OCR A Electrons, Waves and Photons

• Charge is the name that we give to the ability of a body to exert and experience electrical force.
• Charge in not used up or changed to anything else as it moves throught a circuit.
• Current is the rate of flow of charge.
• I = ΔQ/Δt
• Charge is measures in coulombs
• One coulomb is that charge that passes when a current of 1 amp flows for 1 second.
• In metals the charge is carries by electrons
• In an electrolyte, the mobile charges are the positive and negative ions.
  

• Current is measured in Amps.
• One Amp is one coulomb per second.
• To measure current, an ammeter is placed in series in a circuit.
• Conventional Current is from positive to negative.
• Electron Flow is from the negative terminal to the positive terminal.

• Kirchoff's First Law : - 

The sum of the currents that enter a junction in a circuit is equal to the sum of the current that leave the junction.

• Applying an electric force in the form of voltage doesnt cause electrons to rapidly move between the terminals of a cell. The electrons move at a slow speed in the direction of negative to positive (electron flow) still colliding and with the stationary positive ions.
• The mean drift velocity is the average velocity of an electron as it travels through a wire due to a potential difference across it.
• The drift velocity depends on; the current, the cross-sectional area of the wire,the charge carrier concentration (number of charge carriers per unit volume) and the electrical charge from the charge carrier.

         (eg electron is 1.6x10^-19 C)

• The equation relating these is I = nAev or I = nAvq

• We have two terms for voltage;
  • Potential Difference, p.d. (V)
  • Electromotive Force, e.m.f. (E)

• The p.d. across a cell is a measure of its e.m.f. providing there are no other components in the circuit.
• A 1.5v battery gives 1.5J to every coulomb.
• Potential Difference - The electrical energy transferred per unit charge when electrical energy is converted into some other form of energy.

(When electrical energy is transferred from the charge to the circuit.)

• Electromotive Force - The electrical energy transferred per unit charge when one form of energy is converted into electrical energy.

(When electrical energy is transferred to the charge from the circuit, ie battery)

• Energy transferred = Voltage x Charge ( W = V x Q )
• E.m.f. and p.d. are both defined in terms of work done per unit charge, but a key difference is if the work is done on the charge or by the charge.
• The volt (V) is the unit of both e.m.f. and p.d.
• One volt is one joule per coulomb.
• One volt is the potential difference between two points if 1 joule of energy is transferred when 1 coulomb of charge passes between the points.
• When two or more cells are added in series their e.m.f.s are added together. (however if they are connected negative to negative or positive to positive their e.m.f.s are subtracted).
• A voltmeter must be connected in parallel across a component to measure the p.d. across it.
• A potential difference is needed to push a current through a component.
  

• The electrical resistance of a component is a measure of how difficult it is for charge to flow through it.
• Resistance is the measure of opposition to current. The greater the resistance of a component, the saller the current that will pass for a given voltage.
• Resistance = Voltage/Current   (R=V/I) (V=IR) (I=V/R)
• The unit of resistance is the Ohm (Ω)
• One Ohm is one volt per Amp 1Ω = 1VA^1
• An ohmic conductor is one which the current that flows is directly proportional to the p.d. across it, PROVIDED TEMPERATURE IS CONSTANT

• The term I-V characteristic refers to a graph which shows how the current (I) flowing through a component changes as the p.d. across it increases.
• At constant temperature, the current through a metallic conductor is directly proportional to the voltage. This is shown by a straight line on an I-V graphs means that the resistance is constant and the metal is ohmic.

• The characteristic groah for a filament lamp is a curve which starts steep and gets shallower as the p.d. rises.
• The filament lamp gets hotter as more current flows through it, so the resistance increases.This is due to the higher temperature which causes an increase in the amplitude of the vibrations of the stationary ions, which in turn increases the frequency of the collisions with the electrons, impeding the electron flow.

• The resistance in a metal increases as the temperature increases.
• In semiconductors there are less charge carriers therefore there is a smaller amount of current.
• Diodes only allow a large enough current to flow in one direction.

• LEDs are light emmiting diodes.
• Advanttages;
  • They require only a low p.d.
  • They have a long battery life
  • They are very robust
  • They can be used as indicators
  • In large arrays they can be used to illuminate
  • They can switch on instantly.

• The resistance of a wire depends on its cross sectional area, its length and the resistivity of the material it is made of.
• The resistance of a material is directly proportional to its length and inversely proportional to its corss sectional area. R ∝ l / A
• Resistivity is measures in Ωm
• R = ρ l / A
• Resistivity is the property of a material that resists the flow of current.

• The resistivity of a material is temperature dependent. Metal and semiconductors behave differently.
• For metals, Resistivity increases with temperature. As the temperature increases, the atoms of the metals vibrate with increasing amplitude. This makes it more like that conduction electrons will collide with the atoms as they travel through the metal. The electrons lose enegy when they collide, so we see an increase in the resistivity of the metal.
• For semiconductors, high temperatures help the charge carriers (electrons) break free from their atoms, increasing the number of free electrons that can carry the current. So the resistivity of the material decreases as its temperature increases.
• An NTC (negative temperature coefficient) thermistor is a semiconductor. They are very highly temperature dependent.
• An LDR (Light dependent resistor) is very highly dependent on light intensity. As the light intensity increases, more electrons break free from their atoms and so the resistivity decreases.

• Power = Current x Potential Difference ( P = I x V )
• Power is measured in Watts where 1W = 1Js^-1
• Substituting V = IR  and I = V/R into this we get;
  • P = I²R
  • P = V²/R

These are important equations to learn

• Resistors are heated by current flowing through them. Electrons must do work to overcome the resistance. Work done ≡ Energy transferred
• ΔW = VQ
  • ΔE = ΔW
  • as Q = IΔt, we can substitute IΔt into ΔW = VQ
  • ΔE = VIΔt
    
  • ΔE = I²RΔt
  • E = V²/R x Δt
• We often use the kiloWatt hour as a measure of energy transferred.
• Energy transferred (kWh) = Power (kW) x time (h)
• 1kWh = 3 600 000J = 3.6 MJ

• Domestic Appliances are protected from dangerous overloading by the fuse in the plug.
• A fuse if usually made of thin copper wire in a ceramic casing.
• Above a certain value of current, the wire becomes too hot and it melts.
• A fuse should be chosen so thats its rating is just above the maximum current drawn by the device when operating correctly.
• You can calculate this using the appliances power rating, knowing that the mains voltage is 230V and the using the equation, P = I V
• Usually fuses are 3A, 5A or 13A.

• The inside of a cell is made of chemicals or a metal which has resistance. This is the internal resistance 'r'.
• In a circuit with internal resistance, the total resistance = R + r
  • E = I (R + r)
  • E = V + Ir
  • V = E - Ir
• The e.m.f. of a cell = terminal p.d. of the cell + lost volts
• A car batter needs to deliver a really high current and so the internal resistance needs to be very low,
• Internal resistance causes energy loss.
• High voltage power supplies are an exception and have high internal resistance so that the current is smaller. This is safer.
• The effect of internal resistance is to reduce the p.d. across the external circuit.

• When the only component connected to a cell is a high resistance voltmeter, the reading is the cell's e.m.f. This is because when connected only to the voltmeter, virtually no current passes in the cell due to the high resistance therefore no work is done against the internal resistance of the cell.

• When a voltmeter is placed across a cell whilst there are other components, it gives a reading less than the e.m.f. of the cell as there is a current in the circuit and thus through the cell.

• The gradient of an I-V graph measuring the internal resistance of a cell is -r.
• The intercept on the y-axis is the e.m.f. of the cell.
• The experiment would use a variable resistor to change the current.

• Kirchoff's Second Law states;

Around any closed loop in a circuit, the total e.m.f. is equal to the sum of the potential differences.

E = Σ(IR)

• This can be applied to a series circuit or any series path within a parallel circuit.

• When resistors are connected in series, the current flowing through them is the same and the p.d. is shared between them.

• To find the combined resistance of resistors in series, add them

R = R1 + R2 + R3 ..........

• When the resistors are connected in parallel, the current devides up, part of it flowing through each resistor.
• Resistors in parallel have the same p.d. across them.
• The current from the supply is shared between them.
• When an additional resistor is added in parallel, the current always increases. The additional resistor opens up another path for the current without altering the current in any of the existing paths. This results in less resistance in the circuit.

I/R = 1/R1 + 1/R2 + 1/R3

• You can reduce the potential difference provided by a supply by connecting two resistors in series across its terminals. You then tap off the required p.d. by introducing a circuit in parallel with on of the resistors.
• Variable resistors can be used to alter the amount of p.d that is given out.
• A variable resistor allows the length of the resistive wire which current flows through to be varied.
• The larger resistor in a potential divider take more of the p.d.
• You use equal resistors to half the supply of voltage.
• To find Vout use;
  • Vout = R2/(R1 +R2) x Vin
• If one of the resistors in a potential divider is an LDR, then the behaviour of the output voltage depends on the light intensity.
• Thermistors can be used and their behaviour depends on the heat.

• Progressive Waves are waves that move away from the source, transferring energy but no material.
• A Transverse Wave is a wave in which the oscillations are perpendicular to the direction of wave propagation.
  • All electromagnetic waves are transverse
  • These waves can be shown on graphs as displacement plotted against distance or displacement against time.
• A Longitudinal Wave is a wave where the oscillations are parallel to the direction of wave propagation e.g. sound
  • They have alternate compressions and rarefactions of the medium they travel through. 

• Displacement       - is the distance any part of the wave has moved from its                                  mean ( or rest ) position.
• Amplitude             - is the maximum displacement.
• Wavelength         - The wavelength of a wave is the smallest distance                                            between one point on a wave and the identical point on                                  the next wave
• Period                  - The period of a wave is the time for one complete                                           pattern of oscillation to take place.
• Phase Difference - The difference by which one wave leads or lags behind                                  another.
• Frequency            - The frequency of a wave is the number of oscillations                                     per unit time at any point.
• Wave Speed         - The speed of a wave is frequency x wavelength

Speed = distance / time

In a time equal to one period (T), a wave moves one wavelength.

V = λ / T

Frequency = 1 / T therefore substitute this in to get 

V =  fλ

• All waves can be reflected, refracted and diffracted.
• Reflection is when waves rebound from a barrier, changing direction but remaining in the same medium. The wavelength does not change after it has been reflected.
• Refraction is when a wave changes direction when it travels from one medium to another due to a difference in the wave speed in each medium.
• Diffraction is when a wave spreads out after passing around an obstacle or through a gap. The effect is most noticeable when the wavelength is similar to the size of the gap it passes through. 

• You need to be able to state typical values of the wavelengths for different regions of the electromagnetic spectrum.
  • Radio waves     -    0.1m             10⁴
  • Microwaves       -    10^-4                   0.1m
  • Infrared             -    7.4x10^-7          10^-3
  • Visable              -    3.7x10^-7          7.4x10^-7
  • Ultraviolet          -    10^-9                   3.7x10^-7
  • X-Rays              -    10^-12                 10^{-7    -}    
  • Gamma-Rays   -    10^-16                 10^-9  

All electromagnetic waves share the following properites;

• They can all travel through a vacuum
• All contain both a magnetic wave and an electric wave interlocked and at right angles to each other.
• In free space they all travel at a speed of exactly 299 792 458 m/s
• They are all transverse waves.

Radio waves are used in telecommunications (radio and TV).

Microwaves are used by mobile phones, microwave ovens and GPS.

Infrared is used by heaters, night vision equipment and remote contols.

Visible light is used for sight and communications (fiber optics).

Ultraviolet is used by tanning booths, counterfeit detection and detergent.

X-Rays are used in CT-scans and x-ray photography.

Gamma-rays are used to diagnose and treat cancer (radiotherapy)

The ultraviolet region is split into 3 categories; UV-A, UV-B and UV-C.

• UV-A is the least damaging of the three. It has the lowest frequency and thus carries a smaller amount of energy. It can cause tanning and burn the skin.
• UV-B is more dangerous and can also cause burnt skin. UV-B can be absorbed by DNA which can cause mutations and cancer.
• UV-C is the most dangerous with the highest frequency and most energy. It is ionizing radiation as it can knock electrons from their atom. This can cause cell mutation and destruction but is filtered out by the atmosphere.

Sunscreens contain chemicals to filter out UV-B, preventing sunburn and skin damage.

• Polarisation is the process of turning an unpolarised electromagnetic wave, into a plane Polarised electromagnetic wave.
• Electromagnetic waves consist of varying electric and magnetic fields that act perpendicular to each other.
• Transverse waves can travel in all directions as a mixture but the electric and magnetic fields still act at right angles.
• Only transverse waves can be Polarised.
• A plane Polarised wave is a transverse wave oscillating in only one plane.

• Passing electromagnetic waves through a Polaroid filter selects out the waves that are plane Polarised in that plane, so the light transmitted by the Polaroid is plane Polarised in that specific direction.
• If a second Polaroid filter is placed, rotated through 90 degrees, after the first ( the analyser ), the Polarised light will be completely blocked as it is not plane Polarised in the same direction and the second filter.
• Light is also partially Polarised on reflection.

Intensity and Amplitude

• The intensity of a wave is the energy incident per square metre of a surface per second. Measured in Watts per metre squared
• The intensity of a wave is proportional to its amplitude squared.

Malus's Law

• The intensity of light passing through a polarising filter depends on the angle (theta) between the direction of polarisation of the light and the axis of the filter.

• where I₀ is the initial intensity, and θ_i is the angle between the light's initial polarization direction and the axis of the polariser.

When two or more waves of the same type are present at the same time in the same place, the principle of superposition can be used to calculate the resultant wave ( net displacement) at any time.

• The principle of superposition states that when two or more waves of the same type exist at the same place, the resultant wave will be found by adding the displacements of each individual wave.                                               

• Interference        - The addition of two or more waves that result in a new                                     wave pattern.
• Coherence          - Two waves that are of constant phase difference are said                               to be coherent
• Path Difference   - The path difference is the difference of distance                                             between two waves in terms of its wavelength.
• Phase Difference - The difference by which one wave leads or lags behind                                 another, usually measured in degrees or radians.

Constructive Interference - When two waves meet and they are in phase with each other, they constructively interfere. The resultant wave has an amplitude equal to the sum of the two amplitudes of the interfering waves.

Destructive Interference - When two waves meet and they are out of phase with each other, they destructively interfere. If two waves of equal amplitude are out of phase by 180 degrees and interfere, the resultant wave will have no amplitude at that point.

Sound

Interference with sound waves can be demonstrated using two loudspeakers connected to the same signal generator which emits sound waves of equal wavelengths. As you walk along in front of the loud speakers you will hear a loud sound where the waves are in phase and constructively interfere and a quiet sound or even no sound where the waves are out of phase and destructively interfere.

Microwaves

Interference with microwaves can be demonstrated using two microwave transmitters attached to the same signal generator which emits microwaves of equal wavelength. Using a microwave receiver probe, you can detect areas of strong and weak signals where the waves arrive either in or out of phase and thus constructively or destructively interfere.

The Experiment

Firstly, a source of monochromatic light is placed behind a solid obstacle with a small slit (Alternatively, a laser can be shone directly on the double slit). The light then spreads out by diffraction until it reaches another obstacle with two parallel narrow slits. The light arrives here in phase with each other and is therefore coherent. The light spreads out by diffraction until it reaches a screen. There are light patches where the light from arrives in phase and constructively interferes. There are also dark fringes where the light arrives out of phase and destructively interferes.

Evidence for Wave theory of Light

• There was two theories put forward for light; waves and corpuscles.
• Corpuscular theory could explain reflection and refraction of light, but diffraction and interference are uniquely wave properties.
• The Young Double Slit experiment shows light both diffracting and interfering.

You can determine the wavelength of light using young's Double Slit Experiment and the Double Slit Equation.

ax = λD

Where; x = fringe spacing i.e. the width of each dark/bright fringe.

D = distance between the double slits and the screen

a = distance between the two slits.

• A diffraction grating has many equally spaced parallel slits.
• When monochromatic light is passed through a diffraction grating with hundreds of slits per mm, the interference pattern is reinforced and really sharp.
• Light waves from every slit must be in phase to produce a bright fringe. These fringes are more widely separated with dark bands.
• For a grating with slits a distance 'd' apart and angle θ between the incident beam and the nth order maximum is given by;

d sinθ = nλ

• Because it has many slits, a diffraction grating has the advantage that the bright fringes are more widely separated than for a double-slit arrangement, allowing for more precise measurement and thus a more accurate calculation of the wavelength to be determined.

• Stationary waves are formed when two identical progressive waves, travel in opposite directions.
• In a stationary wave, the energy is stored rather than transmitted.
• Stationary waves are most easilly achieved by reflecting a progressive wave back upon itself. Reflection from a denser medium gives a phase change of 180 degrees for the reflected wave. For the phase change to take place, the point of reflection must be fixed.
• Nodes are the points in a stationary wave at which there is no displacement of the particles at any time.
• At anti-nodes, the displacement of the particles in a stationary wave varies by the maximum amount.
• Separation between adjacent nodes ( or anti-nodes ) is half the wavelength.

• Stationary Microwaves
  • A microwave generator is placed transmitting microwaves towards a metal sheet.
  • These are reflected back along the same path, resulting in the formation of a stationary wave.
  • A microwave detector is placed along the wave and detects where there is particularly strong signals (anti-nodes).
  • If we multiply the frequency of the wave by the calculated wavelength, you get the speed. (measure from one maximum to the furthest maximum from it and divide by the number of full wavelengths between).
• Stationary Waves in Stings
  • Set up a string so that it is stretched between a driving oscillator and a fixed point.
  • The outgoing wave reflects at the fixed point and interferes with the outgoing wave.
  • At certain frequencies, a stationary wave pattern is formed.
  • Changing the frequency causes the standing wave to disappear. Changing the length, tension or thickness  of the string causes the stationary wave to appear at different frequencies.

• The fundamental mode of vibration of a stretched sting, is such that the wavelength is twice the length of the sting. There is a node at either end of the string and an anti-node in the centre.
• A harmonic is a whole-number multiple of the fundamental frequency of a stationary wave.
• The fundamental frequency is the lowest possible frequency in a harmonic series where a stationary wave forms.
• The second harmonic has twice the frequency of the fundamental frequency.

• A stationary longitudinal wave in a tube is a specific type of stationary wave, created by blowing across one end of the tube.
• A progressive wave can be started at one end of a closed tube by blowing across the open end. This wave travels down the tube and is reflected at the closed end. This produced two progressive waves travelling in opposite directions, which then interfere to produce a stationary wave.
• To produce a stationary wave the length of the tube must be such that a node is created at the closed end and an anti-node created at the open end. 
• At the fundamental frequency, the length of the air column is one quarter of the wavelength of the sound.
• A stationary wave is formed again at 3 times the fundamental frequency with air column length 3 quarters of the wavelength of the sound.

• In a tube with two open ends, reflection of a sound wave at the open end of the air column does occur.
• Since the tube is open at both ends, an anti-node is present at both ends.
• For a tube with two open ends, at the fundamental frequency, the length of the air column is half the wavelength of the sound.
• A stationary wave is formed again at twice the fundamental frequency with air column length equal to the wavelength of the sound.

• You can create a closed end pipe by placing a hollow tube into a measuring cylinder of water.
• Change the frequency of a loudspeaker until there is a point where the note is much louder.
• The sound waves are reflected of the closed end of the tube where there is water and a standing wave is formed. There is a node at the bottom and an anti-node at the open end.
• At the fundamental frequency, the length of the tube is one quarter of the wavelength of the sound, so by measuring the length of the tube you can calculate the wavelength.
• You can work out the speed by multiplying the wavelength by the frequency of the sound produced by the loudspeaker.

• A photon is a quantum of electromagnetic radiation.
• The energy of a photon is proportional to the frequency with which it is associated.

Photon Energy = hf ( E = hf )

Photon Energy = hc/  λ

• The electron-volt is a measure of energy, as photon energies are very small, the electron-volt i an appropriate unit to use.
• One electron-volt is the energy change of an electron when it passes through a potential difference of 1 volt.

1 eV = 1.6x10^-19 J

• To convert from J to eV : divide by 1.6x10^-19
• To convert from eV to J : multiply by 1.6x10^-19

eV = ½mv^2

• Set up a potential divider circuit with power supply, a variable resistor, an LED of known wavelength, a voltmeter in parallel and an ammeter in series.
• Start off with no current flowing through the circuit, then adjust the variable resistor until a current just begins to flow.
• Record the voltage across the LED and the wavelength of the light the LED emits. This is the threshold voltage.
• Repeat the experiment with a number of different LEDs that produce different optical wavelengths.
• Plot a graph of the measured threshold voltages against 1/λ.
• You should get a straight line graph. Using the equation         eV = hc/λ, the graph has gradient hc/e which you can then use to determine 'h' by substituting in the values of the gradient, the speed of electromagnetic radiation an the charge of an electron.

• If you shine a light of sufficient frequency onto the surface of a metal, it will emit electrons. For most metals, the frequency falls in the UV range.
• Free electrons in a metal absorb a single photon of electromagnetic radiation which makes them vibrate.
• If an electron absorbs a photon with great enough energy to overcome the work function energy of the metal, an electron is released as a photoelectron.
• For a given metal, no photoelectrons will be released if the radiation has a frequency below the threshold frequency.
• The photoelectrons are emitted with varying kinetic energies, the value of the maximum kinetic energy increases with the frequency of the radiation. 
• The number of photoelectrons emitted is proportional to the intensity of radiation.

• According to wave theory, energy is proportional to the intensity of the radiation. This is not true here as the energy is proportional to the frequency of the radiation and the number of photoelectrons released is proportional to the intensity of the radiation.
• With the Wave theory, the energy would be spread evenly over many of the free electrons and each would gain a bit of energy. Eventually they would gain enough energy to be released as a photoelectron. This is not the case, the electrons are emitted as soon as the source is switched on and do not emit any photoelectrons unless the radiation is above the threshold frequency of the metal and has sufficient Energy to overcome the work function of the metal.
• Work Function - the minimum energy required to release an electron from a metal.
• Threshold Frequency - The lowest frequency of radiation that will result in the emission of electrons from a particular metal surface.

• Energy is conserved when a photon interacts with an electron.

hf = Φ + EKmax

• The Kinetic Energy of an emitted electron is independent of intensity as they can only absorb one photon at a time.
• The photoelectric current in a photocell circuit is proportional to the intensity of the incident radiation as with a greater intensity, there are more photons to interact with electrons, so more electrons can absorb a photon and release a photoelectron into the circuit, giving it a greater photoelectric current.  

• Diffraction patterns are observed when an electron is accelerated through a vacuum tube an interacts with the spaces in a graphite crystal.
• A beam of fast moving electrons is produced by a cathode ray tube. The electron beam passes through a thin layer of crystalline graphite. A fuzzy pattern of light an dark rings are produce on a screen.
• In electron diffraction, a smaller accelerating voltage, i.e. slower electrons give more widely spaced rings.
• An increase in the electron speed will squash the patterns together.
• You can only get this diffraction if a particle interacts with an object of about the same size as its de Broglie wavelength.

• Increasing the speed of electrons results in a decrease in their wavelength, and so much smaller values of spacings of particles can be measured. High speed electrons can be used to determine the arrangement of atoms within a crystalline structure or to measure the diameter of a nucleus.

• Electrons in atoms exist only at discrete energy levels.
• Electrons can move down an energy level through emitting a photon.
• Since these transitions are between definite energy levels, the energy of each photon emitted can only take certain allowed values. 
• The energy carried by each photon is equal to the difference in energies between the two levels.

ΔE = E2 - E1 = hf = hc / λ 

Emission Spectra-

• If you heat a gas, many electrons move to high energy levels. As they fall back to the ground state, the electrons emit  energy as photons.
• If you split the light from a hot gas with a diffraction grating, you get a line spectrum. Each line on a spectrum corresponds to a particular wavelength of light omitted by the source.
• Since only certain photon energies are allowed, you only see the corresponding wavelengths.

Absorption Specta-

• You get and absorption spectrum when white light passes through a cool gas.
• At cool temperatures, most electrons will be at ground state. Photons with the correct energy are absorbed by the electrons to excite them. The corresponding wavelengths are then missing from the continuous spectrum, with black lines corresponding to absorbed wavelengths.