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CfE Higher Physics Unit 2 Particles and Waves Higher Physics Particles and Waves H H He n + Energy Pupil Notes Doon Academy page 1 CfE Higher Physics Unit 2 Particles and Waves The Standard Model The Standard Model is a model for classifying sub-nuclear particles and their interactions. The Greeks, a philosopher Democritus, came up with the idea of a fundamental particle, the atom. This word comes from the Greek for indivisible ‘atmos’. He wondered if he could keep breaking an object in half indefinitely. He came to the conclusion that eventually you would get something that couldn’t be split. Next came John Dalton, we only had to wait 2000 years after the ancient Greeks. He used his data from chemistry experiments to propose that not only were substances made of atoms, the atoms of an element were identical and different elements had different types of atom. By the end of the 1800’s J.J. Thomson had discovered the electron, so now physicists knew atoms were actually made of smaller component parts. This started a race to find out what the smaller parts were. Orders of Magnitude The following table is used to determine the size of sub-atomic particles and universally large objects compared to a human. Humans are taken as the “standard size” particle. Particle or Object Neutrino Proton Hydrogen Atom Dust Human Earth Sun Doon Academy Order of Magnitude ≈ 10-24 m 10-15 m 10-10 m 10-4 m 100 m 107 m 109 m page 2 CfE Higher Physics Unit 2 Particles and Waves Solar System Nearest Star Galaxy Distance to a Quasar 1013 m 1017 m 1021 m 1026 m Fundamental Particles The standard model was developed in the early 1970’s in an attempt to tidy up the number of particles being discovered and the phenomena that physicists were observing. At present physicists believe that there are 12 fundamental mass particles split into two groups Leptons Quarks There are also 4 force mediating particles. Photon Gauge Boson Gluon Graviton Hadrons can be made up of a number of different particles, each containing a certain number of quarks. The hadrons are called Mesons and Baryons. The best way to remember how many are in each is: Meson Me –son Two syllables Two Quarks Baryon Bar-y-on Three syllables Three Quarks Doon Academy page 3 CfE Higher Physics Unit 2 Particles and Waves fermions u c bosons t quarks charm top photon d s b Z leptons down strange bottom Z boson e W electron neutrino muon neutrino tau neutrino W boson e muon tau g electron force carriers up gluon Charge and Antimatter Every particle/quark has an associated antimatter particle. The purpose of the antimatter particle is to cancel out the original particle. The antimatter particles have the same mass, but opposite charge to their original particles. Up Anti-Up Electron Positron Anti-Down Down Each quark has an associated charge with it also. When quarks combine to form particle, the overall charge of the particle is 1. Doon Academy page 4 CfE Higher Physics Unit 2 Particles and Waves Example: A particle consists of an up quark, an anti-down quark and a charm 1 quark. The up quark has a charge of and the anti-down quark has a charge of 3 2 . What is the charge of the charm quark? 3 1 2 CQ 1 3 3 1 CQ 1 3 1 3 1 CQ 1 3 3 3 CQ 4 3 Fundamental Forces There are four fundamental forces that dictate how particles interact with each other whether in close proximity or a massive distance away. The fundamental forces are: Strong Nuclear Force Weak Nuclear Force Gravitational Force Electromagnetic Force The strong and weak nuclear forces only act over a very small range – falling away to zero just outside the nucleus of an atom. The electromagnetic and gravitational forces can act over an infinite range. In the nucleus of an atom where there is more than one proton, the electromagnetic force tries to repel the protons from the nucleus. The strong nuclear force is able to overcome this and keep the nucleus together. Weak nuclear force is felt during beta decay – when an electron is released from the atom. Doon Academy page 5 CfE Higher Physics Unit 2 Doon Academy Particles and Waves page 6 CfE Higher Physics Unit 2 Particles and Waves Electric Fields Links to National 5 – Energy Conservation In Physics, when we talk about a field we mean a region within space in which an object experiences a force without being touched. We do not mean a place where cows graze!!! In a gravitational field it is a mass that experiences a force. In an electric field it is a charge that experiences a force. Electric field lines show the direction and strength of force that a charged particle will experience. Electric field lines will always go from positive to negative. If two particles of the same charge are brought together, they will repel each other’s electric field. Doon Academy page 7 CfE Higher Physics Unit 2 Particles and Waves An electric field can be used to accelerate a charge particle from one end to the other. It is accelerated because it experiences a force between the two electric plates. Doon Academy page 8 CfE Higher Physics Unit 2 Particles and Waves Definition of a Volt If 1 joule of work is done in moving 1 coulomb of charge between two points, there is a potential difference of 1 volt between the points. Ew QV Ew = Work Done (J) Q = Charge (C) V = Voltage (V) The work done is the minimum amount of energy required to move the particle from the lower plate to the upper plate and keeping it there. When the particle is released it will accelerate back to the lower plate. Using the conservation of energy, the final speed of the particle as it reaches the plate can be calculated. EW Ek 1 QV mv 2 2 v 2QV m Magnetic Fields Charged particles can also experience a force when placed into a magnetic field. This force will cause a charged particle to move in a different direction – usually in a circular motion. The speed of the particle does not change this time The direction in which the charged particle will experience the force once in the magnetic field can be determined using the “right hand rule”: Doon Academy page 9 CfE Higher Physics Unit 2 Particles and Waves Current – original direction of travel for charge particle. Field – the direction of the magnetic field lines Motion – the direction in which the particle will be forced. N.B. – The right hand rule only applies for NEGATIVELY charged particles. For positively charged particles, the force will in the opposite direction. Current – Right Field – Down Motion – “Out of the page” Doon Academy Current - Down Field – “Into the page” Motion - Left page 10 CfE Higher Physics Unit 2 Particles and Waves Radioactive Decay Links to National 5 – Alpha, Beta & Gamma; Ionising Radiation; Half-Life; Fission and Fusion Radioactive Particles – Atomic and Mass Numbers All stable nuclei have a set number of protons and neutrons. The atoms then consist of set numbers of electrons orbiting at different levels. If an atom becomes unstable, it will emit a particle or energy in the attempt to stabilise itself. The number of particles that a nucleus has can be determined using information from the periodic table. The information is always given in the following format: X Z A A = the element X = Mass Number (protons and neutrons) Z = Atomic Number (protons only) For example 45 21 Sc Element is Scandium It has 21 protons It has an atomic number of 45 24 neutrons Doon Academy page 11 CfE Higher Physics Unit 2 Particles and Waves Radioactive Decay An unstable atom can emit either particles or energy in an attempt to stabilise itself. There are three types of ionisation radiation that are emitted: Alpha (α)– the nucleus of a helium atom with the atomic arrangement of 4 He 2 Beta (β) – a fast moving electron. These are emitted when neutrons decay into protons and electrons. The atomic arrangement is 10 e Gamma (γ) – pure energy. This radiation has no mass or charge associated with it. Examples – Alpha and Beta Decay Ac 219 Fr 24 He 87 223 89 On either side of the arrow, the numbers on the top and bottom lines must equal each other i.e. for alpha decay total of 223 on the top and 89 on the bottom Po 215 At 01 e 85 215 84 Nuclear Fission and Fusion Nuclear fission is the splitting of an atomic nucleus into two smaller nuclei. This process releases a neutron and some energy. There are two types of nuclear fission: Induced – a neutron is fired into an atomic nucleus causing it to split. Spontaneous – an atom will split on its own. Nuclear fusion is the merger of two atomic nuclei to form a new substance. In both processes, fission and fusion, energy is given out in order to stabilise the newly formed substances. This energy is released because a small amount of mass is lost during the reaction. Doon Academy page 12 CfE Higher Physics Unit 2 Particles and Waves The amount of energy being released can be determined using, probably, the most famous Physics equation: E mc2 E = Energy released m = Mass lost in reaction c = Speed of light Example Plutonium undergoes the following fission reaction: Pu 01 n137 Te 100 Mo 301 n 52 42 239 94 The masses of the nuclei and particles involved are shown below Particle Mass (kg) n 1.675 x 10-27 Pu 396.741 x 10-27 Te Mo 227.420 x 10-27 165.809 x 10-27 Calculate the energy released by this reaction. N.B. This is the only question in which you do not round the masses when added together. Only your final answer can be rounded to an appropriate decimal place. Mass Before = 1.675 x 10-27 + 396.741 x 10-27 = 398.416 x 10-27 kg Mass After = 227.420 x 10-27 + 165.809 x 10-27 + (3 x 1.675 x10-27) = 398.254 x 10-27 kg Mass Lost = (398.416 – 398.254) x 10-27 = 0.162 x 10-27 kg E mc2 2 E 0.162x1027 3x108 E 1.458x1011 J Doon Academy page 13 CfE Higher Physics Unit 2 Particles and Waves Interference Links to National 5 – Wave Characteristics Interference occurs when two waves meet. Depending on how these waves meet will determine what is observed. Constructive Interference Constructive interference occurs when two waves meet in phase. If two waves are in phase this means that a peak will meet a peak/ a trough will meet a trough. The two waves will add together to produce a larger wave. This results in a sound wave appearing louder in certain places for example. Destructive Interference Destructive interference occurs when two waves meet when they are not in phase. This means that a peak will line up with a trough. The causes the wave to cancel itself out and nothing will be heard for example. Doon Academy page 14 CfE Higher Physics Unit 2 Particles and Waves Coherent sources Sources are coherenet if they have the same frequency and are in phase with each other. It is possible to create to coherent waves using only one source. If they source wave is passed through two small gaps spaced, roughly, one wavelength apart, it can create two coherent sources. Path Difference When using two different output sources, this can produce either coherent or incoherent waves, in turn creating constructive or destructive interference. An example of this is walking between two loudspeakers that are playing the same note from the same source. As you move from one speaker to the other, the note will apear louder and quieter in places. Doon Academy page 15 CfE Higher Physics Unit 2 Particles and Waves This change in interference is caused by the path difference. The path difference is created as each sound wave has a different distance to travel to reach your ear. As you move between the speakers, the distance change for each sound wave, creating points of constructive and destructive interference. C On the diagram above, the waves are meeting at point P. The distance the wave from source 1 travels can be written as S1P. The distance the waves from source 2 travels can be written as S2P. Path Difference = S2P – S1P Point C on the diagram indicates the first area of constructive interference. This is known as the Central maximum. The path difference will be zero as point C is the same distance from both sources. As an observer moves from point C towards point P, they will hear louder and quieter areas as the path difference is changing. It can be determined whether an area will produce constructive or destructive interference using the following. (Constructive) path difference = mλ (Destructive) path difference = (m + ½)λ Doon Academy page 16 m = 0,1,2,3… (m = 0 is central) m = 0,1,2,3… (m = 0 is central) CfE Higher Physics Unit 2 Particles and Waves Example Calculate the wavelength of the following source when P is the 3rd order maximum. Path Difference = S2P – S1P Path Difference = 550 – 520 Path Difference = 30mm Path Difference = mλ 30 = 3λ λ = 10mm Doon Academy page 17 CfE Higher Physics Unit 2 Particles and Waves Example State, with calculation, whether point P is a point of constructive or destructive interference when the wavelength of the source is 30 mm. Path Difference = S2P – S1P Path Difference = 300 – 225 Path Difference = 75 mm Path Difference = mλ (always assume to be constructive unless calculated otherwise) 75 = 30m m = 2.5 m=2+½ Point P is destructive Doon Academy page 18 CfE Higher Physics Unit 2 Particles and Waves Diffraction Gratings A diffraction grating is a thin film of plastic or glass that can be used to cause an interference pattern using a laser or other monochromatic light source. The film has thousands of narrow slits etched onto it. The distance between each slit on the diffraction grating is incredibly small as there is often thousands of slits per millimetre of film. To calculate the distance between each slit the following formula can be used. Slit Separation Size of film Number of slits Example – There are 15,000 slits per millimeter on a diffraction grating. What is the slit separation? 1x10-3 Slit Separation 15000 Slit Separation 6x10-8 m Doon Academy page 19 CfE Higher Physics Unit 2 Particles and Waves Similar interference patterns are created and there will be areas of constructive and destructive interference (areas or light and dark). On this occasion a screen has to be placed a certain distance from the source in order to observe the interference pattern. The wavelength of light being used can be determined using the angle between the central maximum and area of interference, as well as the slit separation on the diffraction grating. d sin m m 0,1,2,3... (constructive) 1 d sin m m 0,1,2,3...(destructi ve) 2 d = slit separation (m) Θ = Angle between central maximum and point of interference (°) λ = Wavelength (m) Doon Academy page 20 CfE Higher Physics Unit 2 Particles and Waves Example Light from a monochromatic source strikes a diffraction grating of 400 lines per mm. The first order maximum is produced at an angle of 140. Find a) the slit separation b) the wavelength of the source. Length 1x10-3 (a) Slit Separation 2.5x10-6 m Number of Lines 400 (b) m d sin 1 2.5 x10 6 sin 14 6 x10 7 m Example Light of wavelength 6.5 x10 -7 m is shone onto a grating. The angle between the zero and third order maxima is 31.5°. Calculate: (a) (b) The spacing between the slits on the grating. The number of lines per mm on the grating. m d sin 3 6.5 x10 7 d sin 31.5 (a) 0.52 d 1.95 x10 6 d 3.75 x10 6 m Slit Separation (b) Length Number of Slits Length 1x10-3 Number of Slits 266.6 lines per mm Slit Separation 3.75x10-6 Doon Academy page 21 CfE Higher Physics Unit 2 Particles and Waves Refraction of Light Links to National 5 – Refraction; Total Internal Reflection; Critical Angle Refraction of light occurs when a ray of light passes from one medium to another – from air into glass for example. Refraction causes the speed of light to change (slow down). Even though it causes a change in direction this is not the meaning of refraction!!!!!! As the angle of incidence increases, so does the angle of refraction. Each angle is measured between the ray of light and the normal outside and inside the glass respectively. At this stage there is no clear relationship between how much each angle increases by. However, if the sine of each angle is taken, the is a direct correlation between each angle. Doon Academy page 22 CfE Higher Physics Unit 2 Particles and Waves The above graph shows that sin 1 constant sin 2 This constant is called the refractive index (n). In air, the refractive index is 1. sin 1 n2 sin 2 n1 N.B. Be careful not to use Θi and Θr for angle of incidence and angle of refraction and na and ng for the refractive indices. Some questions can begin inside a material other than air so n1 may not always be 1. Example A ray of red light passes from air into water The refractive index of water for this light is 1.33. Calculate the angle of refraction in water. Doon Academy page 23 CfE Higher Physics Unit 2 Particles and Waves n 2 sin 1 n1 sin 2 1.33 sin 70 1 sin 2 sin 70 sin 2 0.7065 1.33 2 45 When light passes from air into glass, the speed decreases and the wavelength also decreases. Frequency will only decrease if the source of light is changed. By how much the speed and wavelength decrease by is also linked to the refractive index a material. n2 sin 1 1 v1 n1 sin 2 2 v2 The Critical Angle Whether a ray of light will refract or totally internally reflect whilst inside a material is all depends on the critical angle. If the angle of incidence is less than the critical angle it will refract. If the angle of incidence is equal to the critical angle it will refract at 90° If the angle of incidence is greater than the critical angle it will totally internally reflect. Doon Academy page 24 CfE Higher Physics Unit 2 Particles and Waves At the critical angle, the value for refraction in air is 90° sin 1 n2 sin 2 n1 sin c 1 sin90 n sin90 n sin c Since sin 90 1 1 n sin c Example A ray of red light passes from air into glass. The refractive index is 1.5 for this light in glass. Show by calculation whether the ray is totally internally reflected or not. Doon Academy page 25 CfE Higher Physics Unit 2 Particles and Waves 1 sin c 1 1.5 sin c 1 sin c 1.5 c 42 n The angle of incidence (63°) is greater than the critical angle (42°) so the light will totally internally reflect. Doon Academy page 26 CfE Higher Physics Unit 2 Particles and Waves Irradiance The irradiance of radiation (light) at a surface is the power per unit area of surface the light falls on. I P A I = Irradiance (Wm-2) P = Power (W) A = Area (m2) This can be used for light rays that spread out the further they get from the source or for point sources i.e. a laser. Example A lamp shines onto a surface of area 4 m2. The irradiance at the surface is 0.02 Wm-2. Calculate the power of the incident light. I P A 0.02 P 4 P 0.08W The irradiance of a light source will decrease over as the distance from the source increases. The diagram below shows how the power is spread out thus reducing the irradiance. Doon Academy page 27 CfE Higher Physics Unit 2 Particles and Waves The relationship between irradiance and the distance from the source can be given as: I1d12 = I2d22 The overall combination of irradiance and distance must be the same before and after the light source has been moved. Example A light source produces an irradiance of 0.2 Wm-2 at a distance of 2m from the light source. What will be the irradiance at a distance of 4m from the source? I1d1 I2d2 0.2 22 I2 42 0.8 I2 16 I2 0.05Wm2 2 Doon Academy page 28 2 CfE Higher Physics Unit 2 Particles and Waves Photoelectric Effect and Spectra A beam of radiation can be regarded as a stream of individual energy bundles called photons. Each photon will carry a certain amount of energy. The amount of energy it has is related to the frequency of that photon. E hf E = Energy of photon (J) h = Planck ’s constant (6.63 x 10-34 Js) f = Frequency (Hz) Electromagnetic radiation above a certain frequency can eject electrons from the surface of some metals. When an electron is ejected from a piece of metal, this is known as photoelectric emission. Below a certain frequency, known as the Threshold Frequency, there will be no photoelectric emission. This is due the photons not carrying enough energy to release an electron from the piece of metal. Doon Academy page 29 CfE Higher Physics Unit 2 Particles and Waves When the frequency increases, along with an increase of irradiance, the photoelectric emission increases causing a larger flow in current. Work Function Each electron requires a minimum amount of energy needed from a photon before it will release itself from a piece of metal. This minimum amount of energy is known as the Work Function. Example The work function of a piece of metal is 5 x 10-19J. A photon of frequency 4.48 x 1014 Hz is incident on the metal. Show, by calculation, whether an electron will be released or not. E hf E 6.63x1034 4.48x1014 E 4.95x1019 J An electron will not be released as the energy of the photon is less than the work function. If a photon is incident on a piece of metal that has an energy which is higher than the work function, the electron will have a certain amount of kinetic energy. Ek hf hfo Doon Academy page 30 CfE Higher Physics Unit 2 Particles and Waves Emission Spectra In the Bohr model of the atom electrons are confined to certain orbits (shells). Electrons can move between energy levels. Light is emitted when an electron falls from a high energy orbit to a low energy orbit. Electrons can also jump from low energy levels to higher ones in a photon is incident on the atom. Just like with the photoelectric effect, the photon must have the right amount of energy in order for an electron to jump. The ground state is the lowest energy level in the atom. The ionistation level is the point at which an electron is ready to be released if given enough energy. Doon Academy page 31 CfE Higher Physics Unit 2 Particles and Waves All energy levels are in negative values. The ground state will have a larger numerical value than W1 but is still a lower energy level. When an electron drops from a higher energy level to a lower one, it can emit visible light photons. The colour of these photons can be determined using the frequency produced. However, all forms of electromagnetic radiation can be emitted from falling electrons. Example (a) (b) Which transistion produces radiation with the longest wavelength? Calculate the frequency of the photon produced when an electron falls from E3 to E2. (a) Longest wavelength Shortest Frequency Smallest energy E4 E3 (b) E3 E2 2.4 ( 5.6)x1019 3.2x1019 J E hf 3.2x1019 6.63x1034 f f 4.8x1014Hz Doon Academy page 32 CfE Higher Physics Unit 2 Doon Academy Particles and Waves page 33
