State Newton’s First Law of Motion A body continues in its unaccelerated state of motion unless acted upon by an external force (or a body stays at rest or continues to move with a constant velocity unless ….) State Newton’s Second Law of Motion The rate of change of momentum (or the acceleration) of a body is proportional to the net force acting on the body and in the same direction as the force. State Newton’s Third Law of Motion To every force exerted by a body A to a body B (action) there is an equal and opposite force exerted by body B to body A (reaction) What features do the action-reaction force pairs have? They act on different bodies. They are of the same nature. They are equal in magnitude but opposite in direction. They act along the same line. Define Momentum Momentum is a vector quantity that is equal to the product of the mass and the velocity of a body. Define Impulse Impulse is a chunk of momentum. It is usually associated with the change of momentum given to a body upon impact with another body. What does the principle of Conservation of Momentum state? In a system of bodies when there is no external force acting the total momentum stays unchanged. Define the moment of a force Moment of a force about a point is the product of the force and the minimum distance of the axis of the force from that point. Moments have direction. They are clockwise or anticlockwise. What does the principle of Moments state? For a body to be in rotational equilibrium the sum of the moments about any point on the body must be zero. What conditions must be met for a body to be in equilibrium? The sum of the forces acting on the body and the sum of the moments of those forces about any point on the body must be zero.

Define Young’s Modulus Young’s modulus is the ratio of stress over strain exerted on a body that has not exceeded the elastic limit. Define Tensile Strain and Tensile Stress Tensile strain is the ratio of the extension over the original unstretched length for a body under tensile stress. Tensile stress is the force per cross sectional area of a body being stretched. What does the area under the Stress – Strain graph of a wire being stretched represent? It represents the energy stored per unit volume of the material for a particular strain. Define Upthrust Upthrust is a force that is experienced when a denser body finds itself in a less dense liquid or gas and is equal to the weight of the displaced liquid or gas and acting in a direction opposite to the gravitational attraction. State Stoke’s Law of Viscous drag The force of viscous drag opposes the motion of a spherical body in a viscous fluid and is directly proportional to the speed and the radius of the sphere as well as the coefficient of viscosity of the fluid. The law applies to laminar flow only. Define Laminar Flow Laminar flow is the flow of a liquid where each point along the flow has a constant velocity over time. Or, laminar flow is the flow of a liquid where the flow can be considered to exist in layers that do not mix and maintain a constant speed over time. Define Turbulent Flow Turbulent flow is the flow of a liquid where the velocity of flow at each point in the flow undergoes sudden and unpredictable changes. The flow is chaotic and also has eddies. Define Energy Energy is a scalar quantity that describes the work done or the work that can be done by a body due to its state of motion or due to its temperature or due to its molecular structure. Define Acceleration Acceleration is a vector quantity equal to the rate of change of velocity

Waves What is a wave? A wave is an oscillation that travels in space and transfers energy to a remote point What is a progressive wave? A progressive wave is one that travels (propagates) in space. It is an oscillatory motion where nodes and antinodes propagate with the speed of the wave in a certain direction in space. What is a standing wave? A standing wave is a stationary wave that is made up from a progressive wave and its reflection. In a standing wave the nodes and antinodes are stationary (they do not change with time) Define transverse waves and longitudinal waves giving two examples for both Tranverse waves are those waves where the oscillations of the medium in which the wave is transmitted oscillate at right angles to the direction of propagation, (light waves, sea waves). Longitudinal waves are those waves where the oscillations of the medium in which the wave is transmitted are parallel to the direction of propagation (sounf waves, seismic waves) List the types of electromagnetic radiation and quote typical wavelengths Radio – 20 m Microwave – 5 cm Infra Red – 2 mm Visible - 600 nm Ultra Violet – 1 nm X-rays - 0.1 nm γ-rays – 1 pm Explain the principle of superposition of waves When two waves of the same nature meet in space then at any point in the space that they meet the resulting oscillation is the net sum of the two oscillations that would be caused by the individual waves. What is interference? Interference is when two waves overlap and produce a pattern of reinforcements and cancellations at various different places.

What conditions must be met for two waves to produce visible interference? They must be of the same nature and must originate from coherent sources What makes two sources coherent? They must have the same frequency and a constant phase difference Define refraction of waves Refraction is the change in speed of propagation of the wave when the wave enters a different medium. Define the refractive index of a transparent material This is ratio of the sine of the angle of incidence to the sine of the angle of refraction with both angles measured from the normal to the surface What is diffraction of waves? Diffraction is the property of waves to bend around obstacles with this being more prominent when the size of the obstacle is comparable to the wavelength of the wave Give two phenomena that demonstrate the diffraction of light Young’s double slit where fringes are observed and diffraction grating where maxima are observed at specific angles from the normal to the grating slide. Define Polarisation of light Polarisation is a phenomenon that occurs only in transverse waves and it describes a wave where the oscillations of the medium exist only in one direction normal to the direction of propagation (or you may say in one plane which includes the direction of propagation). Give an example of a polarized wave. All light that is reflected from a surface (such as water or glass is) partially or fully plane polarized. Microwaves satellite TV signals that are emitted from satellites How can you detect whether light is polarized? Using a Polaroid slide and rotating it by 90% expecting to observe a minimum. If a minimum is observed then the light is plane polarized. If the minimum is zero then the light is totally plane polarized.

What is the Doppler effect? It is a change in the frequency received by a stationary observer when the wave source moves toward (higher frequency) or away (lower frequency) from the observer. Describe an application of the Doppler Effect Detecting the speed of vehicles using a microwave radar (microwave frequency is preferred to radio frequency in order to be able to target a specific car) Describe Purse Echo techniques in Medical Diagnostics Using Ultrasound medics can image the inside of the body using the fact that the ultrasound gets reflected at every boundary between different tissue. (eg fat-muscle-bone-veins-organs-fetus etc). By measuring the delay in reflection of the each pulse at every boundary a computer can produce an image of the body below the ultrasound probe. The typical frequency used in such techniques is 1 to 4 MHz. Ultrasound can also be used with the Doppler effect to detect and measure blood flow in arteries or veins. Electricity What is the minimum quantity of charge that can be found in nature.? State its magnitude in Coulombs The least charge that can be found in nature (as discovered by Millikan) is the charge of an electron. This is 1.6 x 10 -19 C Define emf The electromotive force (emf) of a cell is the energy per Coulomb that passes through the cell and is delivered to the cirtcuit. For example a 5 Volt emf means that 5 joules of energy are supplied to the circuit by the cell for every Coulomb that is supplied to the circuit. Define Potential Difference Potential Difference is the energy per Coulomb that is transferred to electrical component when charge flows thought it. This transferred energy usually is in the form of heat (in a resistor) Define Resistance – Ohms Law Resistance is the ratio of potential difference V across a component divided by the current I flowing through the component. R = V/I. It is measured in Ohms

Define Drift speed It is the average speed with which actual electrons or (other carriers) move in a wire in which a current flows. (Remember here the transport equation I = nqvA where n is the number of free carriers (usually electrons) per unit volume in the material from which the wire is made) What is resistivity ? Resistivity is a measure of the resistance of a specific material. It is defined as the resistance per unit length of a conductor of unit cross-sectional area made from the specific material. Resistivity usually depends on temperature (except in constantan) and almost all conductors become superconductors at low enough temperatures. Recent technological progress has been achieved with the discovery of materials that become superconducting at temperatures as high as 120 K. State Kirchoff’s First Law The total current into any point (or junction) in a circuit is equal to the total current out of that point (or junction). This law follows the conservation of charge – in that charge cannot be created or destroyed. State Kirchoff’s Second Law The total sum of emfs in a closed path in a circuit is equal to the total sum of potential difference drops in the path. This follows from the conservation of energy. What do you understand by the potential divider rule in circuits? The voltages across two resistors connected is series are proportional to their respective resistances: V1/V2 = R1/R2. Define the internal resistance of a source The internal resistance is a modeling concept that accounts for the fact that when a current is drawn from an emf its voltage drops. Usually in circuits the load resistance is much larger than the source resistance. However, maximum power transfer from source to load occurs when the load resistance is equal to the source resistance. (at this situation, though only half the power drawn from the source goes to the load with the other half being consumed as heat in the battery’s source resistance) Describe the effect of temperature in the conduction of metals and semiconductors In metals as temperature rises so does the vibration of atoms and this makes the flow of electrons harder which reduces conductivity (or increases resistivity). In

semiconductors where conduction electrons are freed from atoms there are more such electrons freed as the temperature rises and this causes conductivity to increase with temperature (or resistivity to decrease with temperature – eg thermistor) Light Define Radiation Flux Light intensity at a specific point is measured as the power per unit area received at a specific point and is referred to as radiation flux F. It is measured in W/m2 To determine F at a point a distance r away from a source divide the power at the point of the emission (power of the source) by 4πr2., where is the distance of the point from the source. Explain what observations lead to the discovery of the particle nature of light The fact that light above a certain minimum frequency only could release photoelectrons from a certain metal could not be explained by the wave nature of light and this lead to the quantum theory of light which states that light energy comes in quanta known as photons each of which has an energy equal to h.f Why does conventional wave theory fail to explain the photoelectric effect? If light is a wave then a large enough amplitude for any given frequency should carry enough energy to cause the release of photoelectrons. Again a wave would accumulate enough energy over time to cause the release of photoelectrons. Neither actually is true and this lead Einstein to porpose the particle theory of light . Define Threshold frequency This is the minimum frequency of the incident radiation that will cause the emission of photoelectrons from a certain material. Define Work Function This is the minimum energy of oncoming photons that will cause surface electrons to be released from a specific material - Remember the work function is associated with a specific material. Define the electronvolt It is a small amount of energy equal to 1.6x 10-19 Joules What is the stopping voltage? It is the negative voltage that needs to be applied to the anode of a photoelectric cell to stop released electrons from reaching the anode. It can be determined from

Vs.e = h.f-Φ (actually the stopping voltage times the charge of an electron is equal to the maximum kinetic energy of released photoelectrons) What is an emission spectrum ? It is the set of coloured lines (specific frequencies) against a black background that corresponds to specific energy transitions of electrons in excited atoms. The emission spectrum can extend beyond the visible spectrum. The emission spectrum of a every element is different and therefore the emission spectrum from an excited substance can be used to identify that substance. What is an absorption spectrum ? It is a continuous range of colours including al the possible frequencies where only specific colours (or frequencies) are missing and are replaced by black lines. These lines are characteristic of the gas that has absorbed specific frequencies from the emission of panchromatic light (by say a glowing tungsten filament). What are energy levels ? They are specific energy levels that electrons can occupy in an atom. These are different for every element. Usually electrons occupy the ground state which is the lowest energy level that they can occupy and it corresponds to an unexcited state of the atom. Between the ground state and the ionization state where electrons are have escaped from the atom there are various intermediate but distinct energy states. When electrons are raised to these intermediate states they will fall to lower states and eventually to the ground state giving off photons of specific frequencies that correspond to the specific transitions. What is laser light ? Laser light is light that is the result of simultaneous energy transitions by a very large number of atoms. This makes all photons to be in phase and cause a coherent emission which makes laser light so strong. In ordinary light photons are not in phase in laser light they are in phase.

State Newton’s 2nd Law of Motion in terms of momentum The rate of change of momentum is directly proportional to the net force that applies to the body and in the same direction as the force Be able to describe Newton’s Cradle Impacts between the steel balls conserve momentum (they are also nearly elastic). You should be able to explain why the last ball only flies out Remember that kinetic energy can be written as E = p2/2m where p is the momentum Remember that collisions can take place in two (and three) dimensions. In this case momentum is conserved in all directions. When collisions between two balls are elastic and the masses are equal (as in billiards) then after oblique collision the balls move at right angles to each other. (be able to show this using E1 = p2

1/2m and E2 = p22/2m and because we assume that

energy is conserved E0= E1 + E2 which means p2

0/2m = p21/2m + p2

2/2m and so p20 = p2

1+ p22

But from conservation of momentum p0=p1+p2 this is a vector equation because momenta are vectors. When p2

0 = p21+ p2

2 (which is scalar equation) is also true it means that p1 and p2 must be perpendicular to each other (because the Pythagoras theorem applies only to orthogonal triangles) Circular Motion Define the Radian The Radian is an angle that subtends an arc of length equal to the radius of the circle. Define Angular Velocity It is the rate at which angular displacement changes or the angle covered per unit time – it is expressed in rad//s How is this related to linear velocity? v = ω.r Why is a body in circular motion continuously accelerating even though the speed v may not change? Because its velocity is continuously changing direction so it must be accelerating Define Free fall

This is a situation when a body is accelerating under the influence of gravity. Ie when net force is its weight. How can we achieve accelerations greater than g ? These are achieved as centripetal accelerations: Rotate something at large enough ω and you can achieve any accelerations you wish (within practical limitations). Remember that centripetal acceleration is ω2r or v2/r depending on whether you know ω or v. What is centripetal force? It is force that is required to cause a body to perform circular motion. When a body of mass m performs circular motion with uniform angular speed the centripetal force is given by mω2r or mv2/r Electric and Magnetic Fields Explain what is meant by a field? A field is a condition that creates a force in a given space. (There are three commonly known fields – gravitational which produces a force on mass, electric which produces a force of charges and magnetic which produces a force on moving charges) Define Electric Field strength This is the force per unit charge experienced by a charge in the field. (Units: N/C) How can you determine the force between two charges Q1 and Q2 is space?

F = 1 22

0

.4Q Q

rπε

What is the magnitude of the electric field strength E caused by a charge Q at a distance r from the charge in space?

E = 204

Qrπε

In which direction does it apply ? Electric fields due to point charges apply radially from the point. To find the direction place a positive charge and determine which way it would be pushed. What is the potential at a point in an electric field ? This is the energy per unit charge (unit is the volt) that is required to bring a positive charge from infinity to that specific point in the field.

How can you create a uniform electric field? By applying a constant voltage V to two (metal) plates which are a certain distance d apart. The electric field between the plates will be uniform (constant) and have a value E = V/d (unit V/m) What are equipotentials? These are surfaces in space where the electric potential due to an electric field is the same. For example concentric spheres in radial fields or parallel surfaces in between parallel plates are examples of equipotentials. What is special about the value of charge? It is quantised. It exists in multiples of the electron charge 1.6 x 10-19 C. Describe a Capacitor A capacitor is a device (usually made as two parallel plates separated by a narrow gap) that can store charge. Define Capacitance It is the amount of charge per unit volt that a capacitor can charge ( C = Q/V) How can you determine the energy stored in a capacitor? By the following three ways: E = ½QV or E = ½CV2 or E = ½Q2/C Charging and Discharging Capacitors What is the formula that governs the voltage across a capacitor, the charge on the capacitor or the current that flows from a capacitor when a capacitor C is discharged through a resistance R. V = Vo e –t/RC , where Vo is the initial voltage of the capacitor Q = Qo e –t/RC , where Qo is the initial charge on the capacitor I = Io e –t/RC , where Io is the initial current flowing out of the capacitor How do these formulas change when you charge instead of discharging the capacitor? V = Vo(1- e –t/RC ), where Vo is the final voltage of the capacitor Q = Qo ( 1- e –t/RC ) , where Qo is the final charge on the capacitor I = Io (1-e –t/RC ) , where Io is the initial current flowing into of the capacitor What is the time constant It is the product R x C and is expressed in seconds. It indicates the time it takes for the initial (Voltage, Charge or Current) to fall to 37% of its initial value.

How many time constants are needed to assume that a capacitor is totally charged (or discharged)? About 5 Magnetic Fields How is a magnetic field represented? By flux lines that which show the direction that a north pole of a compass would point How do we measure magnetic fields? By the magnetic flux density B (Unit the Tesla) How can we find the magnetic flux Φ that links a region of area A when a magnetic field of flux density B goes through the region? Φ = Β . Α (unit of flux is the Wb - weber) or Φ = Β.Α. sin θ if the field is not perpendicular but falls at an angle A with the normal to the plane of the region Just like all fields we can define the magnetic field as the force per unit charge moving with unit velocity at a direction perpendicular to the field that is felt by a moving charge in a magnetic field. Ηοw can the force be calculated? F = Bqv for a charge q moving with velocity v at right angles to the field F = Bil for a current i flowing in a conductor of length l at right angles to the field The direction of this force is determined using Fleming’s left-hand rule Thumb = Thrust First = Force Second= Current(or direction of motion of positive charge) Give a common application of the Bil force? The electric motor What does the mass spectrometer do? It separates and identifies specific elements in a mixture What does the mass spectrometer work? Vaporised particles of different mass are charged and then they are accelerated and the beam is bent using a magnetic field. Because Bqv = mv2/r the ratio q/m = v/Br and because the mass is particular to the molecules of a specific substance the

substance can be identified because it follows a unique radius r to reach a detector that is positioned to receive the particles. What do you understand by Electromagnetic Induction? When a changing magnetic field links a conductor then an emf is induced in the conductor. E = - dΦ/dt The magnitude of the induced emf is proportional to the rate of change of flux linkage. Give applications of Faraday’s Law The transformer The generator Explain how the transformer works A alternating voltage is applied in the primary coil and this causes an alternating current to flow. This causes an alternating magnetic field in the iron core which also links the secondary coil. The alternating magnetic field induces an emf in the secondary coil. The ratio of the induced emf to the applied voltage is equal to the ratio of the number of turns of the secondary coil to the primary coil: Vs/Vp = Ns/Np Explain how a dynamo works? A magnet is caused to rotate in a coil and this causes a changing magnetic field to link the coil thus inducing (generating) and emf. Why would a higher current flow in the primary of the transformer if a dc voltage is applied than when an ac voltage is applied? With the ac voltage the alternating magnetic field induces a back-emf (one in opposite direction to the voltage that is applied) and this reduced the net voltage and hence the current that flows in the coil State Lenz’s Law The direction of the induced emf in Faraday’s Law of Induction is in such a way that the resulting current will oppose the flux change that induces the emf. Give examples of Lenz’ Law A magnet falling a copper tube Magnetic braking Particle Physics What is particle scattering

The experiments by Rutherford that fired alpha particles through thin gold foils showing that particle is made up of positively charged nuclei where the mast majority of mass is concentrated and which occupy a small proportion of the atom. What is the de Broglie wavelength? It is defined as the Planck constant divided by the momentum of a particle. Its real application is in determining the effective wavelength of fast moving electrons (used in crystallography) Why do we use accelerators? To accelerate charged particles and cause collisions in order to observe nuclear phenomena. What principles do all accelerators use to accelerate particles? They all use electric fields to accelerate charged particles How can you determine the speed of an electron that is accelerated from the cathode to the anode using a high voltage V? E = e.V = ½ me v2 (solve for v) You should be able to describe the three common particle accelerators: the lineac, the cyclotron and the synchrotron Show that the frequency which is applied to the Dees in a cyclotron in independent of the radius of the circle that is followed by a charged particle Bqv = mv2/r (ie magnetic force acts as centripetal) This gives Bq = mv/r but v/r = ω and ω=2πf So f = Bq/2πm which is not dependent on the radius – it depends on q/m which means that a different frequency is used when accelerating electrons or protons or alpha particles. What principle is used to cause particle beams to turn (in a cyclotron or synchrotro)? A vertical magnetic field is applied at right angles to the direction of motion and this causes charged particles to perform circular motion thus bending toward a circular trajectory What makes the synchrotro more sophisticated than the lineac and the cyclotron? Using modern electronics it can vary the frequency with which electric fields are produced in accelerating elements inside a modern synchrotro as well as the

frequency and the intensity with which magnetic fields are applied to bending elements to ensure that a uniform circular track is followed. This is especially important when relativistic effects become important as particle speeds approach the speed of light. What is the standard model? It is a set of particles from which we (currently) accept that all known matter is made. These particles are the quarks and the leptons What is preserved in nuclear reactions?

- Charge, momentum, mass/energy and (lepton number, baryon number, strangeness)

What do you understand by anti-matter? It is particles that are made from corresponding anti-matter particles. For example anti-hydrogen is made of an anti-proton and an orbiting positron. How does anti-matter react with matter? It annihilates matter releasing energy (usually in the form of photons) Name two properties of Mesons They are made of a quark and an anti-quark They are very short lived and do not exist stably in nature

Define Specific Heat Capacity and Describe an Experiment that you could perform to determine the specific heat capacity of a metal and a liquid Specific Heat Capacity of a material is the Energy per unit mass required to raise the temperature of a material by 1 degree K. In the experiment that you describe make sure you weigh the material or liquid before you start to heat it. The heat energy you give it must be electrical because you can then easily determine E = V.I.t and finally make sure you insert a thermometer to measure the temperature rise ΔΘ = Θf-Θο (ensure you have also recorded the initial temperature Θο). Also mention that you should insulate (thermally) the material or the container of the liquid. Finally c = E/(m.ΔΘ) . [In the case of a liquid state that you should use a light plastic cup to neglect the heat required to raise the container’s temperature.] What is an ideal gas ? List four assumptions about an ideal gas An ideal gas is a gas that obeys the gas laws (Boyle’s Law, Charles Law and the Pressure Law) Assumptions: 1 – Molecules of gas occupy negligible proportion of the total volume 2 – Molecules of the gas collide elastically with each other and the container walls 3 – There are no attractive forces between the molecules that influence their motion 4 – The molecules of the gas spend no time in collisions In the kinetic theory of gases what is meant by the absolute zero temperature? Absolute zero is the temperature where all motion of the gas molecules stops and therefore there is no kinetic energy in the molecules. Remember that the average kinetic energy is proportional to the temperature so zero kinetic energy means zero temperature. State Boyle’s Law The volume of a specific quantity of a gas is inversely proportional to its pressure at constant temperature State the Equation of State of a Gas and explain the meaning of the variables and parameters involved PV = nRT or PV = NkT Where P: pressure of the gas, V: Volume occupied by the gas, n: number of moles of the gas, R: universal gas constant, T: absolute (Kelvin) temperature of the gas (N: number of molecules present in the quantity of the gas N = n.A , where A is Avogadro’s number, K

What is meant by Simple Harmonic Motion? Simple Harmonic Motion is an oscillatory motion about a centre such that the acceleration of the particle is proportional to its distance from the centre of motion and in a direction opposite to the displacement. For a body performing SHM with angular frequency ω and amplitude A what is the maximum velocity of the body during the motion? Vmax = Aω What is resonance ? Resonance is a situation where a body is driven by an external oscillator which oscillates at the body’s natural frequency of oscillation. In such a situation the oscillations have a relatively large amplitude How can resonance damage structures or machinery and how can it be avoided ? It can damage structures and machinery because of the resulting high amplitude oscillations. To avoid this structures and machinery are designed to avoid having a natural frequency of oscillation. Draw the potential energy and kinetic energy of a body performing SHM as a function of the displacement from the centre of motion.

Explain what is meant by the terms “spontaneous” and “random” in describing nuclear decay. Spontaneous means that it happens on its own without any specific stimulus and cannot be controlled. Random means that one can never tell for sure if a specific

Ek Ep

Etotal

x 0

nucleus will disintegrate in any given period of time. There is only a given probability that any nucleus will disintegrate in a specific period of time. What is meant by the term “isotope”? Isotope is an atom of an element with a different number of neutrons ((same atomic number but different mass number) Define half-life for a radioactive sample It is the time taken for the activity of a sample to fall to half the value (from any initial instant when the activity was measured) How many half-lives must pass for the activity to fall to 1/8 of the original value? 3 because 1/8 = ½3 How is the half-life of a sample related to the decay constant λ ? λ = ln2/t½ Define “activity” of a radioactive sample and quote its units Activity is the number of nuclei that decay in a given sample per second. It is measured in Bequerel (counts per second) Describe an experiment to determine the nature of radioactive particles emitted by a radioactive sample and how to measure the activity of the sample. First measure the background count. Then place the sample close to a Geiger Tube and connect to a counter. Measure the count over a sufficient period and repeat by placing a piece of paper and then repeat with a thin sheet of aluminium. If the count changes with the insertion of the paper then we have α radiation. If it changes with the insertion of the aluminium then we have β radiation. If it doesn’t change we have γ radiation. In all cases subtract the background count from the measured count. Define Binding Energy of a nucleus and explain why this is also called Mass Deficit Binding energy or mass deficit is the mass (or corresponding energy using E = mc2) that is lost when the particles (neutrons and protons) than make up a nucleus come together to make a nucleus (this lost energy has become potential energy in holding the nucleons together). It called mass deficit because the mass of the nucleus is less that the mass of the constituent particles.

Explain how binding energy (or mass deficit) is responsible for providing heat energy in fission and in fusion and explain why fusion cannot be easily achieved on earth. When a nucleus breaks down to two smaller nuclei (fission) the mass of the two daughter nuclei is smaller than the mass of the original (heavier) nucleus. This difference becomes kinetic energy of the resulting particles and then heat. The two smaller nuclei are more stable because they have a larger mass deficit per nucleon than the original nucleus. In fusion two lighter nuclei join-up to form a heavier nucleus which again has a larger mass deficit (or binding energy) per nucleon than the original two lighter nuclei. This releases energy just like in fission. However although fission happens spontaneously fusion requires very high pressures and temperatures which cannot be easily created on earth and this is the reason why fusion cannot be used for commercial power production. Describe the chain reaction that takes places in nuclear fission used in power stations and explain how this can be controlled in a power station. When a slow moving neutron collides with a Uranium atom it breaks it up into two lighter nuclei (which produces heat) and three more neutrons. If these neutrons are slowed down (fast neutrons do not cause this reaction) using a moderator then they can induce the same break up in more Uranium nuclei. This is the principle of operation of a fission nuclear power station. This “multiplication of neutrons and break-up of more nuclei” process can quickly run out of control (for example in an atomic bomb) so in a power station control rods are used to control the magnitude of this chain reaction. Outline the safety risks posed by nuclear power The fission based chain reaction is inherently unstable and if for whatever reason the control rods cannot function properly (as in the recent earthquake in Japan) the heat produced becomes too high to dissipate and melts down the reactor which then releases toxic radioactive materials to nature. Due to the high half-lives of uranium and the decay products of fission the damage to the environment surrounding the power station is long lasting. State Newton’s Law of Gravitational Attraction The gravitational attraction between two masses is proportional to the product of the masses and inversely proportional to the square of their distance apart. Derive a relationship which shows that the period of orbit of a satellite around the Earth depends on the height at which is rotates.

Equate the gravitational attraction 2GMmF

r= with centripetal force 2F m rω= :

2

2GMm m r

rω= 2

2GM rr

ω∴ = 23

GMr

ω∴ = 2

2 34 GMT rπ

∴ = 2 3

2 4 rTGMπ

∴ =

State one similarity and one difference between electric fields and gravitational fields Similarity: They are both inverse square laws Difference: Gravitational is only attractive, Electric can also be repulsive Define Luminosity of a Star It is the total power it radiates (spherically). L = σ.T4. A where A is 4πr2. Units W Define Radiation Flux (or Intensity) of a Star It is the power per unit area of the radiation of a star received on earth I = L/4πd2 Units W/m2 Describe the relationship between maximum wavelength of light emitted from a star and its surface temperature. This is Wien’s Law and it states that the wavelength where the emitted radiation is maximum is inversely proportional to the Kelvin temperature of its surface. Explain what is meant by a black body radiator This is a body that obeys the Stefan Boltzman Law ( P = σ.T4). (It would be black in colour if it were at room temperature but you must understand that a black body at 5000K does not look black so blackness in the Stefan-Boltzman Law is more general than what you perceive as black) Explain what is meant by a Main Sequence Star It is a star in its normal life (where regular fusion takes place) and this places it is the main line of the Hertzsprung-Russell diagram Describe the two possible processes by which stars finish their lives When hydrogen is depleted fusion is substantially reduced and this causes the star to swell out and it becomes a red-giant (lower temperature but bigger in size) and then

- depending on their original size Large stars collapse down to a small size and this causes a supernova explosion that creates heavier elements and scatters them in space with whatever is left behind forming either a black hole or a neutron star Smaller stars (up to 5 times our sun) From the red giant stage they release planetary nebula (heavier elements such as carbon, oxygen from the last stages of fusion) and then they shrink back to a small size forming a white dwarf which is bright not from fusion (there is no longer any hydrogen to fuse) but from the high temperature of the material. These white dwarfs are expected to live for 30 billion years and then become

balck dwarfs as they cool down. (we haven’t yet seen a black dwarf because the universe is not old enough for this) Describe the method of trigonometric parallax as a method of determining the distance of stars. What limitations does the method have? A star is observed against distant stars that form a steady background and its maximum angular displacement (against the background) over a period of 12 months is recorded. This angular displacement is used along with trigonometry to determine the distance of the star from the Earth. If θ is half of the maximum angular displacement in the 12 months then the distance d of the star from the Earth (or the sun) is d = 1 A.U./θ where θ is in radians. These angles are usually very small and they are therefore measured in parsecs (which are parallax seconds meaning they are comparable to 1/3600 of a degree. Actually because measuring angles so small is not very reliable this method is limited to determining distances of nearby stars only. What is a parsec and why is it used as a measure of the distance of stars. Determine how far away a star is (in metres) when we say it is 3 parsecs away from the Earth.

1 parallax second of a degree is an angle = 13600

o

= 4.85.10-6 rad

So distance of 1 parsec = 1 A.U./ 4.85.10-6 = 1.496×1011 /4.85.10-6 m = 3.07x1016 m = 3.24 light years So 3 parsecs is 3 x 3.07x1016 m = 9.21x1016 m or 9.72 light years Explain what is meant by Standard Candles and describe how these are used to determine the distances of stars. Standard Candles are stars of known luminosity (eg supernovae) and this allows us to determine their distance from us. When L is known then measuring the radiation flux I reaching the Earth we can use the formula I = L/4πd2 to find d State Hubble’s Law The speed of recession of distant galaxies is proportional to their distance from the Earth. Explain how the Hubble constant is used to determine the life of the Universe and explain how the assumptions made in the calculation can affect the accuracy of the estimation of the life of the Universe. Assuming that the universe has been expanding at the same velocity since the big-bang measuring this velocity (from red-shift and Doppler effect δλ/λ = v/c where v is the speed of a receding galaxy) and knowing the distance of the galaxy d from us (by

using a standard candle in that galaxy) we can determine the time it took for this galaxy to reach that distance from us. t = d/v = 1/Ho and hence we can determine the life of the universe. Obviously the assumption that the universe has been expanding at a constant speed since its creation may be grossly inaccurate. Also the use of standard candles is not a very accurate method of determining the distance of a galaxy so there are considerable uncertainties in the determination of the life of the universe. The Hubble constant is often quoted in Km/s/Mpc (kilometers per second per megaparsec). Show that this unit is actually 1/time and given that Ho= 74 kms-1Mpc-1 find its value in s-1. Km/s is a measure of speed and Mpc is a measure of distance. So speed divided by distance is 1/time . 74 kms-1/Mpc = 74x103 m.s-1/(106x 1 A.U./[2π/360 x 1/3600]) = 74x103 m.s-1/(106x 1.496×1011 /[2π/360 x 1/3600]) = 2.4 x 10-18 s Describe the fate of the Universe and how this depends on the density of the universe The universe will do one of three things 1 – continue to expand (open universe) 2 – stop expanding and reaching a final (constant) distance between galaxies (flat universe) 3 – collapse back to big crunch (closed universe) this depends on the density of the universe (density means total mass of stars and planets and nebula over volume of universe). If the density is sufficiently large for gravitational forces to slow down and perhaps reverse expansion then the universe will either go flat or collapse. If not it is continue expanding. Bright matter that has been measured suggests that the universe has too small a density which would lead to the conclusion of an open universe. However, recently scientists believe that there is a lot of dark matter (which cannot be measured and added to the total mass because being dark it cannot be directly seen – indirectly we can see some of it as for example in black holes attracting huge stars) which may contribute to making the universe flat or closed.