HSC PHYSICS NOTES
32212622433600420003175000175001870710HSC PHYSICS NOTESModule 5: Advanced Mechanics Module 6: Electromagnetism Module 7: The nature of light Module 8: Origins of the Elements450000HSC PHYSICS NOTESModule 5: Advanced Mechanics Module 6: Electromagnetism Module 7: The nature of light Module 8: Origins of the Elements31742734245428Jack Attard 00Jack Attard Advanced MechanicsAnything subjected to more than one force is NOT a projectile. A projectile is an object that is only subject to gravity.Use a triangle and trigonometry to find the initial velocity in the x and y directions from the resultant velocity. Uy = USin() and Ux= UCos()Horizontal velocity is always constant so Vx = SxTTo find vertical velocity Vy=Uy+GxTTo find vertical Height Sy=Vy X T+ 12 X G X T2Time of flight to reach maximum height Vy=Uy+GT therefore time of flight equals that equation multiplied by 2.Range Sx=Vx X TCircular MotionOrbital Speed (Instantaneous tangential velocity) V=2πrTCentripetal Acceleration Ac=v2rCentripetal Force Fc=mv2rWhere: r = Radius of the circle in meters T = Period of Rotation in seconds v = instantaneous velocitym = mass of object in motionNewton’s law states that unless a force is acted upon an object it will travel in a straight line. The force is due to the tension force of the string or rope or cord that is constantly pulling the orbiting object to the center of the circle. Even though the speed of the object may remain the same, the acceleration is always changing because its direction is also changing. This acceleration is towards the center of the circle and is called the centripetal acceleration.The velocity vector is also constantly changing but at any instant it will be at a tangent to the circle, and therefore at right angles to the acceleration and force vectorsCircular motion of moving vehicles turning cornersTo find maximum velocity Fc=mv2r so v2=FcrmCentrifugal force is the apparent force that objects experience when travelling around a curve. The centrifugal force is a “pseudo-force” which arises due to inertia.Angular VelocityAngular velocity ω=2πtOrbital speed and angular velocity v=2πrt but ω=2πt so v=ωr Centripetal acceleration ac=v2r but v=ωr so ac=ω2r2r=ω2rCentripetal Force Fc= mv2r but v=ωr so Fc=mω2r2r=mω2r The concept of torqueTorque=t=rfsinθ Where:t=torque on the systemr = distance from pivot to point where force is appliedF is the force in Newtons (N)When θ=90°, sinθ=1, this means that maximum torque occurs when the force acts at right angles to the bar.Motion in Gravitational fieldsGravitational force Fg=GMmr2 whereG = Universal Gravitational constant =6.67 x 10-11M & m = the weight of the two masses involved in kilogramsUniversal Gravitation and Orbiting SatellitesFg (the gravitational force) is what keeps any satellite in orbit.Weight Force = Gravitational force therefore:mg= GMmr2 so g= GMr2 where g = the strength of the gravitational field in (N.kg^-1) and is the acceleration due to gravityIsaac Newton and OrbitingEscape velocity=Vesc=2GMrwhere:G= Gravitational constantM= the mass of the planet in kgr = radius of the planet in metersSatellites and orbitsGeo-Synchronous Orbits are those where the period of the satellite is exactly the same as the earth itself. If the satellite is directly above the equator than the satellite is also “geo-stationary” which means that it is always directly above the same spot on earth and remains motionless. But it is rather orbiting around at the same angular velocity of the earth itself.Geostationary orbits are above the equator and have to be about 36 000 Km above the surface to have the correct orbital speed.The satellites are ideal for communication and because they orbit relative to the earth radio and microwave dishes can be permanently at the satellite for constant TV, telephone and internet relays to almost anywhere on earth.Orbital speed and radius Fc=Fg so mv2r=GMmr2 so v2=GMr so v=√GMr For any given primary object, there is a relationship between the orbital speed of a satellite and the radius of the orbit. For any given radius of an orbit, there is a certain orbital speed that corresponds to that orbit. The larger the radius orbit results in a slower orbital speed.Kepler’s lawr3α t2 so r3t2= constantThis means that for every planet, the (radius) cubed by the (period) squared has the same value.Kepler, with his law of universal gravitation was able to prove the theoretical basis for Kepler’s law as follows:Fc=Fg so mv2r=GMmr2 so v2=GMr but v=2πrT so 4π2r2t2=GMr so r3t2= GM4π2 Since the right-hand side contains all constant values, this proves Kepler’s law and establishes the force of gravity as the controlling force for all orbiting satellites including planets around the sun.Total Energy of a satelliteGravitational potential energy (GPE) ΔU=mgΔhIf an object is allowed to fall down, it loses potential energy and gains energy in another form such as kinetic or heat energy due to the law of conservation of energy. Work must be done on an object to raise the amount of GPE the object contains.Gravitational potential energy is a measure of the work done to move an object from infinity to a point within the gravitational field.GPE=U=-GMmr Where:U = GPE in Joules (J)G = Gravitational Constant (6.67 x 10-11)m = mass of object (Kg)M = Mass of earth or another planet (Kg)r = distance from center of the primary (m)Kinetic Energy in orbit Ek=12mv2 but for satellites it will be better to express in terms of G, M, r Fc=Fg so mv2r=GMmr2, we multiply both sides by r and divide by 2 and we get mv22=GMm2r so Ek=GMm2r For total energy of a satellite = Ek+U=GMm2r+-GMmr=-GMm2rElectric charges in electric and magnetic fieldsField between parallel charged platesThe field between two charged plates is the only electrical field that is regular and has the same strength at each point.Measurement of electrical charge and fieldThe unit of electrical charge is the coulombThe electrical field strength (E) is defined and measured as the force which a charge of +1C would experience if placed in the field. Electric field strength is a vector as it has a force and also a direction. Since force is measured in Newtons(N) and charge is in coulombs(C) it follows that the unit of electrical field strength is Newton per coulomb(NC^-1)This means if a charge (q) experiences an electrical force (F) than an electrical field with the force of Fq must be presentE=Fq or F=EqEnergy and voltage in an electric fieldV=?Uq Where:V = voltage?U = change in potential energy in JoulesV=Ed or E= Vd where:E= electric field strengthd = distance between the 2 points being compared in metersTo find the energy gained by a charged particle: ?U=VqElectric charges and magnetic fieldsEvery electric current produces a magnetic field. A wire carrying a current has a circular magnetic field wrapped around it. TO predict the shape of the field we can use the right-hand grip rule where the thumb points in the direction of the current and the fingers pointing in the direction of rotation for the magnetic field.To find the magnetic field strength (magnetic flux density) around a straight wire carrying an electrical current can be calculated as follows:B=μοI2πr where:μο = a constant called the vacuum permeability (1.26 X 10-6)B = strength of the magnetic field in teslas (T)I = the current in the wire in amps (A)r = the radial distance from the wire to the point where the field is being measured in meters (M)Trajectory of charges in a magnetic fieldSimilarities and differences of a mass in a uniform gravitational field and a charge in an electric field. In both fields, acceleration is uniform and parallel to the field lines acting on the object. The differences include that gravity is always attractive. Electrical forces can attract or repel. Positive and negative charges accelerate in opposite directions. All masses accelerate at the same rate in the gravitational field. In an electric field, equal charges feel the same force but will accelerate at different rates if their masses are different.Similarities and differences with a mass and a charge entering a field at right angles. In both fields, the trajectories are parabolic. This occurs because there is constant acceleration parallel to field lines and constant velocity at right angles to the field lines. The differences include gravitational trajectory depends only on initial velocity and angle of launch, mass is irrelevant. Exact electric field trajectories depend on velocity, polarity and magnitude of charge and mass.Force on a moving charge in a magnetic fieldIf a magnet is brought near a cathode ray tube, the electron beam is deflected. An electric charge experiences a force if it moves in a magnetic field. This is because a moving charge creates its own magnetic field. Under certain circumstances, the magnetic field produced by the moving charge interacts with the external magnetic field to produce a forceThe maximum force occurs if the velocity of the charge is at right angles to the magnetic field lines.To help understand the direction of the force we can use the right-hand palm rule. where your fingers are pointing straight forward and your thumb is straight up. Your thumb indicates the velocity vector, your fingers direction determines the direction of the magnetic field lines and the face of your palm indicates the direction at which the force is acting.The size of a force in a magnetic field can be determined as follows:F=Bqvsinθ where:B = Magnetic field strength in Teslas (T)q = electric charge in coulombsv = velocity of the charged particle in m/s^-1 = angle between the velocity vector and magnetic field lines.Since 90=1, maximum force occurs at right angles to the field linesIf a positively charged particle enters a uniform magnetic field with a velocity vector perpendicular to the field lines, it will experience a force at right angles to both vectors. Since the force vector is at right angles to its velocity vector, the force cannot cause the particle to alter its speed, only direction.Because it is centripetal force it follows that Magnetic force = centripetal force:qvB=mv2r after cancelling and rearrangement :r=mvqBThis allows us to see how the radius of the motion can be affected by particle mass, velocity and charge.A negative charge will react the same way but in the opposite directionSince the force does not act along its path of motion, it can do no work on the particle and therefore cannot change its kinetic energy.The motor effectThe force between two wires carrying a conductorIf the wires carry current in the same direction than the forces attract the wires and if they flow in opposite directions than they attract.Ampere found that the size of the force depends on a number of factors: The amount of current in the wires, the distance between the wires and the length which the wires are parallel.To find the force per unit of length:FL= μο2πI1I2d where:F = Force in Newtons (F)L = Length in meters(M)μο = magnetic permeability constant ( μο2π = 2.00 x 10^-7)I1 and I2 = the current in the wires in amps (A)d = the separation distance in meters(M)Even though the force between 2 wires carrying a current is weak, the effect can be much more powerful if more than one wire is involved, and if the magnetic fields involved are a lot stronger. If a wire is carrying a current through a powerful magnetic field, the wire will experience a significant and notable force. This is called the motor effect.To work out the force of a wire in a magnetic field we can use:F=BILsinθ whereF = the force in NewtonsB = the magnetic field strengthI = the current in ampsL = the length of the wire in the magnetic fieldθ = the angle between the wire and the fieldSin90=1 and sin0=0 this means the wire experiences the most force when perpendicular to the magnetic field lines. The direction of the force can also be determined by the right-hand palm rule.Torque on a loop of wire carrying current in a magnetic fieldTorque = force x distance between forces so torque on the loop is:t=BILWHowever, the factor (LXW) = the area of the loop so t=BIABut if the wire is made up of more than one strand of wire we must include this into the formula as “n” so we end up with:t=nBIABut as the coil rotates, it reaches positions where the forces on the wire do not cause rotation so the torque varies with the angle so we end up with:t=nIABsinθ where t = Torque on the coil in Newton metersn = the number of loops of wire in the coilI = the current in thee wire in AmpsA = the area of the coil in square metersθ = the angle between the magnetic field and the normal to the plane of the loopMain features of a DC MotorThe Rotor: the part that rotates. It is a coil of wire mounted on an axle to allow rotation. Current is fed through the wire which creates magnetic flux which is the attracted and repelled by the stator which produces torque.The Stator: The part that remains stationary. It may be a permanent magnet or an electromagnet. It provides the magnetic field needed to spin the rotor.The Brushes: Fine flexible wires, or spring-loaded sticks of graphite. The brushes maintain electrical contact onto the rotating metal ring.The commutator: a metal cylinder, split into 2 pieces. As it rotates the direction of the current in the coil is reversed every half rotation. This way the torque is always in the same rotational direction.Another machine that is built around the motor effect is a galvanometer. The more current that flows through its coil the greater the torque on the coil and the greater the deflection of the meter needle working against a small spring. The needle then points to a scale of measurements which can be calibrated to read either current or voltage.Electromagnetic InductionTo find the field strength inside of a solenoid we can use :B= μοNIL where:B = Magnetic field strengthμο = Vacuum permeability constant (1.26 X 10^-6)N = number of turns in the solenoid coilI = the current flowing in the wire in ampsL = the length of the solenoid in metersMagnetic flux and flux densityTo explain his discovery of induction, Faraday introduced the concept that a magnetic field is made up of a series of lines of forces. He showed that if a conductor moves so that it cuts through these field lines, then a current is induced to flow in the conductor.Magnetic field strength = Magnetic flux densityΦ=BAcosθ where Φ = the magnetic flux in Weber (Wb)B = Magnetic field StrengthA = The area through which the magnetic flux occursθ = the angle between the magnetic field lines and the normal to the area of the fluxFaraday’s Lawε=-NΔΦΔT where:ε = induced emf in volts (v)N = number of turns in the wireΔΦ = change in magnetic flux in webers (Wb)ΔT = number of time in secondsLenz’s LawA conductor wire being pushed across a magnetic field. Because the wire is cutting the field lines there will be an induced emf, and current will flow. But when a current flows the motor effect will occur and create a force on the wire,Lenz’s law states “the direction of an induced EMF is such that it produces a magnetic field opposing the change that produced the EMF”.If you push a magnet in a coil, you may feel an opposing force. The current induced in the coil creates a magnetic field which opposes the magnetic field you’re essentially pushingBack EMF in a motor An electric motor rotates due to the torque on the coil due to the applied current interacting with the magnetic field. However, as the coil rotates through the magnetic field, induction also occurs creating an induced EMF. Lenz’s law guarantees that the induced EMF will act against the supplied EMF.Eddy CurrentsWhen there is no designed electrical circuit present, whenever there is relative motion between a conductor and a magnetic field, an EMF is induced and currents will flow. Lenz’s law guarantees that eddy currents will create magnetic fields to oppose the motion that produced them.AC and DC GeneratorsAn AC generator relies on a coil in a magnetic field spinning to create an EMF in the wire. Because it is constantly changing polarity it creates a graph of a sine wave. The graph is constantly alternating hence alternating current.A DC generator uses electricity in the coil to create magnetic flux which is repelled and attracted by stationary magnets to create torque. The current in the coil reverses every ? a rotation but the commutator reverses it to create a direct polarity current hence direct current. The graph looks like a sine graph but does not change polarity instead it bounces.TransformersThe great advantage of using AC electricity is that it can be stepped up to very high voltage for efficient distribution then stepped down again for safe usage by consumers. The stepping up and stepping down that occurs is all due to the use of a transformer.The AC supply to the primary coil produces a fluctuating magnetic field. These field lines keep building, collapsing and reversing direction. This changing field constitutes a change of magnetic flux through the wires of the secondary coil so EMF is induced in itTransformers work by inducing a new EMF into the secondary coil. Whether the secondary voltage is higher or lower than the primary voltage is higher or lower than the primary voltage, is simply a matter of the ratio between the number of turns of wire in each coil.VpVs=npns where: Vp=voltage in the primary coilVs=voltage in the secondary coilnp = number of turns in the primary coilns = number of turns in the secondary coilIn a step-up transformer, the voltage increases and the current decreases by the same factor so that Primary Coil Power = Secondary Coil Power:VpIp=VsIsEnergy per second in primary coil = Energy per second in secondary coil.Electromagnetic spectrumWheatstone first measured the speed of electricity in a wire in 1834 which was refined by Kirchhoff in 1854.Weber and Kohlrausch experimentally measured the ratio of μο and εο. They discovered that 1√μοεο=3.1X108m/s-1Maxwell set out the theory of electromagnetism in four equations:Point charges radiate an electric field outwardsMagnetic field lines are always loops- there are no magnetic monopolesA changing electric field creates a changing magnetic fieldA changing magnetic field creates a changing electric field.InterferometryThe speed of light can be determined by the formula:c=fλ where:c = the speed of light in m/sf = the frequency of the wavelengthλ = the wavelengthSpectral lines and identifying elementsWilliam Wallace Hyde was examining the suns spectrum in 1802 when he noticed several dark gaps which he initially thought to be natural boundaries between colors. German physicist Joseph von Fraunhofer saw the lines in 1814 and catalogues about 500 of them. He showed the spectrum of Venus matched that of the sun and also took spectra of a number of stars.For 20 years from 1848, Foucault, Bunsen and Kirchhoff identified various solar spectral lines known as emission lines of various elements. Light can be considered as a stream of particles. A light particle or a photon consists of oscillating electric and magnetic fields and has an exact amount of energy that is related to its frequency according to:E=hf where:E = the energy of a photonH = Planck’s constantF = the frequency of the lightEnergy required for an electron to move to an outer shell:We use E=hf and f=cλ to get E=hcλThe speed at which electric and magnetic fields are propagated depends on the permittivity of free space and permeability of free space ir of the refractive medium they are travelling through.The refractive index of a material can be given by: n=cvRefractive index changes according to the wavelength of radiation in a materialThis causes dispersion, leading to the spreading out of spectraElectromagnetic radiation can be thought of as a stream of photons, each having a particular wavelength and frequency.Each element has a unique signature of emission and absorption lines due to the different energy levels required to move an electron to a higher energy levelAstronomical applications of spectroscopyThe spectral types of stars are placed in order from hottest to coolest and simplified to eliminate overlapping and confusing spectra. The order is:O, B, A, F, G, K, M.The key features of a star’s spectra include the appearance and intensity of spectral lines, the relative thickness of certain absorption lines and the wavelength at which peak intensity occurs.Stars are blackbodies so the peak wavelength indicates the temperature.The relative velocity of a star either approaching or moving away from an observer can be measured by the blue shift or red shift in the stars spectrum due to the Doppler effect.Finding the luminosity class of a star and its spectral type allows for a very good estimate of the stars absolute magnitude, from which its distance can be calculated.Lower density stellar atmospheres produce sharper but narrower spectral linesLight: Wave ModelIn the 17th century, Newton proposed that light consisted of particles At around the same time Huygens was working on the wave model.Newtons corpuscular theory of light proposed that:Light consists of small particlesThese particles have mass and obey the laws of physics in the same way as any other particle of massThe particles are so extremely tiny that if two beams cross they do not interact or scatter each otherThe theory could explain refraction and Snell’s lawLight travelled faster in optically denser mediaHuygens principles states that each point on a wave behaves as a point source for waves in the direction of propagation. The line tangent to those circular waves is the new position of thee wave front a short time laterHuygens used his principle to propose that waves slow down when they encounter an optically dense mediumThis theory could explain refraction and Snell’s lawThe amount of diffraction depends on the relationship between the size of the opening and the wavelength.This solved Huygens issue with rectilinear propagation, with little wavelengths little diffraction could occurFoucault’s experiment found that the speed of light through water is slower than the speed of light in airFoucault therefore disproved Newtons theory of light, since newton required the speed of light to be faster in waterYoung’s double slit experimentWhen the screen has a high distance away from the slits, the two rays are parallel. The difference in distance travelled is called the path difference ().δ=r2-r1We define an angle () as the angle between the normal to the line joining the two slits and the point of interest. The screen is also assumed to be perpendicular to this line. This allows for us to equate:δ=r2-r1=dsinθWhere d is the distance between the 2 slits.Constructive interference occurs when two waves have the same phase, when peaks line up with other peaks. At these points, there is an antinode or bright spot in the pattern. This occurs when the path difference is equal to a whole number of wavelengths: dsinθ=mλ, m=0,1,2……At the position where peaks meet troughs, the waves are half a cycle out of phase and a node or dark spot appears: dsinθ=m+12λ, m=0,1,2……The angle can be related to the height (y) above the point where the normal line reaches the screen and the distance (L) to the screen: tanθ=sinθ=yLTherefore, the path difference can also be written as: δ=dyL=dyLThe points of destructive interference occur at: y=L(m+12)λdThis also means that if we know the distance between the slits, and can measure the distance between successive bright spots and the interference pattern than we can determine the wavelength of light: λ=dyL In the early 19th century, experiments such as Young’s double slit diffraction experiment providing convincing evidence that light acts like a waveThe electromagnetic field model, as expounded by faraday and refined by Maxwell can explain many behaviors of light as an electromagnetic wave.Diffraction patterns of incandescent light are dependent on the wavelengths and so form peaks and troughs that reveal the spectrum.Young noted that:At some boundaries, such as between water and air, some light was refracted and some was reflected. Particle behavior could not account for this easily which further disproved Newton’s particle model of light.Particle theory could not explain why different colors of light were refracted by different amounts.Fraunhofer diffraction depends on the fact that each side of a single slit acts as point source of waves that can interfere with each other. It produces a large central peakYoung’s double slit experiment is based on light from one slit forming interference patterns with light from another slit.For double slit interference, interference maxima occur at: dsinθ=mλ, m=0,1,2……The distance between peaks in a double slit experiment is given by y=LmλdThe points of destructive interference can be given by y=L(m+12)λdIf Slits have a width (a) and are separated by a distance (d) then the counting factor(m) for the interference fringe that coincides with the first diffraction minimum is given by m=daMalus’s Law and PolarizationBased on the wave model of light, it can be shown that the intensity (I) of the electric field in electromagnetic radiation is proportional to the square of amplitude (A)Polarization refers to the particular direction of oscillation pf the electric field in the transverse plane.The direction of the oscillating electric field depends on the direction of motion of the originating charged particle.Incandescent sources consist of particles vibrating in all directions at different speeds, so the light they give off is not polarized.Plane polarization means the electric fields in the electromagnetic radiation are all oscillating in the same plane.The amount of plane-polarized light that can pass through a polarizer at to the original plane is given by Malus’s Law: I=Imaxcos2θ Light Quantum ModelIn 1893, Wilhelm Wien derived a relationship between the position f the peak and the temperature of a blackbody. He used the idealized black body cavity model to derive the relationship, no known as Wien’s displacement law:λmax=bTWhere b is Wien’s Constant (2.898x10-3)We can use Wien’s law to estimate the temperature of a body based on the color of the brightest light it emits.Planck’s Quanta of energyIn 1900, a German physicist Max Planck derived a formula that correctly matched the experimentally observed spectrum. Planck proposed that the atoms could only oscillate with discrete energies given by: En=nhfThis was a proposition that means energy of the oscillators is quantized. From this Planck deduced that the oscillators could only emit and absorb electromagnetic radiation. The quantization of energy was a revolutionary departure from classical physics that Planck himself was reluctant to accept his own proposal. Although Planck found a mathematical solution to this problem, he was worried that there wouldn’t be a way to physically prove it. It was Albert Einstein who put physical meaning to Planck’s quantum hypothesis.The photo electric effectKmax=Vsq=VsEWhen a light is shone on a metallic surface, no electrons are emitted unless the frequency of the light is above some minimum or critical frequency.When the frequency is above the cut off frequency, the number of electrons is proportion to the intensity.A cut off frequency implies a cut off wavelength, λο=cfο above which no photocurrent is being produced.There is no time delay between the light being incident on the metal and the photoelectrons being emitted, regardless of intensity. This means that the metal does not need to absorb energy over time before it can emit an electron.Different metals have different characteristic cut off frequencies.Einstein used conservation of energy and Planck’s ideas about quantization to explain the photoelectric effect.He came up with the photo electric equation, Kmax=hf-hfο=hf-?This says that if an electron absorbs light energy and is ejected from the metal, it will have a maximum kinetic energy of hf minus the energy needed to leave the plate which is the work function.Experiments by others including Millikan’s oil drop experiment were in accord to Einstein’s theory.The idea of quantization of energy and light behaving like particles was very successful in explaining these experiments. This contributed to the acceptance of the quantum theory which was one of the most important developments in physics in the 20th century.Special RelativityThe speed of light is finiteFrames of reference that are stationary or moving at a constant speed are inertial frames of reference.Galilean relativity says that the laws of physics are the same in all inertial frames.When relating the velocity of an object (A) measured in one frame (B) to that measured in another (C), the velocity of A relative to B is the velocity of A relative to C plus the velocity of C relative to B, Vab=Vac+VcbClassical relativity says there is no absolute frame of referenceMaxwell’s laws of electromagnetism say that the speed of light is a constant regardless of the frame of reference of the observer or the source of light.Light was thought to require a medium which was considered to be fixed.If light travelled at a fixed speed in the aether, and earth moved through the aether, then the speed of light should be seen to vary with earths motionThis was not the case. Therefore, light did not appear to obey conventional relativity.First postulate of special relativity- The laws of physics are the same in all inertial frames of reference.Second postulate of relativity- the speed of light has the same value in all inertial frames of reference.The factor 11-v2c2 is given the symbol “” and V2/c2 is known as so essentially Υ=11-β2Proper time is the time interval between two events occurring at the same place in an inertial frame, as measured by an observer in that inertial frame.If t0 is the proper tie between two events then the observed time allowing that the frame of reference of the observer may be moving is: T=ΥtοIf I0 is the proper length, the observed length allowing that the frame of reference of the observer may be moving is l=lο1-vο2c2The predictions of the theory of special relativity can be seen in in experiments performed on earth and in astronomical observations.The behavior of light from distant, powerful sources like supernova is what we would expect if Einstein’s theory was correct.The time subatomic particles like muons take to decay depends on the relative speeds of the muon and the observer, as Einstein’s relativity predicts.Atomic clocks which are extraordinarily precise show the effects of relativity even when moving at the speed of a commercial jetliner. These speeds are still incredibly slow compared to c.Structure of the atomCathode RaysTravel from a cathode to an anode in a straight lineCan cause fluorescence in glassCan be deflected in magnetic fieldsCan be deflected in electric fieldsCan transfer momentum to a paddle wheel device in a cathode ray tubeAre identical regardless of the cathode material usedBehave as negatively charged particlesThomson’s plum pudding model of the atom has discrete negative particles embedded in a sea of positive charge. In Thomson’s model the atom was still assumed to be a spherical shape. It had the electrons embedded randomly within the atom. Thomson proposed that the rest of the atom was uniformly positively charged with its mass evenly distributed but low in density.Thomson used crossed electric (E) and magnetic (B) fields as a velocity selector for cathode rays where v=EBThe cathode rays with known velocity were then deflected in an arc with radius (r) within a magnetic field only.The ratio of the charge q to the mass m of the cathode rays was calculates as ErB2 The resulting very high q/m ratio meant that the particles have a large negative charge with a small mass.Millikan observed the motion of charged oil drops between two charged plates. He found the smallest unit of change to be about 1.59x10-19 CElectric charge on other oil drops only existed as multiple of this base unit of charge.The observations led to the knowledge that charge is quantized and not continuous.q=mgdvRutherford’s model of the atomHe could account for the results of his experiment however there were some limitations to his modelHe could not explain what the nucleus was made out of Although he suggested electrons were placed around the nucleus he failed to explain how they actually stayed away from the center of the nucleus.Alpha particles were fired from a radioactive source into a thing piece of gold foil in Rutherford’s alpha particle scattering experiment.As expected most alpha particles went straight through but 1 in 8000 rebounded, Rutherford interpreted these results as suggesting the atom has a nucleus,The nucleus was proposed to contain nearly all the mass and all of the positive charge of an atom.Rutherford could not explain why electrons, even though they were accelerating, would not radiate energy and fall into the nucleusRydberg’s equation 1λ=R(1Nf2-1Ni2)The Balmer series for hydrogen occurs when electrons fall to second energy shell and emit a photon, or jump up from the second energy shell when absorbing a photon.Other hydrogen spectrum series occurs for example when electrons fall to the first energy shell or third energy shell.The Rydberg equation predicts the wavelength emitted when an electron moves between specified energy shells in a hydrogen atom.The Rydberg equation does not work for other elementsThe process of photon emission or absorption is governed by the law of conservation of energy ................
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