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A Level Physics

A Level Physics OCR A Unit 5
by

Emily Clark

on 6 June 2011

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Transcript of A Level Physics

Fields, Particles and Frontiers of Physics Atomic Theory Dalton's Ideas
All matter is made up of atoms.
Atoms are indestructable and cannot be divided into smaller particles.
All atoms of one element are exactly alike, but they are different to atoms of other elements.
A given compound always has the same relative numbers and kinds of atoms. Atoms join in whole number ratios.
Atoms are neither created nor destroyed in any chemical reaction.
Dalton believed the atom was a solid sphere. Thomson Model

J. J. Thomson used the cathode ray tube to prove that the atom was made up of electrons.
The discovery would alter Dalton's model.
In addition to the negatively charged electrons, there must be something positively charged because the overall charge of the atom is neutral.
This led to the Plum Pudding model. Rutherford's Scattering Experiment Hans Geiger and Ernest Marsden studied the scattering of alpha particles by thin metal foils. If the Thomson model was right, all the flashes should have been seen within a small angle of the beam. However, Geiger and Marsden observed the alpha particles occassionally scatter at angles greater than 90 degrees. This means the alpha particles are colliding with something more massive than themselves. The Nuclear Model This experiment led Rutherford to some important conclusions:
Most of the fast, charged alpha particles went straight through the gold foil - the atom is mostly empty space.
Some of the alpha particles deflected through significant angles - the centre (the nucleus) of the atom must be tiny but contain a lot of mass.
The alpha particles were repelled back - the nucleus must have a positive charge.
Atoms are neutral overall so the electrons must be on the outside of the atom, separating atoms. Strong Nuclear Force The gravitational force of attraction between two protons is very small. The elctrostatic force of repulsion between two protons is much greater. The protons should repel eachother - the nucleus should not exist. There must be another force acting. Properties:
The strong nuclear force only has a very small range. It is restricted to within nuclei.
It exists between nucleons.
It is independent of charge.
It must bind nucleons together but must be repulsive otherwise the nucleus would collapse in on itself. Capacitors A capacitor is two parallel metal plates separated by the directrix (a layer of insulation). The plates have a large area and are often rolled up (like a swiss roll) to make more compact.
When connected to a d.c. supply, one plate gains a positive charge and the other an equal but opposite negative charge.
We say that:
the charge on the capacitor is Q (in coulombs).
there is a p.d. V across the plates of the charged capacitor. This is a rough sketch of the strong nuclear force between two nucleons as the distance between them increases. It provides repulsion for distances up to 2.4x10^-15m. Between this and 5x10^-15m the force is attractive, and then the separation distance becomes too large.
Two neutrons are in equilibrium when 2.4x10^-15m apart. If moved slightly further away from eachother there will be a large force of attraction to pull them back together. Two protons will have an electrical force of repulsion that must balance with the strong nuclear force attraction. Since the electrical force is only relatively small, the separation distance will almost be exactly the same as for the neutrons.
In a real nucleus the separation of nucleons is almost independent of the number of nucleons within the nucleus. Nuclear Properties Nuclear Density Protons and neutrons have nearly the same mass. As the number of nucleons increase, the volume V and mass M of the nuclei are in direct proportion. This leads to the idea that the density of nuclear matter is constant.

V = c M

The volume is proportional to the radius R cubed.
And:
M = A m(p)
where A is the number of nucleons and m(p) is the mass of a proton.

This can be written:
R^3 = c' A m(p)
It can be shown:
R = (1.2 x 10^-15) A^1/3 The larger the capacitance, the more charge the capacitor stores for each volt applied across its plates. Capacitance is the charge stored per unit p.d. across the plates.

Capacitance = charge on plate / p.d. across the plates

C (farads) = Q (coulombs) / V (volts) The farad is a large unit so usually quoted in microfarads (uf). Electrons flow from the negative terminal of the supply onto the blue plate. A negative charge builds up as electrons collect on it. Electrons from the red plate flow towards the positive terminal, forming an equal but opposite positive charge. The p.d. across the plates rises. Eventually the build up of charge prevents more charge from arriving. The movement of electrons stops and the p.d. across the capacitor is the same as the supply voltage. The electrons are repelled away from the negative plate and attracted to the positive. A current flows lighting the bulb. Definitions The nucleon number A is defined as being the number of protons plus the number of neutrons in a nucleus.
The proton number Z is the number of protons in the nucleus. It tells us the positive charge on the nucleus in terms of e, the elementary charge, and for a neutral atom it will be the number of orbiting electrons.
Nuclide is another term for nucleus.
Two nuclides with the same number of protons but different number of neutrons are called isotopes. Fundamental Particles Leptons Hadrons Exchange Particles Quarks These are relatively light:
electron (e)
muon
tau
relative charge -1
lepton number 1
Also the respective neutrinos
relative charge 0
lepton number 1
and antiparticles.
relative charge +1
lepton number -1 There are 6 flavours of quark and they come in 3 generations:
up (u)
down (d)
charm (c)
strange (s)
top (t)
bottom (b)
There are also 6 anti-quarks carrying opposite charges to the counter parts.

Each quark has a Baryon number of +1/3
Each anti-quark has a Baryon number of -1/3 These are relatively heavy Baryons Mesons Baryons are made up of 3 quarks, anti-baryons are 3 anti-quarks.
There are 120 types of baryons
eg. proton uud
neutron udd
The proton is the only stable baryon. Neutrons are only stable within the nucleus but once free have a life of about 15 minutes Mesons are made up of quark/anti-quark pairs.
They are unstable and soon decay.
There are 140 types of mesons
eg. pion (pi+) ud`
kaon (K-) su` There are 4 types, each connected with one of the four fundamental forces.
Photon (electromagnetic)
Gluons (strong)
W+ W- Z Bosons (weak)
Graviton (gravitational) The Conservation Laws in Particle Interactions During interactions the particles may just recoil and remain unchaged or new particles may be formed. Certain rules must be
obeyed in the interactions.
Mass/Energy Conservation
Charge Conservation (Q)
Lepton Number Conservation (L)
Baryon Number Conservation (B)
Strangeness Number Conservation In order to know the capacitance, we need to know the charge on the capacitor and the potential difference across the plates. P.d. is easily measured using a voltmeter, charge is harder to measure.
We can use Q = I t and one of the three following methods:
use a variable resistor to control the current so it is a steady charging current.
Recording a graph of discharge current against time. The area under the graph is the area passed from capacitor after time t.
Then plot charge against p.d. and the gradient is the capacitance.
Quickly charging and then discharging the capacitor using a reed switch. Plot I against V and the gradient is Cf where f is normally 50Hz. A charged capacitor stores energy in the electric field established between its plates. It can release charge quickly so often used in flash photography, and lasers used in nuclear fusion.
As Q = C V , if you plot V against Q as a capacitor discharges you get a straight line through the origin.
Using W (work done) = Q V , it can be shown the total area under the graph is the energy transferred. Hence the energy stored E by a charged capacitor is given by the area under the graph.

E = 1/2 Q V

Also written:

E = 1/2 CV^2
E = Q^2 / 2C Beta- decay
n --> p+ + e- + -v(e)
(Q) 0 +1 -1 0
(L) 0 0 +1 -1
(B) +1 +1 0 0
udd -> uud + e- + -v(e)
d --> u + e- + -v(e)
The weak force causes this change. Beta+ decay
p+ --> n + e+ + v(e)
(Q) +1 0 +1 0
(L) 0 0 -1 +1
(B) +1 +1 0 0
uud -> udd + e+ + v(e)
u --> d + e+ + v(e)
The weak force causes this change in flavour of quark. Radioactive Decay The decay of a radioactive nucleus is:
random. It is completely unpredictable as to which nuclei will decay at any particular time.
spontaneous. We can't say when a particular nucleus will decay.
The activity of a sample is the number of particles that decay in a unit time. It depends on the isotope and size of the sample.

1 decay per second = 1 Becquerel (Bq)

The probability that each nucleus will decay is the decay constant,

A = N

where A is the activity and N is the number of nuclei at time t. The definition of half - life t1/2 is
the average time taken for the number of radioactive nuclei in a sample to decay by a half. N = N0 e^- t

when t = t1/2 , N = N0 / 2

No / N = e^ t1/2
2 = e^ t1/2
ln 2 = t1/2
t1/2 = 0.693 / Capacitors in Series In series, the charge on each capacitor is Q and the total charge stored is also Q. The supply p.d. is shared btween the capacitors.
V = V1 + V2
Q/C = Q/C1 + Q/C2
1/C = 1/C1 + 1/C2 Capacitors in Parallel In parallel, the supply p.d. is equal to the p.d. across each of the capacitors. The total charge is the sum of the charge on each capacitor.
Q = Q1 + Q2
CV = C1V + C2V
C = C1 + C2 Exponential Discharge of a Capacitor x = x0 e^-t/CR where x = Q, V or I

time constant (tau) = capacitance C x resistance R
The time constant is the time taken for the charge to fall 1/e of its original value

t1/2 = CR ln 2 Electric Fields How do objects become charged?
Charging occurs when electrons are transferred from one material to another.
Friction can transfer electrons.
An object will become positively charged if it has lost electrons, and negatively charged if it has gained electrons. Laws of Electrostatics
Like charges repel.
Unlike charges attract.
Charged objects will attract uncharged objects. Conductors and Insulators
Insulators have few free electrons and so charge does not move through an insulator.
Conductors have many free electrons and so charge can move through a conductor.
A charged conductor will share its charge with an uncharged conductor because electrons will move between the two conductors if they are in contact. An electric charge produces an effect in the space around it - an electric field. An electric field is a region where a 'charge' feels a force.
The electric field strength is defined as the force acting per unit positive charge. Electric field strength (N/C) = Force (N) / Charge (C)
E = F / Q The field can be represented by electric field lines. The arrows always go from positive to negative. Line spacing describes field strength. Point charges have radial fields. Spheres have no electric field on the inside but the outside field acts as if all the charge acts at the centre. Electric fields between oppositely charged parallel plates is nearly constant. Coulomb's Law The force between the charges is directly proportional to each of the forces (Q and q) and inversely proportional to the square of their separation (r).
F = k Q q / r^2 The size of the force also depends on the material between the two charges. In a vaccuum
k = 1/ 4 pi E0
where E0 is the permittivity of a vaccuum.

E0 is usually written as 8.85 x 10^-2 Fm^-1 and is close to that in air, so can be used to calculate forces between charges in air. Radioactive Decay Unstable radioacive nuclei will attempt to become more stable by emitting alpha, beta or gamma radiation. After the parent nucleus emits alpha or beta radiation, the result is a daughter nucleus with different nucleons.

Alpha Decay
The alpha particle is made up of two protons and two neutrons ie four nucleons (He nucleus). The most energetic form of decay, most elements only emit alpha particles of one particular energy. The energy appears as kinetic energy of the ejected alpha particle.

Beta Decay
Beta Decay is a fast moving electron. A neutron decays to a proton and an electron. The electron is immediately emitted and we now have a different element but there is the same number of nucleons.

Gamma Emission
The gamma emission does not change the structure of the nucleus but does make it more stable. After a nucleus has emitted alpha or beta particles it is still in an excited state. It will lose this surplus energy by emitting gamma radiation characteristic of the particular nuclei. Background Radiation Nuclear Stability The heaviest stable element is bismuth (A=83)
There are 90 naturally occuring elements from hydrogen Z=1 to uranium Z=92.
Technitium and promethium are man-made, both are radioactive with relatively short half lives. All elements beyond Z=92 are man-made.

The proton has high mass and high charge. Proton-proton repulsion is large and in the nucleus protons are very close to eachother. Neutrons and the strong force involved with them help keep nuclides together. The heavier the nucleus (more protons), the more neutrons required for stability. The belt of stability is the portion of a graph that contains all stable nuclei. Nuclei above the belt of stability undergo beta emission. Nuclei below the belt of stability undergo positron emission or electron capture. Since the electric field strength E = F/q this can be substituted into Coulomb's Law giving
E = Q / 4 pi E0 r^2

In a uniform field (when a pd is applied across two parallel metal plates) E = V/d

In a cathode ray tube electrons are accelerated. F = Eq or in this case F = eE = eV/d
work done when electrons are accelerated by the elecric field is W = Fd = eVd/d = eV
work done equals gain in kinetic energy:
1/2 mv^2 = eV Modelling the Universe Distances and velocities in our solar system can be measured using radar. Radiowaves reflect off the surface of the planet/asteroid and bounce back. Since we know the speed of the radiowave (speed of light) and the time taken to travel there and back, we can calculate the distance. 2d = ct
Sending two short pulses you can measure the average speed of the object relative to Earth (more accurate using the Doppler effect though). Astronomical Distances Another method of measurement in our solar system is the astronomical unit (AU). 1AU is the mean distance between the Earth and the Sun which is approximately 1.50 x 10^11m. The distance that electromagnetic waves travel through a vacuum in one year is called a light-year (ly). If we see light from a star that is 10 ly away, we are actually seeing it how it was 10 years ago. 1 ly is approx 9.46 x 10^15m. The distance to nearby stars can be measured in Parsecs. The distance to nearby stars can be calculated by observing how they move relative to very distant stars when Earth is in different parts of its orbit. A star is exactly 1 parsec (pc) away from Earth if the angle of parallax is 1 arcsecond (1/3600 degrees). 1 pc is approx 3.09 x 10^16m. Stellar Evolution Stars begin as clouds of interstellar dust and gas. The dust and gas is pulled together by gravity and begins to spin. As the gas spins faster, it heats up and becomes a protostar. More matter is attracted to the protostar and it continues to grow in mass, size and heat. Eventually temperatures of a few million degrees will be reached and hydrogen nuclei undergo nuclear fusion forming helium. Hydrostatic equilibrium is reached - energy from fusion creates enough pressure to stop gravitational collapse. Eventually the core will run out of hydrogen, fusion stops and the core contracts. This contraction provides enough pressure and heat for helium to fuse into carbon and oxygen. This releases a huge amount of energy which pushes the outer layers of the star outwards. After the core has run out of helium, it will contract under its own weight. The star pulsates and ejects its outer layers as planetary nebula. The hot, dense core is left behind which will simply cool down and fade into a black dwarf. Stars eight times more massive than our sun have a lot of fuel but use it up more quickly and so spend less time in the main sequence. In super red giants fusion continues beyond helium sometimes all the way up to iron. The star then explodes cataclysmically in a supernova, leaving behind a neutron star or a black hole. On a large scale, the cosmological principle states that the universe is homogeneous (of uniform density) and isotropic (the same in all directions). If the universe were infinitely large, every line of sight must contain a star. This should make the whole night sky uniformly bright. This suggests that a static infinite universe is not possible. Doppler Effect This can be expressed mathematically by

change in wavelength = relative speed of source and observer
correct wavelength of stationary source speed of wave (ie speed of sound/light)

delta lambda = v
lambda c

For approaching objects observed wavelength = lambda - delta lambda
For receding objects observed wavelength = lambda + delta lambda

The spectra of light from any star is crossed by dark lines. These absorption lines are produced when certain wavelengths of light are absorbed by elements in cooler outer layers of the star. From studying spectra on Earth we know the exact positions of spectra lines.
Edwin Hubble studied the spectra of many galaxies, measured their red shift and their distance from Earth. He observed
the vast majority of galaxies are red shifted (moving away)
the more distant the galaxy the greater the red shift
the graph of recessional velocity against distance was a straight line through the origin.
v = H0 d This suggests that the universe is expanding and gives rise to the Hot Big Bang Model: the universe started off very hot and very dense and has been expanding ever since.

t = d/v = 1/H0 = age of the universe
However H0 hard to get accurately as distances hard to measure. Also it has been assumed galaxies travel at constant velocity although it's likely they will have lost some kinetic energy.

The observable universe is a sphere with centre of the Earth. If the age of the universe is 13 billion years, then the sphere will have a radius of 13 billion light years.

The HBB model predicts that lots of electromagnetic radiation was producd in the very early universe. The radiation should still be observed today as it has nowhere else to go. The original radiation would have been in the gamma ray spectrum. The wavelength of the cosmic background radiation has been stretched as the universe expanded and cooled. Cosmic microwave background radiation (CMB) was detected accidentally by two engineers in the 1960s. The radiation is homogenous and isotropic and corresponds to a temperature of approximately 3K. There are a few temperature fluctuations due to tiny energy-density variations in the early universe, necessary for the initial 'seeding' of galaxy formation. Expansion beats gravity
Universe will expand forever
Will have an infinite age and size
Density of the universe p < pc the critical density of the universe Gravity beats expansion
Universe will expand to a maximum size and then collapse
Will have a finite age and maximum size halfway through its age
p > pc Gravity just cancels out expansion
Universe will expand to a maximum size after infinite time
p = pc The critical density pc is the density
of the universe that would cause
the expansion of the universe to
stop at a maximum volume
after an infinite time.

pc = 3 H0^2 / 8 pi G 14 billion years
Temperature has cooled to about 3K
Slight density fluctuations mean that matter has been condensed by gravity to form galaxies and stars. 300,000 years
Electrons combine with ions and atoms form
The universe becomes transparent. 100 seconds
Protons fuse to form helium nuclei. 10^-4 seconds
The universe is cool enough for quarks to join up and form particles like protons and neutrons. Matter and antimatter annihilate each other, leaving a small excess of matter and a huge number of photons. Up to 10^-4s
The unified force splits into the four forces. Quarks, leptons and photons form. There is a rapid period of expansion called inflation. Magnetic Fields A magnetic field is a region where a force is exerted on a magnetic material or where a current carrying wire feels a force. Magnetic field lines are lines of flux. Lines of flux show the direction of force an N-pole would feel so always go from N-pole to S-pole. Lines of flux never cross, the field can't have two directions at one point, a compass only points in one direction. The strength of the magnetic field is called the magnetic flux density B. It is the measure of the quantity of flux passing at 90 degrees through unit area and is measured in tesla T. The right hand grip rule can be used to show the magnetic field around a long straight wire. The lines of flux are circles around the wire, closer together close to the wire. The right hand grip rule also works for a solenoid. The magnetic field outside the coil is the same shape as a bar magnet and inside the lines are parallel close together and equally spaced. Fleming's Left Hand Rule F = B I l sin(theta)
where
F is the force
B is the magnetic flux density
I is current
l is length of wire in conductor
theta is the angle between B and I F = B Q v F = B I l
F = B Q l / t Charged particles move in circular paths in magnetic fields.
B Q v = m v^2 / r Electromagnetic Induction When a metal rod is moved in a magnetic field, using Fleming's left hand rule, there is a force on the electrons and they accumulate at one end of the rod. An emf is induced. Faraday's Model
An emf is induced if lines of magnetic flux are cut or if there is a change in flux linkage.
You can increase the size of the emf induced by the coil by:
using a stronger magnet
using a coil with more turns of wire
using a coil with a greater cross-sectional area
moving the magnet faster

The induced emf is equal to the rate of change of flux linkage.
E = N . delta phi / delta t Magnetic flux (phi measured in weber Wb) is the product of the magnetic flux density B and the area A through which the flux passes at 90 degrees.
phi = B A
If the area is not perpendicular to the magnetic flux density:
phi = B A cos theta

The flux linkage in the coil is the product of the magnetic flux and the number of turns in the coil.
flux linkage = N phi Lenz's Law
Lenz's Law states the the direction of the induced emf is such that it will try to oppose the change in flux that is producing it. In the diagram, the current flows around the coil so as to repel the incoming magnet. The magnet has to have work done on it to move it against the repulsive force. Work done causes energy to be tramsferred from the system moving the magnet to the electrical energy of the current. To demonstrate that the emf opposes the change in flux linkage, Faraday's Law is often written
E = - N . delta phi / delta t Eddy Currents
A block of conducting material exposed to a changing magnetic field has an emf induced in it. This can cause eddy currents to flow in the metal, which can become large due to low resistance in the metal. Eddy currents always flow to oppose the change that is producing them.
The Heating Effect
These eddy currents can make the metal very hot. This can be used to melt the metal placed in the magnetic field. A ceramic hob induces eddy currents in pans which become hot. To reduce energy loss as heat energy in motors, transformers and dynamos the iron core is laminated. Separating thin metal sheets with insulating layers does not affect the magnetic properties but greatly increases electrical resistance so eddy currents are significantly reduced.
The Magnetic Effect
The currents that flow can be used to help braking in large vehicles or can be attached to a voltmeter and used as a speedometer. The Transformer
An alternating p.d is applied across the primary coil. An alternating current runs through the primary coil producing a magnetic field in the soft iron core. An emf is induced in the secondary coil as the alternating magnetic field means the flux linkage of the coil is constantly changing. For the ideal transformer:
The ratio of number of turns is equal to the ratio of the p.d
Ns / Np = Vs / Vp

Power in = Power out
Vs Is = Vp Ip

Energy is lost as heat, eddy currents and flux leakage.
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