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.
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.
- 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.
- 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.
Hertzsprung - Russell diagram
-
The luminosity scale uses the Sun as a reference. Sp a star with relative luminosity of 100 emits 100 times the power of the sun.
- Neither of the scale is linear, in going from one grid line to the next, the luminosity increase by a factor of 100. And on the temperature scale, the temperature halves from one grid line to the next.
- The stars are not randomly spread throughout the plot but are found to occur in groups of particular types. This suggests that there is a particular sequence of events in the evolution of a star and its subsequent ‘death’.
-
Main sequence stars are ordinary dwarf stars like our Sun that produce energy form the fusion of hydrogen and other light nuclei such as helium and carbon. The vast proportion of the star (over 80 %) fit into this category.
-
Red giants are cooler than the Sun and so emit less energy per square meter of surface. But they do have a higher luminosity (100 times more energy per second than the Sun) - so they have a much larger surface area to emit that amount of energy. They therefore have a much larger diameter than the sun.
-
White dwarfs are the remains of old stars. Although they are very hot, they have a relatively low luminosity showing them to have small surface area.
-
Supergiants are enormous and very bright. A super giant emitting 90000 times the energy of the Sun at the same temperature must have a surface area 90000 times larger. This leads to a diameter that is 300 times the diameter of the star (√90000).
- The formation of a star begins with the gravitational attraction of interstellar hydrogen nuclei. The loss of potential energy leads to an increase in the gas temperature. The gas becomes denser & when the temperature gets hot enough - nuclear fusion begins. This creates helium nuclei and these can also fuse ( as temperature rises) releasing more energy - this is the main sequence of a star.
The luminous stars in the main sequence last only for a short period of time.
- Eventually, sun-like stars collapse as all the hydrogen nuclei in the core are used up. In these stars, the core temperature rises as helium nuclei fuse. Therefore, the hydrogen in the outer layer now begins to fuse - raising the temperature of the outer layer, which expand. As the star expands, the temperature falls, and so it becomes a red giant
Now the fusion of helium nuclei raises the temperature of the core further and even heavier elements forms. The star will collapse to become a small hot white dwarf.
Then, what happens when the white dwarf forms depends on the mass of the star. Stars like the Sun would just fade away but white dwarfs with a mass greater than about 1.4 times the Sun’s mass can either explode into smaller white dwarfs or collapse suddenly and become an intensely bright supernova.
Continuous spectra
- Radiation from a black body produces a continuous spectrum. A black body is a good radiator (both absorbs and emits wavelengths). It is said to be a perfect emitter, as it emits all wavelengths possible for its temperature. The Earth is at a temperature of about 300 K emits mostly infrared radiation and the Sun mostly emits visible light.
At the left side of the scale, the wavelength is relatively shorter, therefore the star would appear blue (the peak would also be higher as the intensity also increase.) Whereas if the peak is on the right side of scale, the star would appear to be red (due to longer wavelengths).
-
So as temperature rises, the peak of the black body radiation moves to a shorter wavelength (the left). Wien’s law can be used to calculate a black body’s T and λmax.
- How black body differ from others can be demonstrated using two thermometers (one with bulb painted black), if both are places near a heat source, the reading of the thermometer with the black bulb rises more quickly, showing it’s absorbing more energy (per second)
- Another experiment is using a cube with 4 different sides (matt black, matt white, smooth black and shiny silver surfaces). If it is heated with a light bulb inside it, as voltage is adjusted, the temperature of bulb would vary. The intensity of the radiation from each surface for a particular temperature can be measured using an infrared sensor. The matt black surface gave the highest reading the shiny silver surface the least.
-
The power radiated by a black body increases rapidly with temperature. Double the temperature of a surface means the power radiated by each square meter of the surface is 16 (24) times greater.
- Using the spectrum of a star, we can find its luminosity as we can determine:
- The wavelength at the maximum intensity occurs
- The temperature of the body using Wien’s law
- The power emitted per square meter from the surface.
If the radius of the star is known from astronomical observation, then the surface area can be found and hence the luminosity.
Line spectra
- Emission line spectra can be seen when light from a gas discharged tube is analyzed using a spectrometer. Each line is present due to a particular defined wavelength of light. Each set of lines that form the spectrum is unique to the element in the discharge tube. Astronomers can determine the chemical composition of stars and interstellar gases using emission spectra.
- Light is emitted when atomic electrons that have moved into excited states give up some of their energy and become relaxed. As there are only certain defined frequencies present in the spectrum provides evidence for energies of electrons being quantized – meaning electrons can only have certain energy levels (quantized energy).
- They can only move between the energy levels by absorbing/ giving up energy in a mounts equal to the difference in energies between the levels. The unique sets of spectral lines are due to different set of energy levels in each element.
- An electron that is free of an atom is defined as having 0 energy, therefore for a bound electron, as energy must be added to release it; its energy within the atom is negative. The lowest possible energy level an electron can occupy is called the ground state (n=1).
The allowed energy levels become closer together as the electrons moves to higher energies. These are the excited states that the electron can occupy. These energy are usually given in electron-vole (eV)
-
Ground state of the electron in a hydrogen atom is -13.6 eV, which is (-13.6 x 1.6 x 10-19) -21.8 x 10-19 J. The amount of energy required to move the electron from ground state to n = ∞ would be 21.8 x 10-19 – this would be the ionization energy of the atom because the electron is now free and has left the atom.
- Electrons in excited states are not stable. Therefore electrons only remain in these excited stated for a short period of time before releasing the energy gained and returning to lower energy states. They lose energy by emitting a photon of electromagnetic radiation. The photon energy (hf) is equivalent to the energy difference between the levels.
hf = E1 – E2 or = E1 –E2
-
Electrons may move to the ground state by emitting a single photon, or if the excited state is higher than n = 2, it emits photons in stages. When an electron moves from an energy level of -3.4 eV to -13.6 eV the energy lost would be -3.4-(-13.6) = 10.2 eV or this could be 16.3 x 10-19. This would be equal to photon energy (hf), so frequency would be:
Radiation emitted = = 2.46 x 1015 Hz
The corresponding wavelength would be, = = 122 nm, which would be in the ultraviolet region of the electromagnetic spectrum.
- The Lyman series is the result of transition into the n = 1 level, giving rise to high energy photons in the UV regions of the spectrum. Whereas the Balmer series comes from transition into the n=2 level, emitting photons in the visible region of the spectrum. The Paschen series is the result of transition to the n = 3 level and releases infrared radiation.
- The spectrums observed from stars aren’t continuous. There are dark lines crossing the spectra showing some wavelengths are either missing or have a much reduced intensity.
The wavelengths that are missing are characteristic of the elements present in the outer regions of the star that the light must pass through before reaching the earth. Just like how emission spectra tells us which elements are emitting the radiation, absorption spectra tells us which elements are absorbing it, so the chemical composition of the outer regions of the stars can be determined.
- The electrons in the gas atoms are excited into higher energy levels. Only photons having energy equal to the difference in energy between two levels can be absorbed by the gas - so only well defined frequencies are removed from the spectrum.
Once the electrons have been excited they’re in an unstable state. As they relax into lower states they radiate energy. However the intensity of a given wavelength in a particular direction is now reduced:
-
The light that is re-emitted from the gas cloud travels in all direction so less would be travelling in one direction.
- The electrons relax in stages emitting lower energy photons that are in a different part of the EM spectrum (longer wavelength than original)
The Sun’s spectrum has the same general shape as the black body curve. The dips are the wavelengths that are absorbed by the gas that surrounds the Sun.
- Without a bright light source, the emission spectrum from a sodium flame consists of a yellow line (wavelength of 590 nm) When a diffraction grating with a very small spacing is used between two lines, two yellow line (that’re close to each other) can be seen on the spectrum - emission spectrum.
If a lamp emitting very bright white light is viewed through the sodium flame, the dark lines cross the lamp’s continuous spectrum in exactly the same place as the lines that are seen in the sodium emission spectrum - absorption spectrum.
-
Pass white light through Iodine vapour (from heating iodine crystals in a sealed boiling tube) the continuous spectrum now has equally spaced dark bands. This isn’t caused by the energy levels of iodine atoms but by the quantized vibration stated that the iodine molecules can exist in. The I2 molecules cannot take in energy in very small amounts as they can only take in well-defined packets of energy.
The expanding universe
- Red shift is the observation that the wavelength of radiation from some stars has a longer wavelength (therefore lower frequency) than radiation from a similar source in a lab on Earth. – The Doppler Effect predicts such a change when a source of radiation is moving away from an observer.
- For the optical spectrum, the wavelengths are moving towards the red end of the spectrum. The faster the motion, the greater the change in wavelengths towards the red end of the spectrum. Since the red shift applies to all waves in the spectrum, even the absorption lines in the spectrum will be shift to the red end.
- The high pitched siren from an ambulance as it approaches the observer changes into a lower one as it moves away, the true pitch is when the ambulance passes by. This effect is observed whenever there is relative motion between the source and the listener.
As long as they’re either moving closer together or further apart, it doesn’t matter whether one or both is in motion. In astronomy, it is the motion of the source relative to Earth that is relevant.
- As the source moves, the waves are bunched into a smaller distance (higher frequency, shorter wavelength) in the direction in which it’s moving, and the wave is stretched in the opposite direction.
-
If a source emitting a frequency f, and the observer is stationary, then f would pass the observer each second, λ = (where λ is the true wavelength of the wave)
If a source is travelling at a speed of vs towards the observers, the wave emitted at the start of 1 s would have travelled a distance v (m/1 = m) and when the last wave in the 1 s interval is emitted, the source is the distance vs closer to observer.
The f waves would now occupy a shorter distance of (v – vs), the wavelength would be (using the above equation): λ =
Whereas the change in wavelength would be: Δλ = - [ ] =
Rearranging the two equation gives: f = and f =
Equating them would give = => =
If the velocity of the source of small compared to the velocity of the wave ( vs < < v ):
=
- Stars systems consisting of two stars rotating about a common center of mass are called binary stars. As they rotate, one star moves away from the earth so the spectra lines are red shifted. The other star moves towards the earth producing a blue shifted spectrum.
The velocities that give rise to the motions can be found from the shifts and the rates of rotation determined. The spectra lines that are emitted from opposite sides of the stars are also blue and red shift – rotational speed can be determined.
- The orbital speed of stars in a galaxy can be found using the Doppler Effect. It is shown that the orbital periods of stars can be far higher than expected from the estimated mass of the material in the galaxies.
This means that some of the mass of the galaxy is unaccounted for - this missing mass is called dark matter.
- Edwin Hubble suggested that the recessional speeds of galaxies at different distances from the Earth (using red shift) the further away they are the faster they are moving (a factor that is consistent with the Big Bang theory). He predicted that the velocity v was proportional to the distance d of a galaxy from Earth.
This gives the Hubble law: v = Hd where H is the Hubble constant
Value of Hubble constant H has changes over the years as measurement of astronomical distances and velocities have been determined more accurately. There were uncertainties in the data Hubble used – giving a value f 500 kms-1 Mpc-1, however using more reliable data, H is thought to be around 65 kms-1 Mpc-1 now.
-
The age of the universe can be estimated from the Hubble constant. Assuming that it holds for all stars, the maximum speed of a star (one that’s at the edge of the observable universe) is the speed of light (c = 3 x 108). 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.