Special Relativity

Resources for Special Relativity

Here is a link to a fantastic little book that started me on my “very short introduction” library. It has been uploaded as a pdf file, but if you enjoy it give the author some credit and pay the guy (Russell Stannard) by buying it!


Frames of Reference

You should all try to make your holiday videos so useful in showing Physics ideas! Who is in motion? Does it remain the same throughout the sequence?

This is covered in the web-based research post but I’ve uploaded it here as an MP4 file.

Just check this off against the content as it isn’t all covered at Higher (some is the AH and some isn’t covered at all).

Neil deGrasse Tyson with his inimitable style explains the Michelson-Morley experiment and shows that despite getting a rubbish result it doesn’t say your results are rubbish! This was big Science progress and it wasn’t explained until Einstein came along. It was the turning point that transformed Science.

Here are further explanations of the Michelson-Morley experiment and a hint of more of the course to come.

Evidence for Special Relativity

Sixty symbols- Nottingham University

Sixty Symbols by Nottingham University are an amazing set of videos, although far more than sixty by now. Check out and keep watching.

…. and here at the end I have uploaded the worked answers (thanks to whoever wrote these excellent questions) so that you can check off your tutorials.

ODU worked ANSWERS_5

Our Universe tutorial solutions


updated October 2019

Higher Past Papers

These papers and marking instructions are reproduced to support SQA qualifications, please check the conditions of use and ensure they are not used for commercial benefit.

National Qualification Higher Physics Papers

Digital Paper
NH 20192019mi H 20192019 Report
NH SpecP1
NH Spec P2
SpecMI H P1
2018 DQPNH 20182018MI H 20182018 Report
2017 DQPNH 20172017MI H 20172017 Report
2016 DQPNH 20162016MI H 20162016 Report
2015 DQPNH 20152015MI H 20152015 Report
NH SpecSpecMI H Spec

If you’d like to work through past papers by topic then Mr Davie has done all the hard work for you and has promised to keep this list up to date. He says


Below are the Revised Higher Past Papers, the content is very very similar to the new National (CfE) Higher, although the marks would be different. These were the last past papers with half marks!

YEARMIExam Feedback
H Rev 20152015MI Rev 20152015 Report
H Rev 20142014MI Rev 20142014 Report
H Rev 20132013MI Rev 2013
2013 Report
H Rev 20122012MI Rev 20122012 Report
H Rev SpecSpecimen
MI Rev Spec

These are the traditional Higher Past Papers (once also known as revised!) Remember some of this material is no longer on the syllabus, and some is relevant to National 5.

H 20152015MI 20152015 Report
H 20142014MI 20142014 Report
H 20132013MI 20132013 Report
H 20122012MI 20122012 Report
H 20112011MI 20112011 Report
H 20102010MI 20102010 Report
H 20092009MI 20092009 Report
H 2008 2008MI 20082008 Report
H 20072007MI 20072007 Report
H 20062006MI 20062006mcH&Int2 stats2006 Report
H 20052005MI 20052005 Report
H 20042004MI 20042004 Report
H 20032003MI 20032003 Report
H 20022002MI 20022002 Report
H 20012001MI 20012001 Report
H 20002000MI 2000
Internal report

U Standards 2000
H Rev Specimen QPSpecimenMI H Rev Specimen

From National Parent Forum of Scotland This great little pdf file gives some ideas of suitable questions from the traditional Higher papers that are suitable for the new National Qualifications.

Thanks to Mr John Irvine and Mr Stuart Farmer for the course reports.

PLEASE both teachers and students READ the Report after tackling the past paper. The course reports give really good background and information about how candidates performed in the exam and what messages you should learn from them.

1999H 1999 PI Solutions
H 1999 PII Solutions
1998H 1998 PI Solutions
H 1998 PII Solutions
1997H 1997 PI Solutions
H 1997 PII Solutions
1996H 1996 P1 Solutions
H 1996 PII solutions
1995H 1995 PI Solutions
H 1995 PII Solutions
1994H 1994 PI Solutions
H 1994 PII Solutions
1993H 1993 PI Solutions
H 1993 PII Solutions
1992H 1992 PI solutions
H 1992 PII Solutions

All the best with your revision!

September 2020



Teamwork by Mr Stewart (Berwickshire HS) and I. He designed and made them and I tweaked them. Thanks Mr Stewart they’re ace!

Contains UPSN, OEQ, Uncertainties and is 4 pages

It is really important that you get to grips with the uncertainty section. You will need this information for your Assignment and it could well form a question on the exam paper.

The key is remembering that ANY measurement is liable to uncertainty. Get that and you’re half way there!

Here is a summary of Key Knowledge for this section new for 2021


Random and systematic uncertainty

Uncertainties and data analysis

  • All measurements of physical quantities are liable to uncertainty, which should be expressed in absolute or percentage form. Random uncertainties occur when an experiment is repeated and slight variations occur. Scale reading uncertainty is a measure of how well an instrument scale can be read. Random uncertainties can be reduced by taking repeated measurements. Systematic uncertainties occur when readings taken are either all too small or all too large.
  • They can arise due to measurement techniques or experimental design.
  • The mean of a set of readings is the best estimate of a ‘true’ value of the quantity being measured. When systematic uncertainties are present, the mean value of measurements will be offset. When mean values are used, the approximate random uncertainty should be calculated. When an experiment is being undertaken and more than one physical quantity is measured, the quantity with the largest percentage uncertainty should be identified and this may often be used as a good estimate of the percentage uncertainty in the final numerical result of an experiment. The numerical result of an experiment should be expressed in the form final value ±uncertainty.


Whenever you do an experiment there will be uncertainties.

There are three types of uncertainty and effects to look out for at Higher.

Systematic Effects

Here the problem lies with the design of the experiment or apparatus. It includes zero errors. Sometimes they show up when you plot a graph but they are not easy to recognise, as they are not deliberate. Systematic effects include slow running clocks, zero errors, warped metre sticks etc. The best way to ensure that these are spotted is to acknowledge their existence and go looking for them. Where accuracy is of the utmost importance, the apparatus would be calibrated against a known standard. Note that a systematic effect might also be present if the experimenter is making the same mistake each time in taking a reading.

Random Uncertainties

These uncertainties cannot be eliminated. They cannot be pinpointed. examples include fluctuating temperatures, pressure and friction. Their effect can be reduced by taking several readings and finding a mean.

Reading Uncertainties

These occur because we cannot be absolutely certain about our readings when taking measurements from scales. Use scales with mirrors where possible, good scales and repeat all measurements.

Repeat all experiments to reduce the reading and random uncertainties. Systematic effects are not improved by taking lots of results.

Which experiment has the best design?

Quantifying Uncertainties

 1.Find the mean

This is the best estimate of the “true” value but not necessary the “true” value.

          2. Find the approximate random uncertainty in the mean (absolute uncertainty)

This can be written as  and it is sometimes referred to as average deviation or absolute uncertainty.

3. Find the percentage uncertainty.


Scale Reading Uncertainty

This value indicates how well an instrument scale can be read.

An estimate of reading uncertainty for an analogue scale is generally taken as:

± half the least division of the scale.

Note: for widely spaced scales, this can be a little pessimistic and a reasonable estimate should be made.

For a digital scale it is taken as

± 1 in the least significant digit displayed.

Or uncertainty in reading ÷reading × 100%

Overall final Uncertainty

When comparing uncertainties, it is important to take the percentage in each.

In an experiment, where more than one physical quantity has been measured, spot the quantity with the largest percentage uncertainty. This percentage uncertainty is often a good estimate of the percentage uncertainty in the final numerical result of the experiment.

eg if one measurement has an uncertainty of 3% and another has an uncertainty of 5%, then the overall percentage uncertainty in this experiment should be taken as 5%



Mrs Physics

January 2022


For some of you this first link will help explain about semiconductors, for others it will freak you out. If you are someone who likes to know and understand the background behind your Physics, then this video will help in your understanding. If you just like to accept what you’ve been taught then maybe give it a wide berth! It explains where these energy gaps come from, what is means to be a semi-conductor. The SSERC meet mentions the words “quantum tunnelling” which appears in AH Physics. If keeping up with the basics is enough then use the hour for more useful revision.  I am 29 mins in, and it has taken my 40 mins, but it is very informative.


Remind you of anyone?

This has now become a topic that is not really enjoyed by most Higher candidates. Here is an intro video to help you out.


More definitions courtesy of


Glossary for Revision
Conductors Conductivity is the ability of a materials to conduct charge carriers (electrons or positive holes) (all metals, semi metals like carbon-graphite, antimony and arsenic)
Insulators Materials that have very few charge carriers (free electrons or positive holes). (plastic, glass and wood)
Semiconductors These materials lie between the extremes of good conductors and good insulators. They are crystalline materials that are insulators when pure but will conduct when an impurity is added and/or in response to light, heat, voltage, etc (silicon (Si), germanium (Ge), gallium arsenide (GaAs)
Band structure Electrons in an isolated atom occupy discrete energy levels. When atoms are close to each other these electrons can use the energy levels of their neighbours. When the atoms are all regularly arranged in a crystal lattice of a solid, the energy levels become grouped together in a band. This is a continuous range of allowed energies rather than a single level. There will also be groups of energies that are not allowed, what is known as a band gap. Similar to the energy levels of an individual atom, the electrons will fill the lower bands first. The fermi level gives a rough idea of which levels electrons will generally fill up to, but there will always be some electrons with individual energies above this
In a conductor: the highest occupied band, known as the conduction band, is not completely full. This allows the electrons to move in and out from neighbouring atoms and therefore conduct easily
In an insulator: the highest occupied band is full. This is called the valnce band, by analogy with the valence electrons of an individual atom. The first unfilled band above the valence band above the valence band is the conduction band. For an insulator the gap between the valence and conduction bands is large and at room temperature there is not enough energy available to move electrons from the valence band into the conduction band, where they would be able to contribute to conduction. Normally, there is almost no electrical conduction in an insulator. If the applied voltage is high enough (beyond the breakdown voltage) sufficient electrons can be lifted to the conduction band to allow current to flow. Often this flow of current causes permanent damage. Within a gas this voltage is often referred to as the striking voltage, particularly within the context of a fluorescent lamp since this is the voltage at which the gas will start to conduct and the lamp will light.
In a semiconductor: the gap between the valence band and the conduction band is smaller, and at room temperature there is sufficient energy available to move some electrons from the valence band into the conduction band, allowing some conduction to take place. An increase in temperature increases the conductivity of the semiconductor as more electrons have enough energy to make the jump to the conduction band. This is the basis of an NTC thermistor. NTC stands for “negative temperature coefficient” (increased temperature means reduced resistance). This makes current increase so conductivity increases.
Optical properties of materials Electron bands also control the optical properties of materials. They explain why a hot solid can emit a continuous spectrum rather than a discrete spectrum as emitted by a hot gas. In the solid the atoms are close enough together to form continuous bands. The exact energies available in these bands also control at which frequencies a material will absorb or transmit and therefore what colour will appear
Bonding in semiconductors The most commonly used semiconductors are silicon and germanium. Both these materials have a valency of 4 (they have 4 outer electrons available for bonding. In a pure crystal, each atom is bonded covalently to another 4 atoms: all of its outer electrons are bonded and therefore there are few free electrons available to conduct. This makes resistance very large. Such pure crystals are known as intrinsic semiconductors. The few electrons that are available come from imperfections in the crystal lattice and thermal ionisation due to heating. A higher temperature will thus result in more free electrons, increasing the conductivity and decreasing the resistance, as in a thermistor
Holes When an electron leaves its position in the crystal lattice, there is a space left behind that is positively charged. This lack of an electron is called a positive hole. Even though electrons are moving, the effect is the same as if it was the hole that moved through the crystal lattice. The hole can be thought of as a positive charge carrier. In complex semiconductors it is easier to calculate what is happening in terms of 1 moving positive hole, rather than many electrons
In an intrinsic semiconductor the number of holes is equal to the number of electrons. The generally small currents consist of drifting electrons in 1 direction and drifting holes in the other.
Doping Semiconductor’s electrical properties are dramatically changed by the addition of very small amounts of impurities. Once doped they are known as extrinsic semiconductors. Solid state semiconductors are much smaller and use much less power than valve transistors.
Doping Doping a semiconductor involves growing impurities such as boron or arsenic into an intrinsic semiconductor such as silicon
An in intrinsic semiconductor is an undoped semiconductor
Fermi level Energy of last occupied level by an electron, below this energy are completely occupied and above it are completely unoccupied
N-type semiconductors If an impurity such as arsenic with 5 outer electrons is present in the crystal lattice then 4 of its electrons will be used in bonding with the silicon. The 5th will be free to move about and conduct. Since the ability of the crystal to conduct is increased, the resistance of the semiconductor is therefore reduced. Because of the extra electrons present, the Fermi level is closer to the conduction band than in an intrinsic semiconductor. This type of conductor is called n – type, since most conduction is by the movement of free electrons (-ve)
P-type semiconductors The semiconductor may also be doped with an element like Indium, which has 3 outer electrons. This produces a hole in the crystal lattice, where an electron is “missing”. Because of this lack of electrons, the Fermi level is closer to the valence band than in an intrinsic semiconductor. An electron from the next atom can move into the hole created, as described previously. Conduction can thus take place by the movement of positive holes. Most conduction takes place by the movement of positively charged holes
Notes on doping The doping material cannot be added to the semiconductor crystal. It has to be grown into the lattice when the crystal is grown so that it becomes part of the atomic lattice. Overall charge on semiconductors are still neutral The quantity of the impurity is extremely small (could be 1 atom in 1 million). If it were too large it would disturb the regular crystal lattice.
minority charge carriers In n – type and p – type there will always be small numbers of the other type of charge carrier, known as minority charge carriers, due to thermal ionisation.
p-n junctions When a semiconductor is grown so that 1 half is p-type and 1 half is n-type, the product is called a p-n junction and it functions as a diode. A diode is a discrete component that allows current to flow in one direction only.
At temperatures other than absolute Zero kelvin, the electrons in the n-type and the holes in the p-type material will constantly diffuse(particles will spread from high concentration regions to low concentration regions). Those near the junction will be able to diffuse across it.
Reverse-biased Cell connected negative end to p-type and positive end to n-type
Forward-biased Cell connected positive end to p-type and negative end to n-type.
Reverse biased – charge carriers When the p-side is attached to the negative side of a battery (V↓a) then the electrons at that side have more potential energy than previously. This has the effect of raising the bands on the p-side from where they were originally. We say it is reverse-biased. Almost no conduction can take place since the battery is trying to make electrons flow “up the slope” of the difference in conduction bands. The holes face a similar problem in flowing in the opposite direction. The tiny current that does flow is termed reverse leakage current and comes from the few electrons which have enough energy from the thermal ionisation to make it up the barrier.
Forward biased – charge carriers When the p-side is attached to the positive side of the battery (V↓a) then the electrons at that side have less potential energy than under no bias. This has the effect of lowering the bands on the p-side from where they were originally. We sat it is forward biased. As the applied voltage approaches the built in voltage, more electrons will have sufficient energy to flow up the now smaller barrier and an appreciable current will be detected. Once the applied voltage reaches the in-built voltage there is no potential barrier and the p-n junction has almost no resistance, like a conductor. The holes are similarly able to flow in the opposite direction across the junction towards the negative side of the battery.
In the junction region of a forward-biased LED electrons move from the conduction band to the valence band to emit photons.
In a forward-biased p-n junction diode, holes and electrons pass through the junction in opposite directions. Sometimes holes and electrons will meet and recombine. When this happens energy is emitted in the form of a photon. For each recombination of electron to hole, 1 photon of radiation is emitted. Most of the time heat energy is released but in some semiconductors like gallium arsenic phosphide, the energy is emitted as light. If the junction is close to the surface of the material, this light may be able to escape. This makes an LED.
The colour of light emitted from an LED depends on On the elements and relative quantities of the three constituent materials. The higher the recombination energy the higher the frequency of light.
The LED does not work in reverse bias since the charge carriers do not/can not travel across the junction towards each other so cannot recombine
Photodiode A p-n junction in a transparent coating will react to light in what is called the photovoltaic effect. Each individual photon that is incident on the junction has its energy absorbed, assuming the energy is larger than the band gap. In the p-type material this will create excess electrons in the conduction band and in the n-type material it will create excess holes in the valence band. Some of these charge carriers will then diffuse to the junction and be swept across the built-in electric field of the junction. The light has supplied energy to the circuit, enabling current to flow (it is the emf in the circuit). More intense light (more photons) will lead to more electron-hole pairs being produced and therefore a higher current. Current is proportional to light intensity.
Photodiode The incoming light provides energy for an electron within the valance band of the p-type to be removed from a positive hole and moved up to the conduction band in the n-type material. As this electron is moved up into the conduction band it has an increase in energy. Since EMF is the energy per coulomb of charge an EMF is generated.
Photovoltaic mode The p-n junction can supply power to a load (motor). Many photo-diodes connected together form a solar cell. This is described as photovoltaic mode. There is no bias applied to a solar cell and it acts like an LED in reverse. The increased movement of charge across a p-n junction can reduce resistance of component containing the junction.
Photoconductive mode When connected to a power supply a photodiode will act as a LDR. This is described as photoconductive mode. The LDR is connected in reverse bias, which leads to a large depletion region. When light hits the junction, electrons and holes are split apart. This leads to free charge carriers in the depletion region. The free charge carriers reduce overall resistance of the diode, allowing current to flow. Conductivity of diode is being changed.
Addition of impurity atoms to a pure semiconductor(doping) decreases its Resistance
Applications of p-n junctions Photovoltaic cell /LED /Photoconductive mode(LDR)
What is photovoltaic effect? A process in which a photovoltaic cell converts photons of light into electricity.
Depletion layer Near the junction, electrons diffuse across to combine with holes, creating a “depletion region”.
Majority charge carriers in n-type The electrons in the conduction band are free move towards the positive terminal of an applied p.d.
Majority charge carriers in p-type The “positive holes” in the valance band move towards the negative terminal of an applied p.d.
Majority charge carriers across the p-n junction (forward biased) With the applied p.d. in the direction shown electrons in the n-type material move to the left and holes in the p-type material move to the right. The depletion layer in the centre becomes thinner and thinner and if the p.d. of the supply is greater than the barrier potential(0.7 V for silicon-based semiconductors) the barrier is broken down and a current flows through the device.
How light is produced at the p-n junction of an LED When the diode is forward biased the free electrons in the conduction band of the n-type material are given energy by the supply to overcome the energy barrier generated by the depletion layer at the junction. Once these electrons overcome the energy barrier they drop down from the conduction band to the valance band of the p-type material and combine with a positive hole in the valance band of the p-type material. As the electron drops between the bands it loses and energy and emits this as light.
Use band theory to explain how electrical conduction takes place in a pure semiconductor such as silicon. Your explanation should include the terms: electrons, valence band and conduction band. most/majority of electrons in valance band or “fewer electrons in conduction band” band gap is small   electrons are excited to conduction band charge can flow when electrons are in conduction band
What charge carriers actually move across the p-n junction? Electrons

Now the following file is for a document from the old Higher course with a macro embedded to click on to show the applications of p-n junctions. I have saved it in compatible mode so I don’t know if the macros will work, but wordpress wont let me upload macro enabled documents (quite rightly). You’ll have to let me know if the buttons function if you download it. Enjoy! semiconductors 2017


This is the first of a selection of fantastic videos on Band Theory from the HIGH SCHOOL PHYSICS EXPLAINED Youtube channel.

High School Physics Explained

Thanks to “Paul” for allowing me to host these videos so that people in D&G can actually watch them in school! Please visit his site and subscribe…… now just how to upload them….

….still trying, but not having any success. I’ll try PLAN F. Thanks to Paul for sending me the videos which are now uploaded. The power of the internet.

Learn the following

The electrons in atoms are contained in energy levels. When the atoms come together to form solids, the electrons then become contained in energy bands separated by gaps.
In metals, the highest occupied band is not completely full and this allows the electrons to move and therefore conduct. This band is known as the conduction band.
In an insulator, the highest occupied band (called the valence band) is full. The first unfilled band above the valence band is the conduction band. For an insulator, the gap between the valence band and the conduction band is large and at room temperature there is not enough energy available to move electrons from the valence band into the conduction band where they would be able to contribute to conduction. There is no electrical conduction in an insulator.
In a semiconductor, the gap between the valence band and conduction band is smaller and at room temperature there is sufficient energy available to move some electrons from the valence band into the conduction band allowing some conduction to take place. An increase in temperature increases the conductivity of a semiconductor.