Module 6 Flashcards
What are capacitors?
Electrical components in which charge is separated. They consist of two metallic plates separated from each other by an insulator.
What is capacitance?
The charge stored per unit p.d. across a capacitor.
What is the unit for capacitance?
Farads (F).
How do you calculate the capacitance of a capacitor?
C = Q/V
If two or more capacitors are connected in parallel, is the p.d. the same across them or different?
The p.d. across each capacitor is the same.
How do you calculate the total charge stored by capacitors in parallel?
The total charge stored is equal to the sum of the individual charges stored by the capacitors/
Qt=Q1+Q2+Q3+…
How do you calculate the total capacitance of capacitors connected in parallel?
The total capacitance is equal to the sum of the individual capacitances of the capacitors.
Ct=C1+C2+C3+…
When capacitors are connected in series, how do you calculate the p.d. across the combination?
The sum of the individual p.d.s across the capacitors.
V=V1+V2+V3+…
When capacitors are connected in series, is the charge stored by each capacitor the same or different?
Same.
How do you find the total capacitance of capacitors connected in series?
1/Ct=1/C1+1/C2+1/C3+…
How can you use a p.d.-charge graph to determine the energy stored in a capacitor?
Area under graph = work done.
W=1/2VQ
W=1/2V^2C
W=1/2Q^2/C
For a discharging capacitor, what do V-t. I-t, and Q-t graphs show?
Exponential decay.
What is the time constant (tau) of a capacitor-resistor circuit?
The product of the capacitance and resistance. It is equal to the time taken for the p.d./current/charge to decrease to e^-1 (about 37%) of its initial value.
What is the electrical field strength of an electrical field at a point in space?
The force experienced per unit positive charge at that point.
E=F/Q
What are the uses of capacitors?
Camera flash, provide back-up power for computers and emergency lighting for when the mains supply cuts out briefly.
Smoothing capacitors help to convert AC to DC.
How do you use electrical field lines to map electrical field patterns?
- the arrow on an electric field line shows the direction of the field
- electric field lines are always at right angles to the surface of a conductor
- equally spaces, parallel electric field lines represent a uniform field (one in which the field strength is the same everywhere)
- closer electric field lines represent greater electric field strength
What is the electric field strength of an electric field?
The force exerted per unit positive charge at that point.
E=F/Q
What is Coulomb’s law?
Any two point charges exert an electrostatic force on each other that is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
What are some differences between electric and gravitational fields?
- Gravitational fields are always attractive whereas Electric fields can be attractive or repulsive
- the property that creates a gravitational field is mass whereas the property that creates an electric field is charge
What are some similarities between electric and gravitational fields?
- Both force per unit (property creating charge)
- Force is inversely proportional to the separation squared
- Point masses/charges produce a radial field
How do you find the electric field strength between two parallel plates?
W=Fd
VQ=EQd
V=Ed
E=V/d
What does the capacitance of a capacitor depend on?
- separation between the plates
- the area of overlap between the plates
- the dielectric used between the plates
What is the equation for capacitance when a dielectric other than a vacuum is used?
C= epsilon(r)epsilon(0) A/d
How do you describe the motion of an electron travelling at right angles to an electric field?
Horizontally:
- there is no acceleration (ignore gravitational effects as mass of electron is so small)
- the time spent in the field is L/v
Vertically:
- vertical acceleration given by a= F/m = EQ/m
- initial vertical velocity is 0
- final vertical component of the velocity v is given by v=u+at. v=0+ EQ/m x L/v = EQL/mv
What is alpha radiation?
Two protons and two neutrons (helium nuclei). They have a charge of 2e.
What is beta radiation?
Fast moving electrons or positrons. Beta-minus has a charge of -e and beta-plus has charge of e.
Why are anti-electron neutrinos released in beta-minus decay?
Conservation of lepton number.
What is gamma radiation?
High energy photons with a wavelength less than 10^-13 m.
Why are alpha particles deflected less than beta particles when passing through an electric field?
Greater mass.
How do you keep safe around radioactive sources?
- Store sources in lead-lined containers
- use a pair of tongs with long handles when transporting sources
What force causes beta decay?
Weak nuclear.
Can gamma decay occur on its own?
No, only occurs in conjunction with alpha or beta decay.
Why is radioactive decay random?
- we cannot predict when a particular nucleus in a sample will decay or which one will decay next
- each nucleus in a sample has the same chance of decaying per unit time
Why is radioactive decay spontaneous?
The decay of nuclei is not effected by:
- the presence of other nuclei in the sample
- external factors such as pressure
What is the half life of an isotope?
The average time it takes for half the number of active nuclei in a sample to decay.
What is the activity A of a source?
The rate at which nuclei decay or disintegrate. It is also the number of alpha, beta, or gamma photons emitted from the source per unit time.
What is a becquerel?
An activity of one decay per second.
What does activity depend upon?
The number of undecayed nuclei present in the source and on the half-life of the isotope.
How is alpha, beta, and gamma radiation deflected in an electric field?
Negative beta-minus particles are deflected towards the positive plate, whilst the positive alpha and beta-plus particles are deflected towards the negative plate. Alpha particles are deflected less than beta particles because of their greater mass. Gamma rays are not deflected because they are uncharged.
How is alpha, beta, and gamma radiation deflected in a magnetic field?
The direction of the force on each particle can be determined using Flemings left hand rule. Gamma rays are not deflected.
What does each finger represent in Flemings left hand rule?
Thumb - Force
First finger - Magnetic field
Second finger - Current
How can you stop an alpha particle?
A few centimetres of air or a thin sheet of paper.
How can you stop a beta particle?
A metre of air or 1-3 mm of aluminium.
How can you stop gamma rays?
A few centimetres of lead.
What is electrical potential energy?
The work done to go against an electrical field (push like charges together or separate opposite charges). It is the area under a force-distance graph. If the force is attractive, the value for electrical potential will be negative.
What is electrical potential at a point?
The work done per unit charge in bringing a positive charge from infinity to that point. The unit is Volts and in the formula booklet is written as V, which is confusing as it is not the same as P.D.
What were the observations and conclusions of Rutherford’s Alpha particle scattering experiment?
- most particles passes straight through the thin gold foil without scattering. About 1/2000 were scattered
- Very few alpha particles were deflected at angles greater than 90 degrees (1/10,000)
- led to the nuclear model of the atom - the atom is mostly empty space with the mass concentrated in a small nucleus. The nucleus has a positive charge because it repelled the alpha particles.
How did Rutherford calculate an upper limit for the radius of a gold nucleus?
- used alpha particles of kinetic energy 1.2x10^-12 J
- the distance d of closest approach between the alpha particle and the gold nucleus can be calculated using the idea of conservation of energy. At this distance, the alpha particle momentarily stops, therefore
- initial KE of alpha particle = electrical potential energy at distance d
- KE = Qq/4pie0d
When are X - rays produced?
Fast moving electrons are decelerated by interaction with atoms of a metal such as tungsten. The kinetic energy of the electrons in transformed into the X - ray photons.
What is an X - ray tube made of?
an evacuated tube containing two electrodes. An external power supply creates a large p.d. between the electrodes. The cathode is a heater, which produces electrons by thermionic emission. These electrons are accelerated towards the anode.
What is Bremsstrahlung?
Breaking radiation. The range of decelerations of the electrons inside the X - ray tube produces a broad background of breaking radiation.
What is attenuation?
The decrease in intensity of an electromagnetic radiation as it passes through matter.
What are the attenuation mechanisms for X - rays?
Simple scatter
Photoelectric effect
Compton scattering
Pair production
How does simple scatter cause the attenuation of X - rays?
1-20keV photons interact with an electron in the atom, but has less energy than the energy required to remove the electron, so the X - ray photon scatters. Hospital machines use p.d.s greater than 20kV, so this mechanism is insignificant for hospital radiography.
How does the photoelectric effect cause the attenuation of X -rays?
Significant for X ray photons less than 100 keV. The photon is absorbed by one of the electrons in the atom. The electron uses this energy to escape the atom. This is the dominant attenuation mechanism in hospital because the machines use 30-100kV supplies.
How does Compton scattering cause the attenuation of X - rays?
Significant for photons with energy 0.5-5MeV. The incoming X - ray photon interacts with an electron in the atom. The electron is ejected from the atom, but the photon does not disappear completely - instead it is scattered with reduced energy.
How does pair production cause the attenuation of X - rays?
Occurs when photons have energy equal or greater than 1.02 MeV. An x- ray photon interacts with the nucleus of the atom. It disappears and the electromagnetic energy of the photon is used to create an electron and a positron.
Why is contrast medium used?
Soft tissues have low absorption coefficients, so a contrast medium is used to improve the visibility of their in ternal structures in x - ray images.
What elements are used as contrast media?
Iodine and Barium, attenuation coefficient is proportional to atomic number cubed.
How are x - rays used therapeutically?
Specialised machines called linacs are used to create high energy x - ray photons. These are used to kill of cancerous cells by Compton scattering and pair production.
What does CAT stand for?
Computerised axial tomography
How does a CAT scanner work?
records large numbers of x-ray images from different angles and assembles them into 3d images with the help of software.
What are the disadvantages of CAT scans?
- take longer and are more expensive than X - rays
- prolonged exposure to ionising radiation, so expose patients to a radiation does equivalent to several years of background radiation.
- patients have to remain very still during the scanning process
What are the advantages of CAT scans?
- they create 3D images of the patients that helps doctors to assess the shape, size, and position of disorders such as tumours.
- they can distinguish between soft tissues of similar attenuation coefficients
What is a gamma camera?
A detector of gamma photons emitted from radioactive nuclei injected into the patient.
What makes a radioisotope safe to use?
if they emit gamma sources so that the radiation can pass through the skin, and if they have a short half-life to ensure high activity from the source so that only a small amount is required to form the image. this also means the patient is not subjected to a high dosage of radiation that continues long after the procedure.
What is the radioisotope most commonly used?
Technetium-99m. Produced from the natural decay of Molybdenum-99.
What are the components of a gamma camera?
gamma photons travel towards the collimator (thin tubes made of lead), so any photons travelling at an angle to the tube are absorbed. Photons traveling at the right angle reach the scintillator (material of material such as sodium iodide). A single gamma photon striking the scintillator produces thousands of photons of visible light. The photons of visible light travel though to the photomultiplier tubes, which converts the photon to an electrical pulse, connected to a computer, which produces an image.
What medical tracer is used in Positron Emission Tomography?
Fluorine-18 is made into fluorodeoxyglucose (FDG), which is similar to naturally occurring glucose but is tagged with fluorine 18.
What is the advantage of using FDG as a tracer?
Bodies treat it like normal glucose. When injected into the patient it accumulates in tissues with a high rate of respiration.
What does a PET scanner detect?
The gamma photons emitted when the positrons from decaying fluorine-18 nuclei annihilate with electrons inside the patient. This produces two gamma photons travelling in opposite directions, so momentum is conserved. The computer can determine the point of annihilation from the difference in the arrival times of theses photons at the two diametrically opposite detectors, and the speed of the photons.
What are the advantages of PET scans?
- non invasive
- can identify onset of certain disorders of the brain such as Alzheimer’s
-can be used to assess the effect of new medicines on organs
What are the disadvantages of PET scans?
- very expensive because of facilities required to produce medical tracers
- only found in larger hospitals
What is an ultrasound transducer?
A device used to generate and receive ultrasound. It changes electrical energy into sound and sound into electrical energy by means of the piezoelectric effect.
What are the benefits of using ultrasound?
non ionising, non invasive, quick
What is a farad?
1 farad is the capacitance of a capacitor that stores 1 C of charge when the p.d. across it is 1 V.
What are the limitations to carbon dating?
It assumes that the ratio of carbon - 14 atoms to carbon - 12 atoms has remained constant over time. Increases emission of CO2 may have reduced this ratio, along with volcanic eruptions.
Why can’t you use carbon - 14 dating on the earths rocks or meteors formed during the creation of the solar system?
It’s half life is not long enough
What element do geologist use to date ancient rocks?
Rubidium - 87
What are the two interpretations of Einstein’s mass-energy equation?
mass is a form of energy (demonstrated by annihilation) and energy has mass (a moving ball has kinetic energy, so its mass is greater than its rest mass)
What is the conservation of mass-energy?
The total amount of mass and energy in a system is conserved.
What is annihilation?
When a particle and an antiparticle meet, their entire mass is transformed into energy in the form of two identical gamma photons.
What is pair production?
A photons energy creates a particle and a corresponding antiparticle.
What is the minimum photon energy required to produce an electron-positron pair using pair production?
1.02 MeV. Rest mass of electron is 0.51MeV, and 2 particles need to be produced.
What is mass defect?
The difference between the mass of the completely separated nucleons and the mass of the nucleus.
What is binding energy?
The minimum energy required to completely separate a nucleus into its constituent protons and neutrons.
How can you compare how easy it is to break up nuclei?
Calculate the binding energy per nucleon. The greater this value is, the more tightly bound the nucleons within the nucleus are.
How does binding energy per nucleon change as the atomic number increases for atoms where A is less than 56?
BE per nucleon increases as A increases.
How does binding energy per nucleon change as the atomic number increases for atoms where A is greater than 56?
BE per nucleon decreases as A increases.
Which element has the greatest binding energy per nucleon?
Iron - 56. It is the most stable isotope in nature.
What are thermal neutrons?
Neutrons with a mean kinetic energy similar to the thermal energy of particles in the reactor core. Nuclei are more likely to absorb them than undergo fission. When they absorb a neutron the nuclei (uranium 235 turns to uranium 236) become highly unstable and have a much greater change of splitting spontaneously.
What is inside a fission reactor?
Fuel rods are spaced evenly within a steel-concrete vessel known as the reactor core. A coolant is used to remove the thermal energy produced from the fission reactions within the fissile fuel. The rods are surrounded by the moderator, and control rods can be moved in and out of the core.
What do fuel rods contain?
enriched uranium, mainly consisting of urainium-238 with 2-3% uranium-235
What is the role of the moderator in a nuclear reactor?
Slow down the fast neutrons produced in fission reactions. The material for a moderator must be cheap and readily available, and must not absorb the neutrons in the reactor.
What are moderators usually made of?
water or carbon. Fast moving neutrons bounce of the massive uranium nuclei with negligible loss of kinetic energy. However, when they collide elastically with protons or deuterium in water, or with carbon nuclei, they transfer significant kinetic energy and slow down.
What are control rods?
Rods made of a material whose nuclei readily absorb neutrons, most commonly boron or cadmium. The position of the control rods is adjusted to ensure than exactly one slow neutron survives per fission reaction. To slow down or stop the fission, the rods are pushed further into the reactor core.
How do you make nuclei fuse?
Bring them close together, within a few 10^-15 metres, so that the short range strong nuclear force can attract them into a larger nucleus.
What do A and Z represent in nuclear physics?
A - nucleon number
z - proton number
What is an atomic mass unit, u?
one twelfth the mass of a neutral carbon 12 atom.
How does the strong nuclear force vary with separation for two nucleons?
Attractive to about 3 fm and repulsive below 0.5 fm. The graph starts with a high positive force but this falls sharply to a negative (attractive) force after 0.5 fm. It reaches a minima at around 1 fm and then gets less negative as the nucleons separate to 3 fm. After this it is negligible.
What are the four fundamental forces?
Strong nuclear, electromagnetic, weak nuclear, gravitational.
What is a fundamental particle?
A particle that has no internal structure and hence cannot be divided into smaller bits.
What are hadrons?
Particles and antiparticles that are affected by the strong nuclear force. e.g. protons, neutrons, mesons. Hadrons decay by the weak nuclear force.
What are leptons?
Particles and antiparticles that are not affected by the strong nuclear force. e.g. electrons, neutrinos, muons.
What is the charge on an up quark?
+2/3e
What is the charge on a down quark?
-1/3e
What is the charge on a strange quark?
-1/3e
What is the quark composition of a proton?
uud
What is the quark composition of a neutron?
udd
What are baryons?
Any hadrons made with a combination of three quarks. e.g. protons, antiprotons.
What are mesons?
Hadrons made with a combination of a quark and an anti-quark
What are neutrinos?
Leptons carrying no charge and a tiny mass.
What is the decay equation for beta-minus decay?
neutron = proton + electron + antielectron neutrino
What is the decay equation for beta-plus decay?
proton = neutron + positron + electron neutrino
What is the piezoelectric effect?
Some crystals (e.g. quartz) produce an e.m.f. when they are compressed, stretched, twisted, or distorted. This effect is a reversible process, so when an external p.d. is applied across the opposite faces of the crystal, the electric field can either compress or stretch the crystal.
How do ultrasound transducers produce ultrasound?
A high frequency alternating p.d. is applied across opposite sides of a piezoelectric crystal. The frequency chosen is the same as the natural frequency of the crystal, resulting in resonance, producing an intense ultrasound signal.
What do modern ultrasound transducers use as a piezoelectric crystal?
Lead zirconate titanate (PZT) or polyvinylidene fluoride.
What are A scans used for?
determining the thickness of bone or the distance between the lens and retina in the eye.
How do B scans work?
The transducer is moved over the patients skin. The output of the transducer is connected to a computer. For each position of the transducer, the computer produces a row of dots on a digital screen corresponding to the boundary between two tissues. The brightness of the dot is proportional to the intensity of the reflected ultrasound pulse.
What is acoustic impendence?
The product of the density of the substance and the speed of ultrasound in that substance.
What is the intensity reflection coefficient?
the ratio Ir/I0. There is more reflection when acoustic impendences are very different
What is impendence/acoustic matching?
when two substances have similar values of acoustic impendence.
Why is coupling gel used for ultrasound?
When a transducer is placed on the skin of a patient, air pockets will always be trapped between the patient and the skin. The air skin boundary will reflect most of the incident ultrasound before it enters the patient. Gel with a similar acoustic impendence to the skin is smeared on the patient and transducer to ensure almost all ultrasound is able to penetrate the body.
How do colour doppler scans work?
The transducer is pressed lightly over the skin above the blood vessel. The transducer sends pulses of ultrasound and receives the reflected pulses from inside the patient. Ultrasound reflected off tissues returns with the same frequency and wavelength, but when reflected of moving blood cells will change frequency.
When is the frequency increased during doppler scans?
When the blood is moving towards the transducer.
What do equally spaced and parallel magnetic field lines represent?
A uniform magnetic field
What are the magnetic field lines for a current carrying wire?
Concentric circles centred on the wire and perpendicular to it. The direction can be determined using the right hand rule, with the thumb pointing in the direction of conventional current.
What is the magnetic field like inside a solenoid?
Uniform, and similar to a bar magnet.
What is magnetic flux density?
The strength of the magnetic field.
What is a tesla?
The magnetic flux density is one tesla when a wire carrying a current of 1A placed perpendicular to the magnetic field experiences a force of 1N per metre of its length.
How can you determine the magnetic flux density experimentally?
Place two magnets on to a top-pan balance. A stiff copper wire is held perpendicular to the magnetic field between the two poles. The wire is connected in series with an ammeter and a variable power supply. Zero the balance when there is no current in the wire. When the current is turned on, the magnets will experience a downward force opposite to the upward force experienced in the wire. The force can be calculated by the change in the mass reading on the top-pan balance.
Why will a charged particle in a magnetic field move in a circular path?
The force acting on it is always perpendicular to the velocity. The centripetal force (mv2/r) on the particle is provided by the magnetic field BQv.
How do velocity selectors work?
- Two parallel horizontal plates are connected to a power supply and produce a uniform electric field between the plates
- A uniform magnetic field is applied perpendicular to the electric field
- The electric and magnetic fields deflect the particles in opposite directions - only particles with a specific speeds will have deflections cancel out and emerge from the narrow slit.
- for an undeflected particle, electric force = magnetic force.
EQ = BQv
v = E/B
How do you induce an e.m.f.?
When a magnet is pushed towards the coil, an e.m.f. is induced across the ends of the coil, and when the magnet is pulled away a reverse e.m.f. is induced. Repeatedly pushing and pulling a magnet will induce an alternating current in the coil.
What is magnetic flux?
The product of the component of the magnetic flux density perpendicular to the area and the cross-sectional area.
phi = BAcos(theta)
What is magnetic flux linkage?
The product of the number of turns in the coil and the magnetic flux.
What is the SI unit for magnetic flux and magnetic flux linkage?
Weber (Wb). 1Wb = 1Tm^2
When is an e.m.f. induced?
whenever there is a change in the magnetic flux linkage in the circuit.
What is Faraday’s law of electromagnetic induction?
The magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage.
What is Lenz’s law?
The direction of the induced e.m.f. of current is always such as to oppose the change producing it. It is an expression of conservation of energy.
What is a step-up transformer?
More turns on the secondary than the primary coil. They increase the voltage and decrease the current.
What are step-down transformers?
fewer turns on the secondary coil than the primary. They decrease the voltage and increase the current.
Why will transformers not work with DC current?
There is no changing magnetic flux.
