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Waves and Cosmology - AQA GCE Physics Revision Notes

Extracts from this document...

Introduction

Matter waves

• As waves can behave as a stream of particles, particles can also behave as a wave

De Broglie wavelength:         λ =         where mv is the momentum of the particle

• Diffraction rings are where electron waves interfere constructively to produce a maximum - energy gained by electron is equal to the kinetic energy of the electron.

Here, electrons are accelerated by a voltage of 2000 V;

2000 x (1.6 x 10-19) = x (9.11 x 10-31) x v2                    Mass of electron = 9.11 x 10-31

3.2 x 10-16 =  x (9.11 x 10-31) x v2

v2 = 7.025247 x 1014

v = 2.65 x 107 ms-1

So the momentum of electron: (9.11 x 10-31) x (2.7 x 107) = 2.5 x 10-23 kgm/s

The de Broglie wavelength:  λ = = = 2.6 x 10-11 m

• If the accelerating voltage increases, energy and momentum of the electron would decrease the wavelength. Shorter wavelength blue light falling on diffraction grating produced fringes that are closer together than longer wavelengths (red light).
• Resolving power is the wavelength of radiation used to determine the smallest object we are able to detect with it. The smaller the wavelength, the better the resolution. I.e. Resolution of visible object is limited by its wavelength of 5 x 10-7 m.

In electron microscope, electrons are accelerated through 30000 V have wavelength         of about 10-12 m, and so can produce images of object as small as a nanometre.

When probing matters, the accelerated particle has to have a wavelength about the         same size as the particle it is colliding with. So for electrons to probe the proton, its         de Broglie wavelength should be about the same as the proton diameter 2.4 x 10-15

Momentum of electron:        λ =   =>  mv = = = 2.75 x 10-19 kgm/s

Kinetic energy required: mv2   =>  = = 4.15 x 10-8 J

This would be around: = 2.59 x 1011 eV

• Bohr mode of the atom suggested that electron accelerated around the nucleus in its orbit. Accelerating electron radiates energy and as its energy is lost; the electron will spiral towards the nucleus (due to electrostatic attraction) and collide into the nucleus, as it doesn’t have enough energy to remain in orbit.

So it is suggested that electrons can only have certain discrete values/ quantized                 energies so there is a stationary wave with whole number of loops in the        orbit.

When n=1, there’s one loop (half a wavelength)

When n=2, there’d be two loops (one whole wavelength)

Fundamental particles

• The standard model suggests that there are 2 types of fundamental particles – leptons and quarks. They each have a n equivalent antiparticle.
• Leptons are small point like particles and electron is a lepton with a charge of -1e and its antiparticle, the positron, has a charge of +1e

• There’re 3 leptons families the electron (e), muon (μ) and tau (τ) each with their associate neutrino (and antineutrinos) that are electrically neutral. Electron and muon are very light particles whereas tau is heavier (around 1800 x that of an electron)
•  Each lepton is given a lepton number, particles (neutrinos) have a lepton number of +1 and the antiparticles (antineutrino) have a lepton number of -1.
• Neutrinos are every hard to detect but come in vast numbers from all directions in space. They can pass through earth without its intensity decreasing and they rarely interact with other particles.
• The beta particles emitted in beta decay have a range of energies from virtually 0 to maximum energy. In beta decay, Etotal of recoil nucleus and β particle are not always constant – leading to a suggestion that a β particle is not the only particle emitted during beta decay, as the Ebefore = Eafter due to the laws of conservation of energy.
• It is predicted that there exist a particle that would carry away the energy and momentum and evidence is found for the existence of neutrinos. In beta decay, antineutrino is emitted to conserve lepton number; they have a very small mass.
• The quark family consist of 6 particles and 6 corresponding antiparticles. Quarks are never found on their own but exist in hadrons – which are formed from different combinations of quarks.
• Quarks are assigned baryon numbers to explain which particle can exist and outcome of interactions. All quarks have a baryon number of 1 / 3, whereas all anti quarks has a baryon number of -1 / 3.
• Strangeness explains the behaviour of massive particles such as kaons, they are created in pairs in collisions and have a longer lasting lifetime (10-10 s not 10-23 s)

The property of strangeness sis conserved during their creation but not when they decay. A strange antiquark has a strangeness of +1 (K0 – ds or sd/ K+ - us) whereas a strange quark has a strangeness of -1 (K- - su)

A particle that contains a strange quark automatically has a strangeness of -1, and if there are 3 strange quarks present, the particle would have strangeness of -3.

• A Feynman diagram demonstrates the interaction between particles.

Particle and their interaction

• When new particles are produced in accelerators, pair production occurs, where a particle is produced along with a corresponding particle.
• When a particle collides with its antiparticles, they annihilate each other (disappear/ destroyed) i.e. when an electron meets a positron a Z0 particle. It has a short lifetime. At low energy, it decays to produce photons of EM radiation (used in PET scanners)

At high energy, Z0 decays to produce another electron – positron pair or a quark – antiquark pair, resulting in streams of new particle.

• Particles consisting of quarks makes up a class of particle makes up a class called hadrons, they experience the strong force and has 2 sub classes – baryons (3 quarks) and mesons (consists of 2 quarks)

The only stable baryon is the proton, all other baryons eventually decays to form a proton and something else. Quarks have baryon number of +1 / 3, whereas anti- quarks have baryon number of -1 / 3

• Baryons have 3 quarks and have a baryon number of -1 or +1, whereas mesons consist of 2 quarks and have a baryon number of 0.
• When particle interact / decay, the event must follow the conservation rules. Energy and mass are equivalent, so energy could be converted into mass and vice verse.
• In particle physics, the total charge, baryon and lepton numbers must also be the same after the event as it is before.
 Particles Baryon number Charge Proton (uud) + + = 1 + - = 1 Antiprotons (uud) + + = -1 + + = -1 Neutron (udd) + + = 1 + + = 0 π+ (ud) + = 0 + = 1 K+ (us) + = 0 + = 1
• Particle containing a strange quark have a strangeness of -1, the K0 meson contains an anti-strange quark so has a strangeness of 1. Particles with 3 strange quarks have strangeness of -3.
• When a strange particle decays through weak interaction, strangeness is not conserved (i.e. when strange quark turns into an up quark). But strangeness is conserved when there is a strong interaction – involving strong force.

Hence, strange particles always occur in pairs, if 2 particles interact to produce a strange particle, than a strange antiparticle must also appear.

π-  +  p  ->  K0  +  λ0

ud  +  uud  ->   ds   +   sud

π-  +  p  ->  π-  +  π+  +  π-  +  p

The K meson and the hyperon (lambda particle) doesn’t produce any tracks in a bubble chamber.

The K0 meson decays into a π- pion and a π+ pion, which annihilates each other, whereas the λ0 decays into a π- pion and a proton. However, in each of these two decays, the strangeness is not conserved.

Forces of nature

• There are 4 forces between the interactions of particles, they are mediated / transmitted by particles called gauge boson.
• The bosons carry the force between particles. I.e. electrons can exchange a photon with a neighbouring electron, leading to the EM force. The exchange particle is a virtual particle as it is not detected during the exchange. It acts as a force mediator.
• The exchange particle can’t be detected in its transfer or it can’t act as the mediator of force. The larger the rest masses of the exchange particle, the lower the time it can be in flight without detection, therefore the lower the range.
• The strong force is the strongest of the forces. It keeps the nucleus together (between nucleons and hadrons). It acts between quarks and therefore between nucleons (protons and neutrons)

It is strong enough the overcome the large repulsive force between the protons in the nucleus or the quarks that make up the protons. The strong force is mediated by gluons - the π+& π- pions are vehicles responsible to carry gluons between hadrons.

The strong force is attractive at nuclear distance however if the distance is too small, the strong force becomes repulsive. If the nucleus gets too big, the strong force breaks and emits alpha particles.

• Electromagnetic force is found exerted between charged particles at rest / in motion. So it affects the charged quarks and leptons. The exchange particle is the photon, photons have no mass and this leads to an infinite range (chargeless)

Therefore when two charged particles exert a force on each other, a photon is exchanged between them. It is its own antiparticle.

• The weak nuclear force is responsible for radioactive decay by beta emission (it also holds the quarks together) in beta decay, a neutron decays to a proton (udd to uud). Here a W-boson is exchanged as a down quark changes to an up quark. The W boson then immediately decays into an electron and an electron antineutrino.

The W bosons (W+ / W-) and Z particles here are very massive, leading to that range of force being very short, only reaches 0.01 of the diameter of a proton (10-18 m) It is the only way a quark can change into another quark (or lepton into another). So the W+, W- and Z bosons are called the intermediate vector bosons. Weak interaction is when changes occurred in quarks (i.e. leptons and hadrons).

• Gravitational force is the weakest of the forces, it has an infinite range and is the dominate force operating within and between galaxies. Theory suggests that the exchange particle for gravitational force is graviton – not been confirmed.
• At high energy, electromagnetic force and weak nuclear force cannot be distinguished. They merge to form the electroweak force. At the time of big bang, all forced were all as one but began to separate as universe cooled down.
• The grand unification theory is to combine the electroweak force with the strong force. Next step is to include gravity - this is the theory of everything.

Middle

Weak nuclear

Between quarks

Bosons

10-6

10-18 m

Gravity

Due to mass

Gravitons

10-40

infinite

Big bang and big questions

• Evidence for big bang theory - suggestions of expansion and cooling of universe:

-        The wavelength of light received from galaxies are longer than expected if they                 were stationary - it has shifted to red end of the visible spectrum. Meaning the                 galaxies is moving further apart - so universe is expanding.

-        Chemical composition of stars, galaxies and space have been analyzed using                         line spectra and the strikes of coloured light showed same patterned as a                         particular element on earth, but shifted slightly to the red end of the visible                         light spectrum, this again shows expansion of universe.

Also the physical processes of stars and galaxies changes as the temperature of         the universe fell due to expansion of the universe.

-        At the early stages of the formation of the universe, high energy photons with                 very short wavelength were produced, but they lose energy as the universe                         expands. As photon energy is lost, the wavelength becomes longer; it is                                 predicted to be at the microwave region now.

This is equivalent with radiation from a black body at a temperature of 2.7 k -         which is the current temperature of the universe. The original radiation would         have been in the visible region, but it has been red shifted as energy is lost from         the photon due to expansion of the universe.

• As a microwave receiver is set up, a signal of wavelength 735 cm was picked up when no signal was sent. It came space and was equally strong in all direction, persisted all the time. The COBE (Cosmic Background Explorer) satellite was launched to look for energy distribution of wavelengths that cannot penetrate the atmosphere. The result showed that the radiation was at black body radiation of temperature around 2.7 K.
 Beginning of time 10-43s The smallest element of time measurable. Grand unification era 10-34s Inflation, 4 forces separates - 1st was gravity Heavy particle era 10-10s W and Z particles existed and decayed Light particle era 10-7-3s Helium-4 nuclei (α), protons & neutrons forms Radiation era 10000 yr EM radiations forms - Origin of CMB radiations. Matter era 300000 yr Form H and He atoms, CMB radiation forms Galaxies formed 108 yr Galaxy forms.
• There have been thoughts about where quarks really are fundamental, as the same has been thought about neutrons and protons and they proved to be made of smaller particles. The large hadrons collider can provide answers.
• The theory of mass is that it’s caused by particles reacting with another particle called the Higgs boson; massive particles interact more strongly with the Higgs boson than lighter ones. Mass is a measure of a body’s inertia (how difficult something is to accelerate). According to this theory, a massive object finds it harder to move due to its strong interaction with the particles in the Higgs field that fills space (Higgs bosons).
• Only 4% of the matter in the universe has been accounted for. However motion of stars and galaxies suggested there’s more mass - dark matter. Dark energy is those which work against gravity - it continually increases the rate at which the universe is expanding.
• There must’ve been an imbalance during the early stages of the big bang where there were more matter then antimatter, because if there were equal amounts of both, they would’ve annihilated each other.
• There are 3 possible future of the universe depending on the density of the universe (density of dark matter?) - can be defined in terms of the density parameter, Ω.

Ω =

-        Ω < 1, Universe would be open and continue to expand forever.

-        Ω = 1, Universe is flat and would only expand to a certain limit.

-        Ω > 1, Universe would cease to expand eventually and collapse to a point; this is                 the big Crunch model.

Light from the stars / stellar spectra

• Luminosity of a star is the total power (energy per second) it radiates.

Luminosity of a star (Wm2) = Power (per m2) x Surface area (4πr2)

The power radiated by each square meter of the surface of a star depends on its surface temperature. Therefore the luminosity depends of both the power per square meter and the surface area of the star.

So comparing 2 stars, if the cooler one emits half the power per square meter compared to the hotter one, its surface area would have to be double that of the other star in order for them both to have the same luminosity.

• The apparent magnitude of a star is just how bright it seems to an observer. Brightness is a comparison of the energy per second that falls on the pupil of the eye. The brightest stars that are visible to the naked eye are referred to as stars of the 1st magnitude, and the dimmest are 6th magnitude stars.
• This scale is defined so that the intensity of light from the brightest star is 100 time that from the dimmest. A decrease of 1 in magnitude is an increase of 1001/5 (2.51) times in the intensity of the light received by the observer.
• How the power emitted by a star compares with other stars is a comparison of the real luminosity of a star – this is the absolute magnitude. A dim star close to earth may seem to be emitting more power than a brighter star that is further away. To make a fair comparison, the brightness of each star is calculated as it would be if it were 10 parsecs (32.6 light years) away from Earth.
 Star Apparent magnitude Distance from earth Absolute magnitude Relative luminosity Sun -26.7 1.5 x 10-5 4.8 1 Sirius -1.44 8.6 1.45 22.5 Vega 0.03 25.3 0.58 50.1
• Stars have many different colours that are related to its surface temperature. Most energy emitted by a cool star is in the infra-red region with some red light. Shorter wavelengths appear in hotter stars so these would look yellow or white. Very hot wavelengths seem blue as the intensity of the short wavelengths increase.

• A continuous spectrum comes hot (incandescent – emission of light as a result of being heated) bodies such as hot/molten iron. In a lab, this can be investigated using glowing metal in the form of a filament lamp. A determination of where the peak of the energy is in this spectrum gives the temperature of the star.
• A line spectrum is the result of excitation of atoms. These spectra only contain certain well defined wavelengths. The wavelengths present are characteristics of the element that produces the light so comparison of the starlight with a laboratory source (of chemical composition) reveals the element in the star. In a lab, this is normally produced when light form electrical discharge tubes, containing gas or vapour, is diffracted through diffraction gratings. Where there’s several separate energy level.
• A band spectrum is produced in the same way as a line spectrum but it is produced by molecules. It consists of bands of light produced by a range of wavelength separated by gaps. Where there are many energy levels close to each other, making it seem like the energy levels are distributed continuously.
• When the continuous spectrum of the light from a star is analyzed, the spectrum contains dark lines. This is an absorption spectrum. Like the emission spectrum, these lines enable analysis of the chemical composition of the star. They are caused by the light passing through atoms and ions in the outer region of the car.
 Star Temperature Colour Cause of absorption line O More than 30000 Blue Ionised helium B 11000 - 30000 Blue - white Helium atoms and hydrogen A 7500 - 11000 White Hydrogen and some ionised calcium F 6000 - 7500 Yellowish - white Ionised calcium and metal atoms G 5000 - 6000 Yellow Calcium atoms and metal ions (i.e. Iron) K 3500 - 6000 Orange Metal atoms M Less than 3500 Red Molecules of TiO2 - band spectra.

Conclusion

8). Therefore the most distant observable galaxy would be at a distance of:

d =  =>  = 4600 Mpc away

This distance would be the speed (c) multiplies by the time (t) it has taken to get there following the big bang (ct).

Therefore  ct =  => leading to an ages 4.8 x 1017 s or 1.5 x 1010 year

• The red shifts of the radiation from quasar are exceptionally large showing them to be moving at speeds approaching the speed of light. These are the most distant objects that are visible.

The nearest quasars show red shifts that corresponding to a speed relative to earth of about 0.15c (0.15 x (3 x 108)) and speeds in excess of 0.93c have been measured for the most distant quasars (which is about 1.3 x 1010 light years away). So light has taken 1.3 x 1010 years to reach the Earth from these distant quasars.

• Quasars (quasi-stellar radio sources) are the brightest objects that have been observed. The most energetic quasar observed have luminosity 1000 times greater than one of the brightest galaxies.

The first quasar discovered from their intense radio emissions. However, those discovered since then emit visible or x-ray radiation with little/no energy in the radio frequency range.

• The energy radiated from a quasar is thought to be caused by a black hole at the centre of a galaxy. All galaxies are thought to have a black hole at their centres; however, in the case of a quasar present, the black hole is so massive that it absorbed the gaseous matter in the galaxy at an enormous rate.

The gaseous matter reaches speeds close to the speed of light as it approaches the black hole and radiates high amounts of X-rays, visible and radio radiation as it does so – leading the radiation from a relatively small region (1 ly across) in the centre of the galaxy being thousands x greater than from the rest of the galaxy.

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