THE LORENTZ FACTOR

The Lorentz Factor is a way of expressing the ratio of the time taken for an event to occur against its proper time. The equation for it is 1/[(1-(v^2/c^2))^0.5]. It looks terrible because blogger doesn't support the nive way of expressing equations, it isn't actually that bad. Anyways, the Lorentz Factor is only noticeable at velocities which are extremely near the speed of light. We don't notice it in everyday life because relative to the speed of light, we are travelling at extremely low velocities. The graph below shows how the value of the Lorentz Factor only becomes significant at above 90% the speed of light.

Yeyeye It's time for some RELATIVITAAAYYY

Frames of References (H1.1):
If you were to sit in a room, next to someone in the same room also sitting down, neither of you are moving, relative to each other. The person next to you is sitting still, he has no velocity. However this is from the frame of reference that it yourself, the observer of this 'event' is yourself. Relative to yourself, he has no velocity. However, if you were to change the frame of reference to an observer from outer space, he/she would see the entire planet as orbiting the sun as well as rotating about it's axis. As a result, both yourself and the person next to you in the room would be moving at a velocity which is equal to the orbit of the earth around the sun and its orbit about the axis of the planet, relative to the observer in outer space. Therefore velocity is not absolute when there are multiple frames of references for the same event. In one frame of reference, the velocity is zero, whereas in another frame of reference, the same event is observed to be travelling at a great velocity. The IB definition of a frame of reference: A system of coordinates that enables measurements to be made or A system of coordinates that enables the position of various objects to be specified.


Galilean Transformations (H1.2):
A Galilean transformation is a way of mathematically quantifying the velocities of two objects as they are relative to each other. If you imagine two particles travelling towards each other at 0.98c, then the relative velocities of the particles relative to each other would be the sum of their two velocities. Since they are both travelling at 0.98c, the Galilean transformation would be 1.96c. However, this is wrong when it concerns velocities greater than the speed of light, because this predicts that their relative velocities exceed the speed of light, and one of the fundamental laws of physics states that nothing can travel greater than the speed of light.

E.3!

E.2.1 - 2.6

E.2.1:
Fusion takes place in all types of stars, and it is this process which releases energy which we perceive as light and heat. Fusion is NOT a chemical reaction, rather it is a physical process. High temperatures and pressures are needed. This is because the high temperature, in other words a lot of heat energy, is required to overcome the electrostatic repulsion between the protons being fused, and therefore to get them close enough such that the strong force become prominent relative to the electrostatic force. High pressure is needed because you need a large density of the protons in order to increase the likelihood of the protons colliding with each other. It is also important to note that there is a mass defect between the 4H being fused to 1He. This mass of the 4H is greater than the mass of the 1He (note: only two of the protons actually make up the helium nucleus, the other two become positrons). This excess mass is where the light and heat energy which we see from stars comes from.

E.2.2:
When the fusion takes place, there is a lot of heat energy releases, and it is known that gases expand when subjected to higher temperatures. As a result, the star (which is essentially a ball of hot gases) will expand and will take shape. However because space is a vacuum, there is nothing pushing down on it externally to stop this expansion, yet it is still occupies a fixed volume. This is due to the fact that the gases themselves all have mass, and we know that gravity is associated to all mass, therefore the gravitational attraction between the particles is equal and opposite to the pressure which is causing the gas to expand and occupy a larger volume. This state is known as the equilibrium between radiation pressure and gravitational pressure.

E.2.3:
Luminosity is defined as the power radiated by a star. Therefore the unit for Luminosity is the Watt. The power received per unit area is known as the apparent brightness.


E.2.4:

 Apparent brightness is how an observer perceives the luminosity of a planet over a given distance. Since light is attenuated following the inverse square law, the equation for the apparent brightness of an object is: 

b = L/4πr² 

Apparent brightness is measured in Wm^-2

E.2.5:

Astrophysics. Yum.

A stellar (globular) cluster is a group of stars which are close together in the universe due to gravity, as a result of them arising from the collapse of the same gas cloud. These clusters can contain from 100,000 to 1,0000,000 stars, ranging within distances of 30-100 light years across.

A light year is defined as the distance which light travels in a year. This is therefore equal to 300,000,000m/s (speed of light) multiplied (365 x 24 x 60 x 60) = 9.46 x 10¹⁵m.

Planets In Our Solar System:

Relative Distances:

13.2.3 - Evidence for Nuclear Energy Levels

13.2.3
When an unstable substance undergoes alpha-decay, there will be alpha paticle emission. If was discovered that the alpha particles given off all had different kinetic energies HOWEVER they were only ever given off in those discrete, or specific, kinetic energies. For example, a substance would emit alpha particles with energies of say, 2,3,4 and 4 MeV. The alpha particles given off would only ever be emitted with those respected kinetic energies, and never anything different or anything in between. This proves that there are discrete energy levels in not only electron orbitals, but also in the nucleus of the atom itself.
Another method of proving nuclear eenrgy levels is from looking at the gamma photon emission of the daughter nucleus. What this means is that when the parent nucleus undergoes alpha decay and emits alpha particles of dsicrete kinetic energies, some will have maximum amount of kinetic energy possible, hence leaving the daughter nucleus in its ground state. However there will also be some that are emitted with not the maximum possible amount of kinetic energy, hence leaving the daughter nucleus in an excited state. As a result of this daughter nucleus having excess energy, the nucleus will emit gamma radiation of a discrete frequency. The energy associated to the photon(s) emitted will be equal to hf.

13.2.4
Whenever beta or beta-plus decay occurred, it was found that the kinetic energies of the electron or the positron were not equal to the mass defect from the neutron changing into a proton or a proton changing into a neutron. As a result of this unexplained 'lost' energy, there must have been another particle (in addition to the electron/positron) which was emitted during beta/beta+ decay to compensate for the lack of energy. It was then proposed that this particle would have to have almost zero mass and a neutral charge. This particle was named the neutrino.
During beta decay an electron and an anti-neutrino is emitted from the nucleus. In beta+ decay, a positron and a neutrino is emitted. There are three 'flavours' of neutrinos: the electron neutrino, muon neutrino and the tauon neutrino (and there respected anti-neutrinos). This explained why during the detection process, only a third of the anticipated neutrinos were detected. Only the electron neutrinos were being detected whilst the two others remained undetected.

Derivation of KE for an electron standing wave: