power
The curvature a lens adds to the wavefronts, measured in dioptres (D)
Focal length =
Radius of Curvature (r)
Convex Lens w/ a very distant object
Image at focal point
Convex Lens w/ object beyond focal point
Image visible (no specific place, depends on distance)
Convex Lens w/ object at focal point
Very distant image
Convex lens, object > 2f
Image -
Real
Inverted
Smaller than object
Convex lens, f < object < 2f
Image -
Real
Inverted
Larger than object
Convex lens, object = 2f
Image -
Real
Inverted
Same Size
Convex lens, object < f
Image -
Virtual
Upright
Larger than object
Smoothing an Image
Apply a mean filter to each pixel
(replace each pixel by the mean of it and its 8 neighbours)
Noise
False/Random data in an image caused by interferance
Removed using a median filter
Improving Brightness
Add/Subtract a constant value from each pixel
Improving Contrast
Multiply by a particular factor
You want the pixel values to be spread across the whole range (light becomes lighter, dark becomes darker)
Edge detection (Laplace Rule)
Enhances edges in an image (highlight regions with an abrupt change of brightness)
Subtract the N, E , S and W vals from 4 * the pixel val
If no edge but is a gradient, it simply smooths
Transverse wave
Oscillations are perpendicular to the direction of the wave
Polarised Light
The wave only oscillates in one particular direction. Produced by polarising filters or reflection and is made of EM waves
A grill is aligned perpendicular to a polarised wave
Little to no energy loss (before grill vs after)
A grill is aligned at 45° to a polarised wave
Some energy lost
A grill is aligned parallel to a polarised wave
Most/All energy lost
What happens when light reflects off a surface at a suitable angle?
The oscillations of the electric fields become restricted to a direction parallel to the plane of the surface.
Unpolarised light
Has oscillations in many directions. Is produced by the Sun and most lightbulbs and is made of EM waves
Analogue signal
Continuous signals that can have any value between a maximum and a minimum. Likely to pick up noise which affects signal quality
Attenuation
A gradual loss of intensity (or amplitude) of a signal
Digital signal
Has only two values, 0 and 1. Due to this, if noise is picked up, the signal quality is not affected. They can be changed/scrambled/interrupted significantly easier than analogue.
Nyquist Theorem
For a signal to be represented well:
Sampling Frequency > 2 * smallest important freq change
Sampling Frequency > 2 * highest freq
Levelling
The conversion of an analogue signal to a digital signal through sampling
Shannon’s Criteria
A formula to find the number of bits per sample required to adequately translate Analogue -> Digital
Transmission Rate
The amount of information sent per second
Electric Current
‘rate of flow of charge’
the amount of charge passing a certain point in the circuit each second
Coulumb
‘The total charge passing a point when a current of 1 Amp flows for a time of 1 second’
Ammeters
Measure the amount of charge flowing through a point in a circuit each second. Must be in series.
Voltmeter
Compares the energy of charge carriers before and after the component. Must be in parallel.
Resistance
The opposition to current for a given p.d.
Ohms Law
For a fixed resistor at a constant temperature, the current through the resistor is directly proportional to the p.d. across it.
Conductance
The inverse of Resistance
Kirchoff’s First Law
The total current entering a junction is equal to the sum of currents leaving the junction
Rheostat
Electrical instrument used to control a current by varying the resistance
Diode
Unidirectional component. Large amounts of current can only flow in one direction (eg A to B). Little/no current can flow in the other direction (eg B to A)
Thermistor
A resistor which resistance changes depending on the temperature it is at.
Thermistor - PTC
as temp increases, resistance increases
Thermistor - NTC
as temp increases, resistance decreases
Competing effects in a thermistor
Heat up causes greater lattice ion vibrations - resistance up
Heat up releases more electrons, so more current - resistance down
LDR - light dependant resistor
High resistance in standard conditions. When illuminated, electrons are released - resistance down
Calibrated
Correlating the readings of an instrument with known readings in order to check accuracy of instrument
Response Time
The time it takes for a sensor to respond to a change in outside conditions
Sensitivity
The change in reading on the instrument per unit change in outside condition
Resolution
The smallest change an instrument can detect
Electromotive Force (EMF)
Energy per unit charge transferred into the circuit at the power supply. ε
Energy gained per unit charge by the charge carriers in a circuit
Internal resistance
The resistance of the power supply.
Treated as an extra resistor in series with the external circuit
Terminal p.d.
The sum of the p.d. of all the load resistors. Always less than EMF because of internal resistance (not included in ‘load’ resistors)
Longitudional
The oscillations are parallel to the direction of motion
Amplitude
Maximum displacement of a wave
Frequency
The number of oscillations that occur each second
Displacement (wave)
Distance of a point on a wave from its position of equilibrium
Compression (wave)
Lots of particles in a set area
Rarefaction
Very few particles in a set area
Wave Speed
The speed at which energy is transmitted by a wave
The speed at which a wave front propagates
Coherent
Two waves with the same frequency, same wavelength and a constant phase relationship
Superposition
Two waves meeting and combining. Their displacements add together
Constructive Superposition (coherent)
When two coherant waves meet and combine (and are in phase), the displacements add together.
(a +ve displacement plus a +ve displacement or -ve plus -ve)
Destructive Superposition (coherent)
When two coherent waves meet and combine (and are antiphase) the displacements subtract.
(a -ve displacement plus a +ve displacement or +ve plus -ve)
Incoherent waves or not antiphase waves superposing
Can get very complex as can end up with a mix of constructive or destructive
When does a standing wave form
When two progressive waves of the same frequency and wavelength travel in opposite directions and superpose
Node (standing wave)
A place where the waves always meet in antiphase (undergo destructive superposition). They are always stationary on the middle line
Antinode (standing wave)
A place where the waves always meet in phase (undergo constructive superposition). They are always at the same point but can be max +ve or max -ve (two different wave forms)
Phase difference
The difference in phase (or angular difference) between two points on a wave (or the same point on two waves)
In phase
One complete cycle apart (0° or a multiple of 360°)
Can be written in radians
Antiphase
A half cycle out of phase (a multiple of 180° excluding multiples of 360°)
Out of Phase
Not in phase or antiphase.
Diffraction
The spreading out of a wave into a ‘shadow region’ as the wave travels through a gap or past a barrier
When does the greatest diffraction occur
When the gap/barrier is the same as the wavelength of the incident wave
Interference
Occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave. Often occurs after diffraction
What colour of light diffracts the most/least?
Red diffracts most and violet the least as red has a longer wavelength
What happens when white light is diffracted
Different wavelengths of light separate out as they are diffracted different amounts
Single slit diffraction
Produces a fringe pattern, central fringe is much brighter + 2x the width of the other fringes
Double slit diffraction
Fringe intensity is max at n = 0
The intensity decreases symmetrically as n increases
All fringes are a uniform thickness
Diffraction grating diffraction
Fringes have a similar intensity
Fringes are symmetrical about n = 0
Fringe width < distance between fringes
Fringes equally spaced
Total Internal Reflection
Occurs when the angle of incidence exceeds the critical angle
Path length
The difference between a wave source and a point in space
Often measured in multiples of λ
Path difference
The difference in path lengths between two sources to the same point.
What happens when a wave is transmitted from low - > high density medium
Wave speed decreases
Wave length decreases
Frequency remains constant
Refraction
The bending of light as it hits a boundary between two media of different optical densities at an angle
Refractive Index
The ratio of the speed of light in the first medium to the speed of the wave in the second medium
Absolute refractive index
The ratio of speed of light in air (or a vacuum) to the speed of light in the medium
Charge carried by one electron
1.6 * 10^-19 C
Electrons in 1 C of charge
6.3 * 10^18 electrons
Capacitor
Stores charge (and therefore pd) on parallel conductive plates, separated by an insulating layer (dielectric)
Radioactive decay is ___
Random
Exponential
Spontanious
Radioactive decay (Spontaneous)
Is not affected by external conditions
Radioactive decay (Exponential)
The rate of decay is proportional to the number of radioactive (parent) isotopes present
Radioactive decay (Random)
Can’t predict exactly when each nucleus will decay
Can give a probability it will decay in a fixed time interval
The photoelectric effect
The emission of electrons from the surface of a material due to the exposure of a material to EM radiation
Threshold Frequency
The minimum frequency of the EM required for a specific material to undergo the photoelectric effect.
Intensity and the photoelectric effect
Once the threshold frequency has been reached, the higher the intensity the more electrons are released from the surface of the material
Frequency and the photoelectric effect
Once the threshold frequency has been reached, the higher the frequency the higher the maximum KE of the emitted electrons.
Key Problems with Wave Theory (photoelectric effect)
Threshold Frequency - All frequencies should have eventually caused emission (but didn’t)
Increase in Intensity - Should have increased emissions for all frequencies, not just those above threshold
The metal should not have immediately released electrons, it should have taken time (esp on lower frequencies)
Photon
A quanta of light
Intensity
energy arriving per m^2 of area per second
Intensity is proportional to
Number of photons arriving each second - as a particle
Amplitude^2 - as a wave
An increase of intensity (photoelectric effect)
Increases the number of photons each second - increases the number of photoelectrons leaving the metal each second (if above threshold freq)
Work Function, Φ
The minimum energy required to release an electron from the surface of a metal (y-intercept)
Planck’s constant
Used to calculate the energy of a photon (can be found using the gradient of a KE (eV) and frequency graph)
How do LED’s work
Photons are released when electrons cross the p-n junction to fill layers in the p type layer. The plastic shell covering the LED directs the photons outwards.
N-type layer
The impurities mean that there is a surplus of electrons
P-type layer
The impurities mean that there is a deficit of electrons
Striking voltage
The minimum voltage required to have electrons flow of across the p-n junction. Also related to the wavelength of the photon emitted as the electron drops back to ground state when it passes through the p-n junction
Ground state
When an electron is in its lowest possible energy level
Excited state
When an electron is at a higher energy level than its ground state - happens to outermost electron first
How do electrons move between energy levels
Absorbing/emitting the energy from a single photon
Emission Spectra
A representation of the different discrete photon energies emitted when the electrons of an element drop down from an excited state
Absorption Spectra
A representation of the different discrete photon energies absorbed by the electrons in an element (they become excited)
Diffraction inside a material
Will occur when electron waves have a similar wavelength to the spacing between atoms in a material
de Broglie equations
Link wave behaviour and particle behaviour
Resultant force
The sum of all the forces acting on the body
Newton’s First Law
“An object at rest remains at rest and an object in motion remains at a constant velocity unless a resultant force acts”
INTERTIA
Newton’s Second Law
“The acceleration of an object is directly proportional to the magnitude of the resultant force (in the same direction) and inversely proportional to the mass of the object”
F = ma
Newton’s Third Law
“If body A exerts a force on body B, then body B exerts an equal size force in the opposite direction on body A”
Newton’s Third Law 5 Key Rules
Same type of force
Same magnitude
Act along the same line of motion
Act in opposite directions
Act on two different bodies
Ideal collision
Momentum is conserved - provided no external resultant force acts
Elastic collision
All KE is conserved
Inelastic collision
KE is not conserved, momentum is
The Law of Conservation of Momentum
“The total momentum of a system before an interaction is the same as the total momentum after”
Work done
The energy transferred to or from an object via the application of a force along a displacement
Electron Diffraction (not observed)
They form diffraction patterns as they are behaving as a wave (wave function). As the electron can theoretically take any path to get to its destination, diffraction patterns are seen. The high probability areas form bright fringes and low probability areas form the gaps between.
Electron Diffraction (observed)
Observation collapses the wave function, and the electrons behave as particles. They can only accept one probability, and particle like behaviour is the most likely.
Scalar
Has a magnitude but no direction
SHM
Simple Harmonic Motion is when a body oscillates about a fixed point (equilibrium).
Ideal SHM
The periodic time is constant
When does SHM occur
When a body is oscillating about a fixed point (equilbrium)
A restoring force must always act on the body towards equilibrium. The size of the restoring force is proportional to the displacement from equilibrium.
Damping
A decrease in the amplitude of oscillations due to a loss of energy to the surroundings.
The amplitude decreases due to damping is _____, because ____
Exponential
The amplitude decreases by the same factor (or ratio) with each successive cycle.
Energy can be lost by _____. (SHM)
Hysteresis of elastic
Plastic deformation of materials
Friction/Air-resisitance
Free Oscilation
No external force acting on the system (aside from the intial force)
Forced Oscillation
Oscillations affected by a periodic driving force from outside the system
Natural Frequency
The frequency at which a system oscillates when no external forces act
Resonate
An increase of amplitude which occurs when the frequency of the driving oscillator is similar to the natural frequency of the oscillator
Damped forced oscillations
Max amplitude of the forced oscillations decreases
The frequency at which the max amplitude occurs decreases
The peak gets less sharp and wider
Ground resonance
When rotating or oscillating machines are in contact with the ground and improperly damped, they can resonate and oscillate dangerously. This can destroy the oscillator and the machine it is attached to.
Base Isolation Systems
Used to damp earthquake oscillations. Decoupling the building from the ground using deformable dampers or ball bearings. This means the ground vibrations are inefficiently transmitted to the building
Centripetal force
A resultant force acting towards the centre of a circle, causing the object to accelerate towards the centre of the circle. Acts at a right angle to the path of the circles motion. Not a ‘true’ force, caused by another identifiable pheonomenon.
A field
A region of space where a force acts on an object
A gravitational field
A region in space where a gravitational force acts on an object with mass
Gravitational field strength, g
The force acting per unit mass.
Multiply by mass to get Force in a gravitational field, F
The area under the graph of it against r will give gravitational potential, Vg
Gravitational Potential, GP
The work done in moving a unit mass from infinity to a point in the field
Multiply by mass to give GPE, Eg
The gradient at a point of a graph of it against r will give gravitational field strength, g
Gravitational Potential Energy, GPE
The work done in moving an object from infinity to a point in a field
Divide by mass to give GP, Vg
The area under of a graph of it against r gives the Force, F
Force, F (gravitational fields)
The force between two point masses
Divide by mass to give gravitational field strength, g
The gradient at a point of it against r will give gravitational potential energy, GPE
The direction of the gravitational force is ______.
Opposite to the direction of the displacement as gravity is an attractive force
Kepler’s Laws (1)
All planets have an elliptical orbit, with their star at one focus of the elipse
Kepler’s Laws (2)
A line joining the planet to the sun sweeps out equal areas in equal times
Kepler’s Laws (3)
The period of orbit is related to the average distance from the star.
T^2 α r^3
Escape Velocity
The speed at which an object must be travelling to overcome the gravitational attraction of a planet. Found by the area between the curve and the axis on a g-r graph.
Object KE > GPE at surface (or point in field)
Equipotentials
A line joining all points in space w/ an equal gravitational potential
Polar Orbiting
Orbits in a N-S direction
Orbit takes ~2hrs
Can view many swathes of the Earth as it rotates
Often used for things like weather
Geostationary Orbit
One orbit in 24 hr
Satellites remain above the same point on Earth at all times
Almost always equatorial
Used for things like GPS
RADAR
RAdio Detection And Ranging
Uses EM waves to measure the distance to an object
World Line
A line plotted onto a space-time diagram (shows how an object’s displacement varies with time)
Doppler effect
The apparent change in wavelength or frequency of a wave when the source moves relative to the observer
Doppler effect - towards the observer
The frequency appears to increase and the wavelength appears to shorten
Doppler effect - away from the observer
The frequency appears to decrease and the wavelength appears to lengthen
Paralax
The apparent change in position of an object relative to a fixed background when viewed from a different angle - can be used to approximate distances to nearby stars
1 AU
The mean distance between the Earth and the Sun (1.496 * 10^11 m)
Disadvantages of Parallax
Parallax angles are VV small
Due to the resolution of modern instruments, we can only use it on nearby stars
Parsecs (pc)
The distance to a point in space where the parallax angle is 1 arc-second (3.09 * 10^16 m)
Standard Candles
Objects of a known luminosity
Cepheid Variables
The luminosity of these stars vary periodically (the period is directly related to the luminosity). This means we can use distant Cepheid Variables to estimate distances to far away galaxies (using its period to estimate its luminosity and then use that to estimate distance)
Supernovea
Exploding stars that form when as star runs out of fuel for fusion, contracts and then explodes
Aether
The medium it used to be believed that light travelled through.
Einstein’s First Postulate
The laws of physics are the same in all inertial frames of reference
Einstein’s Second Postulate
The speed of light is constant, regardless of the relative motion of the source and observer.
Time Dilation
The concept that time is observed differently for objects with differing relative motion (eg stationary vs moving)
Why does time dilation occur
Because the speed of light cannot vary, the time it takes for the light to cover a distance must APPEAR to change. Time in the ‘slower’ perspective moves slower
The Lorentz Factor
The faster an object moves through the space, the slower it moves through time
Used to calculate relativistic effects
Length Contraction
Where distance is measured differently the faster an object is going.
The faster it goes, the smaller the length
Logarithmic Scale
Increases by a common multiple not by a common value.
- Encompasses a wide range of values
- Difficult to interpolate between scale markers
- Negative values and 0 cannot be represented
Cosmological Redshift
Galaxies aren’t moving away from us, the space between is expanding (stretching)
This stretches the wavelength
Key Assumption for Hubble’s Constant
That the recessional velocity of the galaxy has been constant all throughout history
CMBR (four key points)
Cosmic Microwave Background Radiation
-Radiation sourced from deep space
-Part of the Big Bang
-Comes from the universe itself (not any objects w/in), sources from behind the stars
-Is microwave by the time it reaches Earth
Era of Recombinition
The plasma of the early universe cooled down enough for electrons and protons to form atoms of hydrogen.
CMBR was released at this point (λ = 1mm)- the universe became transparent
300,000 yrs after the Big Bang
Temp is 3000K
What is CMBR evidence of?
That the universe was once much hotter
The universe is 1000x bigger than it used to be
The early structure of the universe was very uniform w/ only very slight temp + density variations
Specific Heat Capacity
The energy required to increase the temperature of 1kg of a substance by 1K
Conduction
Kinetic Energy (vibrations) of atoms are passed to adjacent atoms, transferring energy through a solid
Radiation
The transmission of heat from waves resulting from disturbances in a particle’s electric field as it vibrates
A good conductor
Has lots of conduction electrons which are able to efficiently move through the solid and transfer energy when they collide with metal atoms
The amount of radiation emitted depends on? (Heat)
Temperature (KE of particles)
- 0K = 0 vibrations = 0 radiation
Surface Area of an object
Type of surface
- Dull/Dark are good emitters + absorbers
- Shiny are bad emitters + absorbers
How does temperature affect the nature of the radiation emitted? (Heat)
The higher the temp, the greater the amount (intensity) of radiation and the higher the frequency of the radiation emitted (VV hot objects glow)
Convection
The transfer of heat energy by the motion of fluids (liquids/gases) due to difference in density. Can be gravity or pressure driven
Pressure (gas)
Caused by the molecules colliding with the sides of their container
The Kinetic Theory of Gases (4 Key assumptions)
Attraction between molecules is negligible
Volume of molecules small compared to volume of container
Molecules behave as elastic spheres (KE conserved)
Duration of the collision is much less than the time between collisions
Brownian Motion
The erratic motion of small particles - provides evidence for the existence of molecules in gas or liquids.
Three ways to increase gas pressure
Put more molecules in the container
Decrease volume of the container
Increase the average energy of the molecules
Mean Square Speed
Directionally proportional to the temperature. If the temp doubles the mean square speed doubles and the root mean square speed increases by a factor of √2
Two gases at the same temp
Their molecules have the same average KE.
At a fixed temp, if the molecules have a larger mass their average speeds will be lower. Inversely proportional to the mean square speed
Internal Energy of an Ideal Gas
The sum of kinetic and potential energies of the particles in the gas.
However, potential energy is 0 in an ideal gas as there is no/negligible interactions between particles
How does gas pressure change with volume? (Kinetic Theory)
If the volume is decreased, a greater number of molecules hit the inside of the container per second. Therefore a greater force will be exerted, which means a greater pressure.
This works in reverse for an increase in volume.
How does gas pressure change with temperature? (Kinetic Theory)
If the temperature is increased, molecules will be moving at greater speeds so more molecules will be hitting the side of the container per second. This means a greater force will be observed and therefore a greater pressure.
This works in reverse for an decrease in temperature.
Temperature
A measure of the average amount of energy that particles have
Particle energy: E ≈ kT
Activation Energy
Minimum energy threshold for a reaction to take place
Examples of processes where activation energy is key
Chemical reaction
Nuclear fusion
Semiconductors
Why do all particles of a gas at a given temp not have a KE equal to the ave value?
Particles move at random, colliding frequently. On each collision, energy is exchanged at random between the two particles. Some will gain over several collisions (more energy than ave) and some will lose over several collisions (less energy than ave).
The Boltzmann factor
The ratio of the number of particles in two different states
OR probability of a particle having activation energy ε in an environment of temperature T
When does the particle energy = the activation energy
When the Boltzmann factor is e^-1 (0.37)
Magnetic Field
A region of space which a force acts on:
- The poles of a magnet
- A current carrying conductor
- Moving charged particles
Ways to increase the Field Strength of a circular iron core (3)
Increase the current
Increase the number of turns on a coil
Have a shorter circular core (smaller core)
Right Hand Thumb Rule
Thumb in direction of wire (and current)
Fingers show direction of the field
Solenoid
A coiled electrical conductor given a magnetic field by an electrical current
Current flows from
Positive to Negative
Magnetic Flux Density, B
A measure of magnetic field strength
Tesla, T OR Webers per m^2, Wbm^-2
Magnetic Flux, Φ
The total flux intersecting at a given surface OR
“the product of the flux density and area of surface where the magnetic field lines intersect”
Weber, Wb
Magnetic Flux Linkage
“The product of the flux and the number of turns in the coil”
permittivity, μ
How well the core material transmits the magnetic field
The extent to which a medium concentrates lines of electrostatic flux (Fm^-1)
What happens if a crack/air gap forms in a core
The permeance of the circuit decreases
There will be less flux for the given number of turns
Fleming’s Left Hand Rule
Thumb - Direction of Force (F)
Pointer finger - Magnetic Field (B)
Middle finger - Current (I)
Testing F = BIL
A current is passed through a conductive metal rod clamped tightly and held suspended in a magnetic field
The magnet is placed on an electric balance
The rod experiences a force due to the magnetic field
The magnet experiences an equal size force in the opposite direction. (If the force on the rod is upwards, the force on the magnet is downwards and vice versa)
DC motors
Use a commutator to ensure that the current on one side remains in a constant direction.
The current through the coil switches direction every time the coil rotates through the vertical axis.
This means the direction of force remains constant and the turning force is maintained
Electromagnetic Induction
Generating an electromotive force (EMF) by moving a conductor relative to a magnetic field
Induction
The generation of EMF by forcing conductors to cut through lines of magnetic flux
Flemming’s right hand rule
(When a conductor is moved in a field)
Thumb - Direction of Motion
Pointer Finger - Direction of magnetic field
Middle Finger - Direction of induced current
Lenz’s Law
“The induced EMF is in a direction that opposes the change causing it”
Faraday’s Law
“The EMF induced in a circuit is directly proportional to the rate of change of flux through the circuit”
Transformers (Current turned on in input circuit)
Induces a B field in core.
Flux changes from zero to a value
Change in flux induces an EMF in the output coil
Transformers (Current turned off in input circuit)
Flux changes from a value to zero
Change in flux induces and EMF the output coil (in opposite direction)
Transformers (No change in current - constant)
No change in flux, so no EMF induced in output coil.
What type of current do transformers work with? Why?
They only work with AC. This is because they need a constantly changing mag flux through the secondary current in order for them to work and for EMF to be induced.
How to vary output p.d. for a given input (Transformers)?
Change the number of turns on the coil
Change the frequency at which the AC supply alternates
Energy loss from a transformer
Energy may be lost through:
- Heat/Sound
- Power lost in coils (in order to minimise this use materials w/ low resistivity)
Eddy Currents
Form in the core of a transformer. As the mag field forms, they form at right angles to the mag field.
They are loops of electrical current induced by a changing magnetic field (flow in closed loops w/in conductors)
Reducing eddy currents
If a core is laminated parallel to the field then this limits the size of eddy currents and therefore the energy lost to them.
What happens when a magnet falls through a copper tube?
As the magnet falls, the flux cutting the copper tube changes
This induces an EMF in the copper tube
As copper is a conductor, eddy currents form in the tube (which induce their own magnetic field)
As per Lenz’s Law, the current flows in a direction that will generate a mag field that opposes the falling of the magnet
This provides an upwards force on the falling magnet, which reduces its rate of fall (slows it down)
How does a Speaker work?
AC occurs in coil - signal has same profile as the soundwave that will be produced
Changing current causes the coil to experience a force and oscillate w/ the same profile as the current
Causes the diaphragm to vibrate w/ the required frequency + amplitude to produce the sound
How does a Microphone work?
Soundwaves hit the diaphragm and cause it to vibrate
This makes the coil oscillate up and down in the magnet
This induces an EMF w/ the same signal (frequency + amplitude) as the soundwaves
Electric Field
A region of space within which charged particles feel a force
What affects the size of the force experienced?
The electrical field strength
The particle charge
Electrical field strength
The force acting per unit charge at that point
Units NC^-1 or Vm^-1
Potential Difference
Work done per coulomb of charge
Electric Potential
Work done in moving a unit positive charge from infinity to a point in an electric field
Electrical fields on a charged particle
The direction in which the force acts on a +ve charge (-ve experience force in the opposite direction to the field lines)
Uniform Electric Fields
A field in which the value of the field strength remains the same at all points
Equipotential (electric fields)
Lines of equal electric potential (at a right angle to the field lines)
What must be overcome to allow fusion?
The repulsive force between nuclei. In the suns core it must be Thermal Energy that overcomes the electrostatic potential energy and allow fusion to occur.
Millikan’s Oil Drop
Atomiser used to spray tiny droplets of oil (which are negatively charged due to an x-ray source stripping them of electrons) into the space between two parallel plates.
The pd between the plates is adjusted until the majority of the droplets are suspended between them
The weight of the droplet is equal to the force pulling the droplet upwards
The charge on the droplet is then calculated. Only discrete values of charge were calculated, and the lowest common denominator was the charge on the electron.
How does an electron gun work?
Through thermionic emission.
A metal filament is heated by passing a current through it. As it gets hotter the thermal velocity of the conduction electrons increases.
This then increases the chance of an electron escaping from the positive ions in the metal lattice
Linear Accelerator (LINAC)
Electrons are fired from an electron gun and accelerated by an electric field. They are then focused into a narrow beam by a small hole in the anode.
The are then accelerated through drift tubes of alternating charges until they reach their target.
They are accelerated in a straight line.
How does a Drift Tube work?
An electron accelerates towards a positively charged tube. When it enters the tube and passes through it, it is unaffected by the electric field and neither gains or loses velocity.
As it exits the tube, the charge switches and it accelerates away from the negative tube and towards the next +ve tube.
An AC current is used to alternate the charge on the tubes
Why do adjacent drift tubes increase in length?
AC changes the charge in a fixed frequency (and therefore time period).
As the electron accelerates it takes less time to pass the same distance, so the tubes must be longer in order to be in sync with the changing current.
Deflection of electrons
Fleming’s left hand rule
The higher the mass, the smaller the deflection for the same charge, field strength and distance
How does a cyclotron work?
Two metal “Dees” are attached to an alternating pd (they sit between two poles of a magnet, one above and one below)
Charged particles are released between the Dees and accelerate across the gap due to the electric field
The mag field causes a spiral path of increasing radius (as velocity increases)
The voltage alternates in step with the frequency of rotation of particles, keeping everything synchronised
Advantages of a cyclotron
Compact and efficient
Disadvantages of a cyclotron
Strong uniform mag field is needed, difficult to control
At high energies, relativistic effects come into play
- mass does not remain constant, so the particle becomes out of synch with the dees
Syncotrons
A cyclic particle acceleration that uses the concepts of both the LINAC and cyclotron to accelerate charged particles
Acceleration chamber (sycotron)
Uses electric fields to accelerate the particles
The frequency of voltage oscillation must be changed to synchronise with with the arrival of particle bunches at decreasing time intervals
Bending chamber (syncotron)
Uses mag fields to create a centripetal force
To maintain a circular path of constant radius, the mag field has to increase
Particle tracks
Charged particles moving through a vapour/liquid leave a chain of ionised particles on which bubbles/condensates can nucleate
Detectors are placed in uniform magnetic fields, allowing us to infer a number of things from the particle track
Tells in a particle trail
Direction - charge on particle (flemmings LH rule)
Radius - momentum on particle
Thickness - relates to speed (slower = thicker)
Thickness - Relates to ionising power
Length - relates to life of particle
Atomic Number (Z)
The number of protons in the nucleus
Nucleon/Mass Number (A)
The total number of nucleons in the nucleus
Neutron Number
The number of neutrons in the nucleus
Isotope
Same atomic number, different mass number
(same protons, more/less neutrons)
JJ Thompson
Discovered electrons using cathode ray tubes - proved atoms are not most fundamental particle
James Chadwick
Discovered the Neutron
Rutherford, Geiger and Muller
Discovered vast majority of mass and all +ve charge is concentrated in nucleus of atom
Rutherford’s Alpha Particle Scattering Experiment
Prev atomic models said small spheres of -ve charge suspended in +ve charge (Plum Pudding)
Alpha particles where fired at a thin sheet of gold foil with a phosphor around.
Some deflected as expected (small/no change)
Around 1/8000 deflected over 90°, which defied plum pudding model
Rutherford Scattering
Also known as Coulomb Scattering and Elastic Scattering
Relies on static electric (coulomb) forces
The distance of closes approach is set by this and the speed of incoming particles
Energy + velocity of outgoing scattered particles is the same as the energy + velocity they started with
The deflection of charged particles on a collision course/passing close to a nucleus
Fundamental Particles
Particles that cannot be broken down any further
Approx Diameter of an Atom
1*10^-10 m
Approx Diameter of an Electron
1*10^-18 m
Approx Diameter of a Nucleus
1*10^-14 m
Approx Diameter of a Nucleon
1*10^-15 m
Approx Diameter of a Quark
1*10^-18 m
Anti-Particle
A particle with the same mass but opposite charge and opposite quantum spin.
An antimatter version of a particle
Up Quark
Has a relative charge of +2/3
Down and Strange Quark
Have a relative charge of -1/3
Three main categories of Fundamental Particles
Quarks - include the up and down quarks (are what protons + neutrons are composed of)
Leptons - include electrons and neutrinos
Force Carriers
Photon, γ (Particle Physics)
A force carrier for the electromagnetic force.
Responsible for interactions between charged particles
Range: No Limit
Relative strength: 10^0
Gluon, g (particle physics)
A force carrier for the strong nuclear force
Holds together protons + neutrons in nuclei of atoms
(Holds together quarks to form hadrons)
Range: 10^-15 m
Relative Strength: 10^3
Z boson and W boson
Both are force carriers.
Responsible for radioactive decay of subatomic particles, inc beta decay
Range: 10^-18 m
Relative Strength: 10^-10
Gravity (particle physics)
Responsible for the attraction between objects with mass.
Range: No limit
Relative strength: 10^-34
Has a suspected force carrier called the graviton, but it has not been found as of yet
Hadrons
A combination of bonded quarks
Baryon
Made from thee quarks or three antiquarks
Meson
Made from a quark - antiquark pair
Properties of a Hadron
Charge - Determined by the quarks used
Baryon Number - 1 if a baryon OR 0 if a meson
Strangeness:
“-1” if one strange quark
“-2” if two strange quark (ect)
“1” if one strange antiquark
“2” if two strange antiquark (ect)
Properties that must be conserved under particle interaction
Lepton number
Charge
Baryon Number
Momentum
Mass + Energy (E = mc^2)
Pair Production
The creation of a particle-antiparticle pair from a high energy photon
Pair Annihlation
When a particle-antiparticle pair collide and annihilate, their combined masses convert to two photons
Rest Energy
The energy a particle at rest would produce if converted into energy (E = mc^2)
m = Rest Mass
Particle Energy
The energy associated with a particle in motion.
Atomic Mass Unit, u
Defined as 1/12 of the mass of a carbon-12 atom
1.66 * 10^-27 kg
MeV/c^2 to kg
- 1.610-19 (convert to J/c^2)
/(310^8)^2 (divide by c^2)
Standing wave model
Electrons surrounding a nucleus can be modelled as standing waves trapped in a ‘well’ of potential w/ a fixed width
This model doesn’t quite predict the energy level we actually observe.
It has only ever worked for a hydrogen nucleus
Why do we fire electrons at matter?
To obtain an image of the matter.
Often used to observe structures smaller than the wavelength of visible light.
The greater the momentum the smaller the wavelength and the smaller the resolution
What wavelength allows us nuclei to diffract electrons?
A de Broglie wavelength of approx 10^-15 m
An interference pattern forms as electron waves pass either side of the nucleus
How was the structure of the proton determined?
Deep Inelastic Scattering of High-Energy Electrons.
At low energies, photons behave as a blur of charge
When high energy electrons are fired at protons, relativistic effects cause it to appear as though the electrons interact with a flat surface with stationary centres of charge
Therefore the electrons deflect as they pass through the proton. A jet of particles are also created in the interaction.
Deep (proton structure)
The electrons are able to penetrate deep inside the hadron
Inelastic (proton structure)
Not all energy is converted in the collision - some energy into mass/new particles
Scattering (proton structure)
Scattering + diffraction pattern suggests 3 points of deflection - three sub particles in proton
High-energy (proton structure)
Have to have high momentum in order to have a short enough wavelength
Decay Constant, λ
The probability a particular nucleus would decay in a unit time
Activity
Number of decay’s per second
Proportional to number of parent isotopes
Becquerel, Bq
Alpha decay, α
2 protons, 2 neutrons
Charge of +2e, mass of 4u
Deflected in magnetic field
Travels slowly (<5% speed of light) - quickly loses energy
Only travels a few cm through air
Absorbed by a sheet of paper
Heavily ionising
Alpha decay equation
parent isotope -> daughter isotope + alpha particle (α)
Beta decay, β
Formed of an electron (or in rare cases a positron)
Charge of -1e, mass of 9.11 *10^-31 kg
Deflected in a magnetic field
Energy ranges between 0.2 and 3.0 MeV (travels up to 99% speed of light)
Less likely to interact w/ air molecules, less ionising, travels further
Does not travel in a straight line (as low mass, deflects easily)
Absorbed by approx 3mm Aluminium
β- decay
Neutrons in the nucleus undergo β- decay, releasing and e- and turning into a proton
parent isotope -> daughter isotope + β- + anti-neutrino
β+ decay
Protons in the nucleus undergo β+ decay, releasing a positron and turning into a neutron
parent isotope -> daughter isotope + β+ + neutrino
Gamma decay, γ
Uncharged, high-frequency EM radiation
Can be diffracted, reflected, refracted and produces interference patterns
Travels at the speed of light
Decreases in intensity w/ distance from a point, inverse square law
Interacts very little w/ air molecules
Unaffected by magnetic fields
Can penetrate several cm of lead
Why does gamma occur?
Occurs when a nucleus is in an excited state and falls to a more stable state, releasing a photon
No particles are lost from the nucleus of an atom
Excited nuclei marked with a *
Half Value Thickness, HVT
The thickness of a particular material that is required to halve the intensity of radiation
N-Z Plots
Plotting the number of neutrons against the number of protons for all known isotopes allows us to estimate the type of radioactive decay an isotope may undergo (or N against Z)
Proton to Neutron Ration
Small nuclei tend to have a 1:1 ratio of neutrons to protons
Larger nuclei tend to have a 1.5:1 ratio of neutrons to protons
Radiation on a Body
When radiation is incident on a body, some is reflected (scattered), some is absorbed and some transmitted
Radiation deposits its energy in matter through ionisation and this takes place in the cells of tissues, giving rise to damage to important molecules
Absorbed Dose, D
Mean energy absorbed per unit mass when exposed to radiation
Equivalent Dose, H
Similar to Gray (absorbed dose), but multiplied by a Quality factor. The quality factor depends on the biological damage done by a particular type of radiation.
Q value for electrons, muons and photons
Q = 1
Q value for high energy protons and neutrons
Q = 10
Q value for Alpha particles (and other atomic nuclei)
Q = 20
Radiation Sources (Natural vs Man-Made)
80% Natural Sources
20% Man-Made Sources
Natural sources (% of the 80%)
53% Air (mainly Radon gas)
16% Cosmic radiation (depends on altitude)
20% Terrestrial sources (rocks and soil)
12% Food and Drink
Man-Made sources (% of the 20%)
96% Medical uses
3.9% Consumer goods
0.09% Nuclear Testing/Accidents
0.001% Nuclear Power
The max legal radiation dosage per year?
20 mSv/yr
This is the maximum unavoidable dose (eg background radiation or hazards of a particular job)
Where does all of our energy ultimately come from?
Atomic Nuclei
Energy from sun - Fusion
Nuclear reactors - Fission
Geothermal energy - (mostly) Radioactive Decay
Energy from radioactive decay
During decay, the total mass of the products is slightly less than the total mass of the initial nuclei
Binding Energy
Forces hold the nuclei together, so work must be done to separate a nucleus into individual nucleons
The energy needed to split a nucleus into its nucleons is known as the binding energy
Significance of a high binding energy per nucleon
Isotopes with the highest binding energy require more energy to break apart, therefore are more stable
An elements binding energy can be found by the mass deficit of the atom relative to individual nucleons
When is energy released (radioactive decay)
When light nuclei combine (fusion) or when heavy nuclei split (fission)
This increases the binding energy, creating more stable nuclei, and releasing energy to the surroundings
Fission
Large unstable nuclei (like Plutonium or Uranium) will decay spontaneously (decay can also be triggered by the nuclei being hit by a neutron)
The nuclei splits into two (unevenly sized) nuclei (some neutrons are also released, along with some energy
Energy can be released as radiation, but is primarily released as KE (heat) which allows things like the heating of water to drive turbines
The extra neutrons produced may collide with further heavy nuclei if present, resulting in a chain reaction
What is binding energy often given as?
A negative number
It can be thought of as the energy required to break the break the nucleus apart - to overcome the strong nuclear force. When it is plotted as such, it can be thought of as an “energy valley” with a minimum near iron, nuclei more and less massive than iron will move towards it via fission/fusion
Other names for Fusion
Nuclear Burning
Hydrogen Burning
Nucleosynthesis
The stages of fusion (proton-proton chain reaction)
1) Two protons fuse to form a deuterium nucleus - they need a lot of KE to overcome electrostatic repulsion (2 protons -> 1 proton + 1 neutron + some change)
2) A proton and a deuterium combine together to form a Helium-3 nucleus
3) Two Helium-3 nuclei combine to form a Helium-4 nucleus and two protons
Once all the hydrogen in the core of a star is used, helium burning may begin
