5.5.2 Electromagnetic radiation from stars

When electrons are bound to their atoms in a gas they can only exist in one of a discrete set of energies - the energy levels of an electron:

• An electron cannot have a quantity of energy between two levels
• The energy levels are negative because external energy is required to remove an electron from the atom.
• The energy leve with the most negative value is the ground state/ground level
• An electron with zero energy is free from the atom

An atom is said to be excited when an electron moves from a lower to a higher energy level within an atom in a gas. Raising an electron into a higher energy level requires external energy - for example when photons of specific energy are absorbed by the atom. Similarly, when an electron moves from a higher energy level to a lower energy level it loses energy. As we know, energy is conserved. This means that as the electron makes a transition between levels a photon is emitted from the atom (this can be known as de-excitation). In order for an electron to make a transition from -3eV to -6.8eV (for example) it must lose 3.8eV. It emits this in the form of a photon with energy 3.8eV. The energy of a photon emitted in an electron transition from a higher to lower energy level is given by the equation:

E = hf

NOTE: it is important to realise that each element has its own unique set of energy levels.

Different atoms have different spectral lines - the spectra from starlight can be used to identify the elements within stars without a direct sample (as a ample of a star is pretty hard to obtain lol). There are three kinds of spectra:

• Emission line spectra - each element produces a unique emission line spectrum because of its unique set of energies
• Continuous spectra - all visible frequencies/wavelengths are present. The atoms of a heated solid metal (e.g. a filament lamp) will produce this type of spectrum
• Absorption line spectra - this type of spectrum has a series of dark spectral lines against a continuous spectrum. The dark lines have the same wavelengths as the bright emission spectral lines for the same gas atoms.

If the atoms are excited then when the electrons drop back into the lower energy levels they emit photons with a set of discrete frequencies specific to the element. This produces a characteristic emission line spectrum and each spectral line corresponds to photons with a specific wavelength. These spectra can be observed in a laboratory from heated gases. Each coloured line represents a unique wavelength/frequency of photon emitted when an electron moves between two specific energy levels.

A bit more on absorption line spectra: This is formed when light from a source that produces a continuous spectrum passes through a cooler gas. As the photons pass through the fas some are absorbed by the gas atoms, raising electrons up into higher energy levels and so exciting the atoms. Only photons with an energy exactly equal to the difference between the different energy levels are absorbed (meaning that only a specific wavelength are absorbed) - this creates dark lines in the spectrum. These lines show which photons have been absorbed. When the electron drops back down to a lower energy level the photons are re-emitted in all directions so the intensity in the original direction is reduced. 

We need to know about how we detect which elements are present on stars (without a sample). Basically, when the light from a star is analysed it is found to be an absorption line spectrum. Some wavelengths of light are missing - these are the photons that have been absorbed by atoms of cooler gas in the outer layer of the star. If we know the line spectrum of a particular element we can check whether the element is present in the star (if a particular element is present its characteristic pattern of spectral lines will appear as dark lines in the absorption line spectrum).

A diffraction grating is an optical component with regularly spaced slits/lines that diffract and split light into beams of different colours travelling in different directions. These beams can be analysed to determine the wavelengths of spectral lines in the laboratory/from starlight. It is slightly different to the double slit (Youngs Double Slit experiment) in which it consists of a large number of lines ruled on a glass/plastic slide and each line diffracts like a slit producing a clearer and brighter interference pattern than the double slit. The direction of the beams produced depends on the spacing of the lines/slits of the grating and the wavelength. 

Like in the double slit, maxima and minima are still formed. The interference pattern is the result of the superposition of the diffracted waves in the space beyond the grating.  The formation of maxima at a particular point depends on the path difference and the phase difference of the waves from all the slits.

The zero-order maxima (n=0) is formed when the path difference is zero, that is at an angle θ=0. The angle θ is measured relative to the normal to the grating/to the direction of incident light. For the nth order maxima the path difference QY at an angle θ will be equal to nλ. Also, the distance PQ is the separation between adjacent lines/slits on the grating. 

We can use the following equation to determine any of the above features:

sinθ = QY/QP = nλ/d

dsinθ = nλ

NOTE: n must be an integer value. 

Thus us known as the grating equation. It can be used to accurately determine the wavelength of monochromatic light.


At any given temperature (above absolute zero) an object emits electromagnetic radiation of different wavelengths and different intensities. We can model a hot object as a black body. This is an idealised object that absorbs all the electromagnetic radiation that shines onto it and (when in thermal equilibrium) emit a characteristic distribution of wavelengths at a specific temperature.

Wein's displacement law relates the absolute temperature (T) of a black body to the peak wavelength (λmax) at which intensity is a maximum. It's a bit confusing because λmax isn't the maximum λ, it's actually the most abundant λ. The law states that λmax is inversely proportional to T:

λmax ∝ 1/T

Therefore, for any black body emitter λmax T = constant. the constant is Wein's constant - 2.90x10^-3 mK.

Modelling objects as approximate black bodies helps scientists to determine temperatures of objects simply by analysing the electromagnetic radiation they emit. It is important to realise that, as the temperature of an object changes, the distribution of the emitted wavelengths changes. As temperature increases, the peak wavelength reduces and the peak of the intensity-wavelength graph becomes sharper.

Stephan's law: The total power radiated by a star is called luminosity. Stephan's law states that the total power radiated per unit surface area of a black body is directly proportional to the fourth power of the absolute temperature of the black body. Luminosity can be found using the equation below:

L = 4πr²σT⁴

NOTE: σ is known as the Stephan constant (5.67 x 10^-8 WmT^-2K^-4).

Stephan's law shows that the the luminosity (L) of a star is directly proportional to:

• it's radius² (L ∝ r²)
• it's surface area (L ∝ 4πr²)
• it's surface absolute temperature⁴ (L ∝ T⁴)

We can use both Wein's displacement law and Stephan's law to estimate the radius of a distant star. Once the radius is known we can calculate it's density and mass using Newton's law of gravitation.

5.5.1 Stars

Okay so we need to know some definitions:

• Planets - An object in orbit around a star with three important characters:
• A mass large enough for its own gravity to give it a round shape
• It has no fusion reactions
• It has cleared its orbit to most other objects
• Planetary satellites - A body in orbit around a planet
• Comets - Small irregular bodies made up of ice, dust, and small pieces of rock. All orbit the sun. Can develop tails as they near the sun. Range from a few hundred metres to tens of kilometers across
• Solar systems - Contains the sun and all objects that orbit the sun.
• Galaxies - A collection of stars, and interstellar dust and gas. On average it will contain 100 billion stars.
• Universe - A collection of all the galaxies

Nebulae are gigantic clouds of dust and gas. They are formed over millions of years as the tiny gravitational attraction between particles of dust and gas pulls the particles towards each other forming vast clouds. The gravitational collapse accelerates as the dust/gas gets closer together and denser regions form which pull in more dust and gas, gaining mass and getting denser. They also get hotter as gravitational energy is eventually transferred to thermal energy. In one part of the cloud a prostar forms - this is a very hot, very dense, sphere of dust and gas but is not yet a star.

Nuclear fission needs to occur for a prostar to become a star. Fusion reactions produce kinetic energy. Extremely high pressures and temperatures inside the core are needed in order to overcome the electrostatic repulsion between hydrogen nuclei in order to fuse them together to form helium nuclei. Sometimes, as more and more mass is added to the prostar, it grows so large and the core becomes so hot that the kinetic energy of hydrogen nuclei overcomes the electrostatic repulsion and hydrogen nuclei are forced together to make helium nuclei - it is here that a star forms. 

The star now remains in a stable equilibrium with almost a constant size since gravitational forces compress the star but the radiation pressure (from the photons emitted during fusion) and the gas pressure (from the nuclei in the core) push outward. The forces balance so an equilibrium is maintained. This is known as the stars main sequence. How long a star remains stable depends on the size and mass of it's core. The cores of large, massive supergiant stars are hotter than those of small stars so they release more power and convert the available hydrogen to helium in a shorter time meaning they are only stable for a few million years. Smaller stars (e.g. our sun) are stable for tens of billions of years. As stars run out of hydrogen in their core (because it's all fused to form hydrogen), the star begins to move off it's main sequence. 


Stars with a mass between 0.5 - 10 times our sun (M_☉) 
These stars eventually evolve into red giants. At the start of this phase the reduction in energy released by the fusion in the core means the gravitational force is greater than the radiation/gas pressure force and the core shrinks. Pressure increases enough to start fusion in the shell around the core. Red giant start have inert cores (fusion no longer takes place). This is because very little hydrogen remains and also the temperature is not high enough for the helium nuclei to overcome the electrostatic repulsion between them. Hydrogen fuses to helium in the shell around the core. This causes the periphery of the star to expand as the layers slowly move away from each other. These layers cool as thy expand making the star go red. 

Most of the layers of the red giant will drift away as planetary nebula. The core then becomes a very dense hot (30,000K) core as a white dwarf. No fusion reactions occur here, it only emits energy because it leaks photons created in its earlier evolution. According to the Pauli exclusion principle, no two electrons can exist in the same energy state. When the core of a star begins to collapse under the force of gravity, the electrons are squeezed together. This creates a pressure that prevents the core from further gravitational collapse. This pressure created by the electrons is known as the electron degeneracy pressure. 

It is important to realise that the electron degeneracy pressure is only sufficient to prevent gravitational collapse if the core has a mass less than 1.44M_☉. This is the Chandrasekhar limit. This limit is the maximum mass of a stable white dwarf.

Stars with a greater mass of 10M_☉

Since their mass is much greater their cores are much hotter meaning they use up their hydrogen supply in a shorter amount of time. As with smaller stars, when the hydrogen in the core runs low it begins to collapse under gravitational forces. As the cores of these larger stars are much hotter the helium nuclei (formed from fusion of hydrogen) are moving fast enough to overcome electrostatic repulsion and the helium nuclei fuse into heavier elements. These changes in the core cause the star to expand which forms a supergiant (sometimes known as a super red giant).Temperatures and pressures are high enough to fuse even massive nuclei forming a series of shells inside the star. This process continues until the star develops an iron core. Iron nuclei cannot fuse as the reaction would produce no energy. This makes the star very unstable and the star dies by supernova (type 2) - a catastrophic implosion of the layers that bounce off the solid core leading to a shockwave that ejects all the core material into space. Supernovae create all the heavy elements (everything above iron in the periodic table was created in a supernova (such events distribute these heavier elements throughout the universe.

After a supernova the remnant core is compressed into either a:

• Neutron star - if the mass of the core is greater than the Chandrasekhar limit, the gravitational collapse continues, forming a neutron star. These are almost entirely made up of neutrons and are very very dense.
• Black hole - if the core has a mass greater than 3M_☉ the gravitational collapse continues to compress the core resulting in a gravitational field so strong that an object must be travelling greater than the speed of light to escape it.

The last thing we need to know in this section of the spec is the Hertzsprung-Russell diagram. This is a graph of stars in our galaxy showing the relationship between luminosity and their average surface temperature. The luminosity of a star is the total radiant power output of the star. The luminosity and temperature of stars can both vary widely so the HR (Hertzsprung-Russell) diagram scales are logarithmic.

Lower mass stars evolve into red giants moving away from their red sequence. Then they lose their cooler outer layers and slowly move across the diagram crossing the main sequence line ending up as white dwarfs. Higher mass stars start at point X before rapidly consuming their fuel and swelling into red supergiants at Y before going supernova.

3.4.2 Mechanical properties of matter

As we know from 3.4.1, the area under a force-extension or force-compression graph is the work done in extending/compressing the spring. This means that:

W = F x

The work done on the spring is transferred to elastic potential energy within the spring and is fully recoverable because of the elastic behaviour of the spring. This means that:

E = 0.5 F x

Since a spring obeys Hooke's law, we can also substitute F = kx into the equation if we don't know F:

E = 0.5 k x²

From this equation we can see that E (elastic potential energy) is directly proportional to extension squared.

It is important to realise that the extension of a wire depends on the length of the wire, its diameter, the tension in the wire, and the material of the wire...

Tensile stress
Tensile stress is defined as the force applied per unit cross-sectional area of the wire:

Tensile stress = force / cross-sectional area

σ = F / A

Tensile strain
Tensile strain is defined as the ratio of extension to original length of a material:

Tensile strain = extension / original length

Ɛ = x / L

NOTE: Don't forget that tensile strain is written as a percentage and not a decimal.


Stress-strain graphs
A stress-strain graph for a brittle material:
Brittle materials show elastic behaviour until breaking point with plastic deformation only. They obey Hooke's law.



A stress-strain graph for a polymeric material:
Polymeric materials consist of long molecular chains. They behave differently depending on their molecular structure and temperature. For example, rubber and polythene both stretch before breaking but rubber shows elastic behaviour and polythene shows plastic behaviour.
        



A stress-strain graph for a ductile material:

In this graph...

• Stress is proportional to strain from the origin to the limit of proportionality (this is the straight bit of the graph, the bit with uniform gradient). In this region the material obeys Hooke's law.
• The elastic limit sits just past the limit of proportionality. Elastic deformation occurs up to this point.
• Plastic deformation occurs beyond this point.
• The upper and lower bounds of the yield strength bit are the upper and lower yield points (where the material extends rapidly) - this may not occur in all ductile materials.
• The stress at ultimate tensile strength (UTS) represents the materials ultimate tensile strength.....duh. This is the maximum stress that a material can withstand when being stretched before it breaks.
• Beyond the point of UTS, the material may become longer and thinner at its weakest point (necking).
• The material eventually snaps at its weakest point.
• The stress value at the point of breaking is the breaking strength of the material.

The higher the ultimate tensile strength the stronger the material.

Within the limit of proportionality, stress is directly proportional to strain. The ratio of stress to strain for a material is constant - it is known as the Young modulus:

Young modulus = tensile stress / tensile strain

E = σ / Ɛ

The Young modulus is the gradient of the linear region of the stress-strain graph. It depends on the material (e.g not it's shape/size). We need to know how to experimentally determine the Young modulus of a metal (wire)...

• Measure the wires diameter (micrometer) across various points and take an average. Do A = π r².
• Apply various loads
• Measure it's length each time
• Calculate the extension by extended length - original length (x - L)
• Take readings for at least 6 different masses
• Plot a stress-strain graph
• Determine the gradient of the linear region of this graph - this is the Young modulus

3.4.1 Springs

To alter the shape of an object, you must have a pair of equal but opposite forces. Forces that produce extension are known as tensile forces, whilst forces that produce compression are known as compressive forces. E.g a helical spring undergoes tensile deformation when tensile forces are exerted and compressive deformation when compressive forces are exerted.

The force extension graph of a helical spring is a straight line (from the origin) up to a point known as the elastic limit. In the linear region the spring undergoes elastic deformation (it will return to its original shape once the force is removed). Beyond the elastic limit, it undergoes plastic deformation - a permanent structural change and the spring will not return to its original shape once the force is removed.

Provided the force is less than the elastic limit, the spring obeys Hooke's law. Hooke's law states that the extension of the spring is directly proportional to the force applied. This is true as long as the elastic limit is not exceeded:

F = kx

Where k is the force constant. A spring with a large force constant is difficult to extend whereas a spring with a small force constant is easy to extend. F=kx can also be applied for compression (where x represents the compression of the spring).

We need to know how to investigate Hooke's law...

• Attach a spring at one end using a clamp, boss, and clamp stand secured to the bench using a G-clamp/large mass
• Set up a metre rule with a resolution of 1mm close to the spring
• Suspend slotted masses from the spring
• Record the total mass added and the new length of the spring after each mass is added
• Repeat for at least 6 different masses
• Plot a graph of force against extension

This will produce a force extension graph. We need to know about force extension graphs in a little more detail (particularly the force-extension graphs of springs and wires). The area under a force extension graph is the work done. Firstly, it is important to realise that the loading and unloading curves of a force-extension graph may not be the same.

Metal wire
The loading graph follows Hooke's law until the elastic limit of the wire is reached. For forces less than the elastic limit the unloading curve will follow the same curve as the loading curve. However, if the elastic limit is exceeded the wire will undergo plastic deformation (see above) and the unloading curve will be parallel to the loading curve.

Rubber
Rubber bands do not obey Hooke's law. It will return to it's original shape if the force is removed however the loading and unloading curves are not the same. The characteristic 'loop' formed is known as the hysteresis loop. The area of this loop represents the thermal energy released when the material is loaded and then unloaded. It can also be seen that more work is done in loading (stretching) than unloading the rubber band.

Polythene
Much like rubber bands, polythene does not obey Hooke's law. Thin strips of polythene are very easy to stretch and suffer plastic deformation under relatively little force.

4.5.3 Wave–particle duality

The wave-particle duality is a model used to describe how all matter has both wave and particle properties. De Broglie realised that all particles travel through space as waves and anything with mass that is moving has wave-like properties (these waves are known as matter waves/de Broglie waves).

Usually we would describe electrons as particles (as they have mass and charge) and as a result they can be accelerated and deflected by electric and magnetic fields. But under certain conditions we can also make electrons diffract - they spread out like waves as they pass through a tiny gap and even form diffraction patterns. If an electron gun fires electrons at a thin piece of polycrystalline graphite the electrons pass through the gaps between individual carbon atoms. The gaps are so small the electrons diffract and form a diffraction pattern. The electrons are behaving as particles when they are accelerated by the p.d. and they behave as waves when they diffract. They then behave as particles again when they hit the screen.

De Broglie realised that the wavelength of a particle was inversely proportional to its momentum. Further investigation lead to the de Broglie equation…

λ = h/p

The de Broglie equation can be applied to all particles. For example, protons and neutrons have also been shown to have wave properties and form diffraction patterns. However, as particles become larger their wave properties become harder to observe. The mass of a proton is much greater than the mass of an electron so at the same speed their momentum is significantly greater so their wavelength is much smaller and therefore harder to observe.

4.5.2 The photoelectric effect

The photoelectric effect: when Heinrich Hertz shone UV radiation onto zinc in 1887 electrons were emitted from the surface of the metal. The emitted photons are known as photoelectrons.

We need to know a simple demonstration of the photoelectric effect - this can be done with a gold-leaf electroscope. If we briefly touch the top place with the negative electrode from a high voltage power supply we will charge the electroscope. Excess electrons are deposited onto the plate and stem of the electroscope. Any charge developed on the plate and stem of the electroscope spreads to the stem and the gold leaf - since the stem and gold leaf now both have the same charge they repel each other and the leaf lifts away from the stem. If a clean piece of zinc is placed on top of a negatively charged gold-leaf electroscope and UV radiation shines onto the zinc surface the gold leaf slowly falls back toward the stem because the electroscope gradually loses its negative charge. This is because the UV (incident radiation) has caused the free electrons to be emitted from the zinc. These are photoelectrons. Three key observations resulted:

1. Photoelectrons were only emitted if the incident radiation was above a certain frequency (the threshold frequency) - no matter how intense the radiation was.
2. If the incident radiation was above the threshold frequency emission of photoelectrons was instantaneous.
3. If the incident radiation was above threshold frequency, increasing the intensity of the radiation increased the number of electrons emitted (not the kinetic energy at which they were emitted). To increase maximum kinetic energy you increase the frequency of the incident radiation.

These observations cannot be explained with the wave model of light so Einstein published the photon model in 1905. He suggested that each electron in the metals surface requires a certain amount of energy in order to escape from the metal and that each photon could transfer its exact energy to one surface electron only in a one-to-one reaction. Remember, if threshold frequency is not met (this depends on the energy of the photon, E=hf) the photoelectron will not be released regardless of the intensity (number of photos per second).

Depending on their positions within the metal electrons would require different amounts of energy to free them. Einstein defined a constant for each metal - the work function. This is the minimum energy required to free an electron from the surface of the metal.

Provided threshold frequency is met, increasing the intensity of incident radiation means more photons hit the metal surface per second so more photoelectrons are emitted per second. The rate of emission of photoelectrons is directly proportional to the incident radiation intensity.

Using the principle of conservation of energy there must be some leftover energy after the electron was freed from the metal - this is the maximum value of kinetic energy that any emitted photoelectron can have. The only way to increase maximum kinetic energy is to increase the frequency of the incident radiation - each photon has more kinetic energy so each electron has more kinetic energy after it has been freed from the metal. From this, Einstein derived his photoelectric effect equation. The energy of each photon must be conserved - it frees a single electron (in a one-to-one reaction) then any remainder is transferred into the kinetic energy of the photoelectron. According to the principle of conservation of energy he produced this equation…

hf = ϕ + KEmax

NOTE: Since all terms are energies, they should all be in joules, or all be in electronvolts. 

It is important to realise that some electrons in the surface of the metal are much closer to the positive metal ions than others. Their relative positions affect how much energy is required to free them. The work function is the minimum energy required to free an electron from the metal - most electrons need a little more energy than the work function to free them. This means that only a few of the emitted photoelectrons have the maximum kinetic energy, most travel a little slower. Also, if a photon strikes the surface of the metal at the threshold frequency for the metal then no energy will be left over from the incident photon to be transferred into kinetic energy. The equation becomes hf₀ = ϕ.

Lastly….. so we already know that the only way to increase the maximum kinetic energy of photoelectrons is to increase the frequency of the incident radiation. A graph of maximum kinetic energy against frequency of radiation on the surface gives a gradient equal to Plancks constant and a y-intercept equal to the negative work function. It is important to realise that since energy metal has a different work function the threshold frequency for each metal is different.

4.5.1 Photons

In 1900 Planck discovered that electromagnetic energy could only exist in certain values - it appeared to come in quanta (little packets). This proposed that electromagnetic radiation had a particulate nature (tiny packets of energy) rather than a continuous wave. Einstein called these ‘packets’ photons.

Nowadays we have more of an understanding that we can use different models to describe electromagnetic radiation. E.g we can use the photon model to explain how electromagnetic radiation interacts with matter and the wave model to explain it’s propagation through space.

So, now we know a photon is like a little packet of energy. We also need to know that the energy of each photon is directly proportional to its frequency. We can use the following equation to show this:

E = hf

NOTE: E (energy of the photon) is in joules, f (frequency of electromagnetic radiation) is in Hz, and h is the Planck constant.

If we were to combine E = hf with the wave equation (c= fλ) we are able to express the energy of a photon in terms of its wavelength and the speed of light through a vacuum:

E = (hc)/λ

NOTE: It is important to note that this equation has both wave elements (λ) and particulate elements (the energy, E, of a photon).

From the equation E = (hc)/λ we can see that the energy of a photon (E) is directly proportional to its wavelength (λ) so the smaller the wavelength the larger the energy of the photon.

Okay so if we think about it, one joule is pretty big at the subatomic scale of the quantum level. To combat this, we use electronvolts (eV) when measuring energies at the quantum scale. The energy of 1eV is defined as the energy transferred to or from an electron when it moves through a potential difference of 1V. But what actually is the quantity of 1eV? Well, we know the work done on an electron is VQ (W=VQ=Ve (e standing for the elementary charge)). So…

W = 1V x 1.60 × 10^-19 C = 1.60 × 10^-19 J.

This means that 1eV is equal to 1.60 × 10^-19 J

Using LEDs

We need to know a little experiment with LEDs to determine a value for the Planck constant. We can do this by considering the energies of the photons they emit. LEDs convert electrical energy into light energy by emitting visible light photons (of a specific wavelength) when the p.d. across them is above a critical value. At this p.d., work is being done (this is given by W=VQ) - this energy is about the same energy as the emitted photon. 

Connect a voltmeter across an LED. Add a safety resistor next to the LED (outside the voltmeter connections) and connect the whole system to a variable resistor/potentiometer connected to a power supply to vary the p.d out. We can us the voltmeter to measure the minimum p.d. that is required to turn of the LED. Place a black tube over the LED to help show exactly when the LED lights up. Provided we know the wavelength of the photons emitted by the LED then we can determine the Planck constant because…

At the threshold p.d. the energy transferred by an electron in the LED (work done) is approximately the energy of the single photon…..

W = VQ = Ve = E = hf = (hc)/λ…………. Ve=(hc)/λ

To obtain a more accurate result we can use a variety of LEDs that emit a known wavelength of photons then we can plot a graph of V against 1/λ. The gradient will be (hc)/e.

3.1.1 Kinematics

Displacement is the distance something is from it's starting position (the distance it has been displaced).

Instantaneous speed is the speed at an instant point - e.g. the speed at a certain point in time

Average speed is the total distance divided by the time taken

Velocity is the change in displacement divided by the time taken

Acceleration is the change in velocity divided by the time taken


We need to be able to draw displacement, speed, velocity, and acceleration graphs. Don't worry, we did all of that in GCSE lol. Refresh your mind here.

2.3.1 Scalars and vectors

Scalar quantities have just magnitude

Vector quantities have magnitude and direction

To determine the resultant of a vector we can use Pythagoras (provided they are perpendicular) or SOHCAHTOA.

2.1.2 S.I. units

Know the SI units (we don't need to know candela):

• mass (kg)
• length (m)
• time (s)
• current (A)
• temperature (K)
• amount of substance (mol)

And be able to put other units into base units (e.g a Newton is a kgm/s^2)

Lastly, we need to know about the following prefixes:

• pico (p)
• nano (n)
• micro (μ)
• milli (m)
• centi (c)
• deci (d)
• kilo (k)
• mega (M)
• giga (G)
• tera (T)

2.1.1 Physical quantities

Ensure we know what units represent which physical quantities, e.g Amperes represents current.

1.1.2 Implementing

Basically, we need to know how to use practical apparatus. We all already know how to do this from our practical endorsement experiments.

1.1.4 Evaluation

Following on from an experiment we need to be able to:

• Evaluate results and draw conclusions
• Evaluate how the scientific community use results to validate new knowledge and ensure integrity
• Refine experimental design by suggestion of improvements to the procedures and apparatus.
• Precisely and accurately measure data of measurements and data, including margins of error, percentage errors and uncertainties in apparatus 
• Identify:
• anomalies in experimental measurements
• limitations in experimental procedures

1.1.3 Analysis

Following on from an experiment we need to be able to:

• Process, analyse, and interpret qualitative and quantitative experimental results
• Reach valid conclusions (where appropriate)
• Use appropriate mathematical skills for analysis of quantitative data
• Use appropriate significant figures
• Plot and interpret suitable graphs from experimental results
• Select and label axes with appropriate scales, quantities and units
• Measure gradients and intercepts.

1.1.1 Planning

Basically, in an exam they might ask us to design/explain an experiment. We need to be able to do the following:

• Design experiments
• Include a selection of suitable apparatus, equipment and techniques for the proposed experiment
• Apply scientific knowledge based on the content of the spec (this spec lol)
• Identification of variables that must be controlled (if applicable)
• Evaluate whether an experimental method is appropriate to meet the expected outcomes

6.1.1 Capacitors

Capacitors are electrical components which separate charge. They consist of two metallic plates separated by an insulator (a dielectric - e.g air/ceramic/paper/mica). When a capacitor is connected to a cell of e.m.f Є (for example) the electrons only flow from the cell for a short time as they cannot travel between plates (because of the insulator). During the brief current, electrons from the cell flow onto one plate (they are deposited onto a plate, this plate has a net negative charge as it gains electrons) and this repels electrons from the other plate so electrons are removed from the other plate (this plate has a net positive charge as it is deficient in electrons). Charge is always conserved - we can confirm this as the current in the circuit must be the same at all points. The same amount of electrons that has been deposited onto one plate has left the other plate so the have an equal but opposite charge (they have a net charge of 0). This means there is a p.d. across the plates. When the p.d. across the plates is equal to the e.m.f (Є) of the cell, the current in the circuit falls to 0 and the capacitor is fully charged.

The capacitance of a capacitor is defined as the charge stored per unit p.d. across it. It is measured in farads (F). From the equation below we can see that one Farad equates to one coulomb per volt. We can use the following equation to determine capacitance:

Q = V C

The greater the amount of positive and negative charge stored on the plates the greater the p.d. across them. This means that charge is proportional to p.d meaning that, from the equation above, capacitance is constant.

Okay so when we are connecting capacitors in circuits we cannot get them mixed up with resistors!! This is a big no no, they have the opposite rules...

• In parallel the total capacitance is C = C1 + C2.....
• This is because the pd. across each capacitor is the same and charge is conserved so total Q (total charge stored) equates to the sum of the individual charges stored by each capacitor....Q = Q1 + Q2... Therefore since Q = VC and V is constant then C = C1 + C2....
• In series the total capacitance is 1/C = 1/C1 + 1/C2.......
• This is because in series the sum of the p.d.s around each loop equals the e.m.f so V = V1 + V2.... We know that the charge stored in each capacitor is the same so Q is constant. Q = VC so V = Q/C so 1/C = 1/C1 + 1/C2...

There's a little bit more about capacitors in circuits. Firstly, how to investigate combinations/perhaps an unknown capacitor value. Set up a circuit with a safety resistor, an ammeter, a few capacitors and a voltmeter across each capacitor and a variable power supply (a power supply where we can vary the output voltage) and also a switch. Close the switch - current will briefly flow through the circuit. We can determine the charge stored in each capacitor by measuring the voltage across it and multiply it by the capacitor reading (Q = V C). You will see that in each instance in SERIES the charge stored in each capacitor will be the same for a certain voltage (this value will vary as voltage across the circuit varies).

To determine the series rule for capacitors (1/C = 1/C1 + 1/C2...) connect a multimeter set to capacitance across two capacitors in series. The reading will show the figure obtained is we were to do the sum 1/C = 1/C1 + 1/C2...