E = hf E = photon energy h = plancks constant = 6.63 x 10-34 f = frequency
refractive index n = speed of light in free space/Speed of light in a medium
Snells Law n = sin i/sin r
Critical angle = 1/n critical angle = sin 0c n = refractive index
hf = work function + Ek max hf = photon energy Ek max = max kinetic energy
hf threshold = work function
hf = E1 - E2 E1/E2 = excited energy levels
lambda = h/plambda = wavelength h = plancks constant p = momentum
p = mv p = momentum m = mass v = velocity
1 eV = 1.9 x 10-19
Up + 2/3 e 1/3 Mp
Down - 1/3 e 1/3 Mp
Charm + 2/3 e 1.7 Mp
Strange - 1/3 e 0.5 Mp
Top+ 2/3 e 186 Mp
Bottom - 1/3 e 4.9 Mp
e = 1.6 x 10-19
Mp= 0.938 Gev/c2 = 1.67 x 10-27 Kg
Reflection and Refraction
The laws of reflection tell you were a ray will go when it is reflected. The normal is the line at 90 degrees to the reflecting surface st the point where the incident ray strikes it.
Law 1 = Angle of incidence = angle of reflection.
Law 2 = incident ray, reflected ray and normal are all in the same plane.
Light travels fastest in a vacuum. It travels more slowly in other media. When light changes speed, it is refracted. If a ray enters a medium head-on it travels straight on. If a ray enters a medium obliquely, it changes direction.
The refractive index, n of a medium related the speed of light in the medium to the speed of light in free space.
Total Internal Reflection
Total internal reflection of light may occur when a ray is travelling inside a glass block.
Total - 100% of the light is reflected
Internal - because the ray is reflected inside the material
Reflection - because the light is reflected not refracted.
Total internal reflection can only happen when a ray travelling through a material of higher refractive index reaches the boundary with a material of lower refractive index. Total internal reflection happens for any angle of incidence equal to or greater than the critical angle.
A ray of light can travel along inside a solid glass fibre. Each time it reaches the outer surface of the glass it is reflected back inside, since i is nearly 90 degrees.
Optic fibres are made from plastic or glass, surrounded by a cladding material with a slightly lower refractive index. Rays that travel straight down the centre of the fibre have the shortest route and take least time, Oblique rays have further to travel, so take longer.
Energy Levels and Ionisation
The electrons in an isolated atom can only have fixed amounts of energy, these are called the energy levels of the atom. An electron will normally occupy the lowest available energy level, called its ground state. If it receives the right amount of energy, an electron can move to a higher level and the atom is said to be excited. It may fall back to a lower energy level and lose energy. This energy is emitted as a single photon of light of a particular frequency.
Ionisation means giving an atom enough energy that an electron is completely removed from the atom. this is called the ionisation energyand can be provided by heating, or by collision with a high speed electron, or by the atom 'capturing' a photon of sufficient energy.
To remove an electron completely from an atom requires energy to overcome the force of attraction between the negative charge on the electron and the positive charge on the nucleus.
The atoms of a gas at low pressure may be excited by a flame or by high-speed electrons. The excited gas atoms fall back down to their ground states and emit photons of distinct energies corresponding to differences between energy levels.
Looking at the flame through a diffraction grating gives lines of different colours called a line spectrum - evidence for energy levels. The atoms of any given element all have the same set of energy levels. Each element produces a unique line spectrum that can be used as identification.
A fluorescent light tube contains mercury vapour gas at low pressure, and two electrodes. A large number of electrons are released from the cathode and accelerated by the potential difference between the anode and cathode. Some of these electrons ionise gas atoms by collision, producing more electrons.
Some of teh electrons collide with gas atoms which become excited and emit photons of ultraviolet light as they fall back to the ground state. These photons in turn excite atoms of a coating material on the inside of the tube, which emit visible light. Because the coating atoms are close together, there are so many possible transitions that all colours of the visible spectrum are produced.
The Photoelectric Effect
When light shines on certain metals, electrons break free. This is the photoelectric effect. When light interacts with a metal we must assume it acts as a particle (photon) rather than a wave. The energy of a photon of light is captured by a conduction electron in the metal and the electron escapes the surface of the metal.
If a photon is captured by an electron in the metal, some of its energy is used to overcome the work function - the least amount of energy required for an electron to escape the surface of a metal, the rest of the energy becomes the electrons kinetic energy. The electrons highest up the well are the most energetic. When one of these electrons captures a photon and escapes it will have the maximum possible kinetic energy.
The photoelectric equation- hf = work function + Ek max
The frequency of the light myst be above a certain minimum value, the threshold frequency. Below this value an individual photon does not have enough energy for an electron to overcome the work function. Negative intercept ony axis gives work function. slope gives plancks constant. the intercept on the x axis gives the threshold frequency.
Electron - e 0.0005 Mp
Electron Neutrino 0 0
Muon - e 0.1 Mp
Muon Neutrino 0 0
Tau - e 1.9 Mp
Tau Neutrino 0 0
e = 1.6 x 10-19 C
Mp= 0.938 Gev/c2 = 1.67 x 10-27 Kg
Particles in an atom
Proton mass = 1 charge = + 1
Neutron mass = 1 charge = 0
Electron mass = negligible charge = - 1
Protons and neutrons are nucleons (particles found in the nucleus)
charges are un units e = 1.6 x 10-19
Isotopes = Isotopes have the same number of protons so the same atomic number but a different number of neutrons so a different mass number.
Z = proton number/atomic number (bottom Number)
A = nucleon number/ mass number = number of protons = neutrons (top number)
Electrons = number of protons so that the atom is uncharged
The central positive charge of an atom is found in the nucleus, the negative charge is spread out around the nucleus, evidence for this comes from Rutherford's Alpha-particle scattering.
A narrow beam of alpha-particles was aimed at thin gold foil.
An alpha-particle is made of two protons and 2 neutrons so has a positive charge.
The direction of the alpha-particles after they had passed though the foil was determined using a detector.
Most of the alpha-particles went straight through.
A few were deflected more than 90 degrees.
Most atoms went straight through = Atoms are mostly 'empty space'
Few are deflected back towards the observer = positive charge is concentrated in a tiny volume
Leptons, Mesons and Baryons
Leptons =electron, muon, neutrino - thought to be indivisible (fundamental)
Hadrons = mesons =pion and kaon- made form a quark and an anti-quark
Hadrons = baryons = protons and neutrons - made from3 quarks, anti-particle = 3 anti-quarks
Proton = u u d
Neutron = u d d
Pion + = u
d Pion - = ud Pion 0 = u u or d d
Kaon + = u
s kaon - = us Kaon0 = d s Kaon 0= ds
Kaon + = 1 Kaon - = - 1 Kaon 0 = 1
Kaon 0 =- 1
Strong Nuclear = strongest, short range. It only acts between neighbouring nucleons. It binds quarks and anti-quarks
Exchange particle = Gluon - Charge = 0 Mass = 0
Electromagnetic = Infinite range, holds atoms and molecules together. Responsible for chemical, mechanical,and electrical properties.
Exchange particle = Photon - Charge = 0 Mass = 0
Weak Nuclear = Range does not extend beyond the nucleus. Responsible for B- decay and fusion reactions in stars.
Exchange particle= W+= +e W- = -e Zo = 0 Mass of all three = 89 Mp
Gravity = Weakest but acts over an infinite range. Pulls objects towards the earth, holds stars and galaxies together.
Exchange Particles= Gravition
Beta plus Decay
p = n + e+ + Y
1 = 0 + +1+ 0
1 = 1 + 0 + 0
0 = 0 + -1 + +1
Y must have; 0 charge, 0 baryon number and +1 lepton number
Y = electron neutrino
Particles that contain strange quarks are called strange particles and are long lived. +3 - -3 depending on the number of quarks. Strangeness is considered in interactions using the strong nuclear force. Can or cannot be reserved in interactions using the weak force. The Strangeness of a baryon indicates the presence of strange quarks within.
Proton and anti-neutrino
Ve + p = e+ = n
Electron Capture p + e- = n + Ve
Beta minus n = p+
Ve + e-
Neutrino - Neutron n + Ve = p + e-
Wave - particle Duality
Electrons can be diffracted- this shows that, when they pass through a fine grid, they behave like waves. A beam of fast moving electrons is produced in a cathode ray tube. The electron beam passes through a thin layer of crystalline graphite. A diffraction pattern of fuzzy, light and dark rings is produced on a screen.
To make the electrons go faster, increase the accelerating voltage. The diameter of the rings decrease. this shows that the wavelength decreases as the electrons go faster.
E = hf
lambda = h/p
p = mv
The de brogile equation applies to all particles, no matter how big.