Unit 1 PHYA1 Particles, Quantum Phenomena … · Web viewPHYA1 Particles, Quantum Phenomena and Electricity Written Examination . 70 marks, 6 or 7 structured questions 1 ¼ hours

AS unit 1 phya1

particles

quantum phenomena

electricity

GCE PHYSICS

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. MB Cuthbert (20/04/2015) Page 1 of 32

AS Examination

Unit 1 . PHYA1 Particles, Quantum Phenomena and ElectricityWritten Examination . 70 marks, 6 or 7 structured questions1 ¼ hours40% of the total AS marks20% of the total A-Level marks available June

Unit 2 . PHYA2 Mechanics, Materials and WavesWritten Examination . 70 marks, 6 or 7 structured questions1 ¼ hours40% of the total AS marks20% of the total A-Level marks available June

Unit 3 Investigative and Practical Skills in AS PhysicsPHA3X, Externally Marked Route X . 55 marksPractical Skills Verification (PSV . teacher verification)Externally Marked Practical Assignment (EMPA . 55 marks)20% of the total AS marks 10% of the total A-Level marks available June only

A2 Examination

Unit 4 . PHYA4 Fields and Further MechanicsWritten Examination . 75 marks,1 ¾ hoursSection A is 25 multiple choice questions, each worth one mark.Section B is a written paper of 4/5 structured questions and consists of 50 marks.20% of the total A-Level marks available June

Unit 5 . One of Units PHA5A, PHA5B, PHA5C, PHA5DWritten Examination . 75 marks.1 ¾ hoursSection A: Nuclear and Thermal Physics . 40 marksCompulsory section 4/5 structured questionsSection B one of the following options.Each paper has 4/5 structured questions and 35 marks.Options: A - AstrophysicsB - Medical Physics20% of the total A-Level marks (Section A 10%, Section B 10%) Available June only

Unit 6 . Internal Assessment Investigative and Practical Skills in A2 PhysicsPHA6X, Externally Marked Route X . 55 marksPractical Skills Verification (PSV . teacher verification)Externally Marked Practical Assignment (EMPA . 55 marks) 10% of the total A-Level marks Available June only

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity

This module involves two contrasting topics in physics: particle physics and electricity. Through the study of these topics, students should gain an awareness of the on-going development of new ideas in physics and of the application of in depth knowledge of well-established topics such as electricity. Particle physics introduces students


to the fundamental properties and nature of matter, radiation and quantum phenomena. In contrast, the study of electricity in this module builds on and develops previous GCSE studies and provides opportunities for practical work and looks into important applications.

Syllabus extract:

Constituents of the atomProton, neutron, electron.Their charge and mass in SI units and relative units.Specific charge of nuclei and of ions.Atomic mass unit is not required.Proton number Z, nucleon number A, nuclide notation, isotopes

Stable and unstable nucleiThe strong nuclear force; its role in keeping the nucleus stable; short-range attraction to about 3 fm, very-short range repulsion below about 0.5 fm;Equations for alpha decay and β- decay including the neutrino.

Particles, antiparticles and photonsCandidates should know that for every type of particle, there is a corresponding antiparticle. They should know that the positron, the antiproton, the antineutron and the antineutrino are the antiparticles of the electron, the proton, the neutron and the neutrino respectively.Comparison of particle and antiparticle masses, charge and rest energy in MeV.Photon model of electromagnetic radiation, the Planck constant, E = hf =hc/λKnowledge of annihilation and pair production processes and the respective energies involved. The use of E = mc2 is not required in calculations.

Particle interactionsConcept of exchange particles to explain forces between elementary particlesThe electromagnetic force; virtual photons as the exchange particle.The weak interaction limited to β-, β+ decay, electron capture and electron-proton collisions; W+ and W- as the exchange particles.Simple Feynman diagrams to represent the above reactions or interactions in terms of particles going in and out and exchange particles.

Classification of particlesHadrons: baryons (proton, neutron) and antibaryons (antiproton and antineutron) and mesons (pion, kaon).Hadrons are subject to the strong nuclear force.Candidates should know that the proton is the only stable baryon into which other baryons eventually decay; in particular, the decay of the neutron should be known.Leptons: electron, muon, neutrino (electron and muon types).Leptons are subject to the weak interaction.Candidates will be expected to know baryon numbers for the hadrons.Lepton numbers for the leptons will be given in the data booklet.

Quarks and antiquarksUp (u), down (d) and strange (s) quarks only.Properties of quarks: charge, baryon number and strangeness.Combinations of quarks and antiquarks required for baryons (proton and neutron only), antibaryons (antiproton and antineutron only) and mesons (pion and kaon) only.Change of quark character in β-and β+ decay.


Application of the conservation laws for charge, baryon number, lepton number and strangeness to particle interactions. The necessary data will be provided in questions for particles outside those specified.

Particles and Radiation

Constituents of the Atom

Basic Structure of the Atom The structure of the atom was unknown until the early 20 th century:

The nucleus consists of protons and neutrons at the center of the atom.Protons are (+) charged while neutrons are neutral. Both have similar massesElectrons are (-) charged, 1/1800 the mass of neutrons/protons, and in motion around the nucleus.

The Nuclear AtomRutherford thought (Helium nuclei) particles would be the ideal particle to probe the atom.

He developed his famous gold foil experiment to investigate the inner structure of the atom. This classic diffraction experiment was conducted in 1911 by Hans Geiger and Ernest Marsden at the suggestion of Ernest Rutherford.

particles were shot at a thin gold foil. A zinc sulfide detection screen surrounding the foil would fluorescence whenever radiation struck the screen. The gold foil had to be as thin as possible to avoid multiple scatterings.Geiger and Marsden expected to find that most of the alpha particles travel straight through the foil with little deviation, with the remainder being deviated by a percent or two. This thinking was based on the plum pudding model.

What they found, to great surprise, was that most of the particles passed right through the foil, implying the atom is mostly empty space.A few particles were wildly deflected, implying a large concentration of (+) charge in the center of the atom.Rutherford’s model of the atom included a dense, positively charged nucleus containing protons.Electrons were thought to orbit the nucleus like planets

orbit the sun.

The NeutronIn 1932, Chadwick used particles to strike Be metal. A very penetrating type of radiation was formed.This type of radiation had no charge and had a similar mass to a proton. It was called the neutron.By the early 1900s, the atomic model consisted of neutrons and protons in the nucleus.


Nucleon number and proton number.

Nucleon number (A) (mass number) is the number of protons plus the number of neutrons in the nucleus i.e. the total number of nucleons.Proton number (Z) (atomic number) is the number of protons in the nucleus.

In general a nucleus X is represented by A

X Z

Alpha particle: 4 2+ Proton: 1 Electron: 0 Neutron: 1 He H e n 2 1 -1 0

Isotopes

Two atoms may have the same number of protons but different numbers of neutrons i.e. they have the same proton number but different nucleon number. Each atom is said to be an isotope of the other. They are chemically indistinguishable because they have the same number of electrons and occupy the same place in the periodic table. Most elements are isotopic mixtures.Hydrogen has three forms:

Hydrogen 1 Deuterium 2 Tritium 3 H H H

1 1 1 Ordinary hydrogen contains 99.99% of the Hydrogen – 1 atoms. Water made from deuterium is called heavy water.

Stable and unstable nuclei.

Chemical Properties of an atom are governed by the number of protons in the nucleus (proton number Z)Stability depends on both the number of protons and neutrons (nucleon number A)The term nuclide is used to specify an atom with a particular proton-neutron combination. 6 7 Li and Li are isotopes and nuclides3 3

9 10 Be and B are nuclides (they have the same number of neutrons but a different number of protons4 5 Stable nuclides

The lightest nuclides have almost equal numbers of protons and neutrons. The heavier nuclides require more neutrons than protons, the heaviest about 50% more. Most nuclides have both an even number of protons and neutrons. This implies that 2p+ and 2n0 i.e. an

alpha particle, form a particularly stable combination – oxygen, silicon & iron form over ¾ of the earth’s crustUnstable nuclides

Disintegrations tend to produce new nuclides near the stability line and continue until a stable nuclide is formed.

A nuclide above the line decays so as to give an increase on proton number i.e. beta emission (neutron changes to a proton and electron)

A nuclide below the line disintegrates so that its proton number decreases. In heavy nuclides this occurs by alpha emission.


Number of neutrons against number of protons

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Protons

Neut

rons

Stability Line Actual atoms

Theoretical atomsWith p+ = n0

The balancing of nuclear equations.

Alpha ( ) Radiation

Most emitters are heavy nuclei – proton number greater than 82. It is believed that an particle is created some time before its emission in the nucleus. The decay of a parent nuclide into a daughter nuclide by emission:A A - 4 4 2+ X Y + He + QZ Z - 2 2 Unstable Recoiling High velocityparent daughter particleQ is the energy released in the decay. The nucleus loses 4 nucleons. A and Z are balanced across the equation – charge and nucleon number are conserved. Each decay results in a precise quantity of energy (Q), which is specific to each isotope. Q appears as Kinetic energy of the daughter nucleus and the emitted particle. The particle carries most of the kinetic energy.

A typical emitter is thorium-228 which decays to radium-224

228 224 4 Th Ra + He + Q90 88 2

Beta ( ) Radiation

Neutron rich nuclei decay by - emission. A - particle is a high speed electron emitted from the nucleus. Negative sign is used to distinguish it from the + particle, which is a positron (antiparticle to the electron) emitted by an unstable, proton rich nucleus.

A - particle is produced when a neutron in the parent nucleus decays. Neutrons are normally stable when contained in the nucleus but can decay when the nucleus has too much energy usually due to an excess of neutrons.A Neutron decays into a proton by emitting a - particle. The nucleus changes to a different element with the same nucleon number, but with the proton number increased by 1

1 1 0 0 n p + e + + Q


0 1 -1 0 - emitted with antineutrino

continuous range of energies

A - particle is created in the nucleus at the instant of decay, when it is ejected at extremely high velocities, approaching that of light. No overall change in nucleon mass but proton number increases by 1. Charge and mass number are conserved.

- emission is accompanied by the simultaneous emission of an antineutrino – virtually massless, highly penetrating particle which is very difficult to detect. Each decay results in the release of a precise quantity of energy Q which is specific to each isotope. The total energy released in decay is shared between the daughter nucleus, the - particle and the antineutrino. The - particles are observed to have a very wide range of energies from almost zero up to nearly the total Q value of the decay.

Al is a typical - particle emitter:

29 29 0 0 Al Si + e + + Q13 14 -1 0

Gamma ( ) Radiation

and decay often produce a daughter nuclide which is in an unstable, excited state. This can decay further by emitting a photon of electromagnetic radiation of very high frequency. This is a gamma ray. It causes no change in the proton and nucleon numbers of the parent nuclide.

Overall effect of ray emission is to reduce the energy of the nucleus. The nucleus remains unaltered physically apart from having less energy. radiation does not consist of particles of matter as it is electromagnetic radiation of very short wavelength ( < 1 X 10-11 m ) and very high energy. radiation is indistinguishable from X-rays or cosmic rays of the same wavelength – has a separate name because it is of a different origin. It produces very little ionisation therefore it is very penetrating. In all cases of radioactive decay, the energy released in the decay comes from the direct conversion of a quantity of matter into energy. Such a large amount of energy is released that there is a measurable change in the mass of the particles involved.

Particles, antiparticles and photons

Antiparticles

For every type of matter particle we've found, there also exists a corresponding antimatter particle, or antiparticle. Antiparticles look and behave just like their corresponding matter particles, except they have opposite charges. For instance, a proton is electrically positive whereas an antiproton is electrically negative. Gravity affects matter and antimatter the same way because gravity is not a charged property and a matter particle has the same mass as its antiparticle. When a matter particle and antimatter particle meet, they annihilate into pure energy! On the left (in the previous picture) electrons and positrons are produced from photons. They move in opposite directions in a magnetic field because of their opposite charge.

Neutrinos have no electrical charge they almost never interact with any other particles. Most neutrinos pass right through the earth without ever interacting with a single atom of it.

Neutrinos are produced in a variety of interactions, especially in particle decays. In fact, it was through a careful study of radioactive decays that physicists hypothesized the neutrino's existence.


For example: (1) In a radioactive nucleus, a neutron at rest (zero momentum) decays, releasing a proton and an electron.

(2) Because of the law of conservation of momentum, the resulting products of the decay must have a total momentum of zero, which the observed proton and electron clearly do not.

(3) Therefore, we need to infer the presence of another particle with appropriate momentum to balance the event.

(4) We hypothesize that an antineutrino was released; experiments have confirmed that this is indeed what happens.

Because neutrinos were produced in great abundance in the early universe and rarely interact with matter, there are a lot of them in the Universe. Their tiny mass but huge numbers may contribute to total mass of the universe

and affect its expansion.

Fundamental Forces (Interactions)

The universe, exists because the fundamental particles interact. These interactions include attractive and repulsive forces, decay, and annihilation.

There are four fundamental interactions between particles, and all forces in the world can be attributed to these four interactions.

What's the difference between a force and an interaction? A force is the effect on a particle due to the presence of other particles. The interactions of a particle include all the forces that affect it, but also include decays and annihilations that the particle might go through.We call the particles which carry the interactions force carrier particles.

At a fundamental level, a force isn't just something that happens to particles. It is a thing which is passed between two particles.

You can think about forces as being analogous to the following situation: Two people are standing on an ice pond. One person moves their arm and is pushed backwards; a moment later the other person grabs at an invisible object and is driven backwards. Even though you cannot see a basketball, you can assume that one person threw a basketball to the other person because you see its effect on the people.

FORCE FORCE CARRIER RELATIVE STRENGTH RANGE


PARTICLE (Bosons)

STRONG GLUONS 1 10-15 m

ELECTROMAGNETIC PHOTON 10-2 infinite

GRAVITY GRAVITON 10-39 infinite

WEAK W+, W- , Z 10-5 10-18 m

Some facts about fundamental interaction: Friction is caused by residual electromagnetic

interactions between the atoms of the two materials. Nuclear bonding is caused by residual strong

interactions between the various parts of the nucleus. The planets orbit because of the gravity that attracts

them to the sun! Even though gravity is a relatively weak force, it still has very important effects on the world.

Weak and Gravity interactions act on neutrinos. Weak (W+, W-, and Z) interactions have heavy carriers? All 4 interactions act on the protons in our bodies. Gluons are force carriers cannot be isolated. Gravitons (Gluons have been observed indirectly.) are

force carriers which have not been observed.

Grand Unified Theory (GUT)

Today, one of the major goals of particle physics is to unify the various fundamental forces in a Grand Unified Theory which could offer a more elegant understanding of the organization of the universe. Such a simplification of the Standard Model might well help to answer our questions and point toward future areas of study.

Physicists hope that a Grand Unified Theory will unify the strong, weak, and electromagnetic interactions. There have been several proposed Unified Theories, but we need data to pick which, if any, of these theories describes nature.

If a Grand Unification of all the interactions is possible, then all the interactions we observe are all different aspects of the same, unified interaction. However, how can this be the case if strong and weak and electromagnetic interactions are so different in strength and effect? Strangely enough, current data and theory suggests that these varied forces merge into one force when the particles being affected are at a high enough energy.

Current work on GUT suggests the existence of another force-carrier particle that causes the proton to decay. Such decays are extremely rare; a proton's lifetime is more than 1032 years.

Physicists believe that as you go back in time, and the universe was hotter, that the four forces separated out from one single, simple, force. There is experimental confirmation that the electromagnetic and weak nuclear force were once a single force we call the electroweak force.Grand Unified Theory (GUT) and Theory of Everything (TOE)


TOE

…………………………………………………………………………………………. Current theory

…………………………………………………………………………….. Current knowledge

Classification of particles

Ordinary matter is made up of protons, neutrons and electrons. However in high-energy collisions, many other particles can be created. Most are very short-lived. Matter particles can be divided into two main groups: HADRONS and LEPTONS.

LEPTONSThese particles exists on their own

QUARKSThese particles only exist bound together

Charge = -1 Charge = 0 Charge = + ⅔ Charge = - ⅓Constituents of ordinary matter

1st Family

ELECTRON(e-)Responsible for electricity and chemical reactions.

ELECTRON NEUTRINO (e)Rarely interacts with other matter.

UP (u) DOWN (d)Protons are made up of two up quarks and one down quark.Neutrons are made up of one up quark and two down quarks.

These particles existed in the early moments after the Big Bang. Now they are only found in cosmic rays and at particle accelerators

2nd Family

MUON (-) A heavier relative of the electron.

MUON NEUTRINO ()A relative of e

CHARM (c)A heavier relative of the up quark.

STRANGE (s)A heavier relative of the down quark

3rd Family

TAU ( -)A heavier relative of the electron and muon.

TAU NEUTRINO () TOP (t)The heaviest quark

BOTTOM (b)A heavier relative of the down and strange quarks.


MATTER

LEPTONS HADRONS(Made from Quarks)

GAUGE BOSONS(Force carriers)

Leptons

Leptons are fundamental particles and cannot be broken down into smaller particles. Lepton is a Greek word meaning “small coin”. They do not interact via strong forces but interact with the via the other three fundamental forces. There are 6 different “types” of Leptons together with their Lepton number:

Electron (e-) Positron (e+) Electron neutrino (e) Electron antineutrino (e)

Muon (-) Antimuon (+) Muon neutrino () Muon antineutrino ()

Tau ( -) Antitau ( +) Tau neutrino () Tau antineutrino ()

Lepton Number:

Each Lepton is designated a Lepton Number (L) of +1 and the antileptons have a lepton number of -1.

Conservation of Lepton Number

An important conservation law is the conservation of lepton number. This rule is a little more complicated than the conservation of baryon number below because there is a separate requirement for each of the three sets of leptons, the electron, muon and tau and their associated neutrinos.

The first significant example was found in the decay of the neutron. When the decay of the neutron into a proton and an electron was observed, it did not fit the pattern of two-particle decay. That is, the electron emitted does not have a definite energy as is required by conservation of energy and momentum for two-body decay. This implied the emission of a third particle, which we now identify as the electron antineutrino.

The assignment of a lepton number of 1 to the electron and -1 to the electron antineutrino keeps the lepton number equal to zero on both sides of the second reaction above, while the first reaction does not conserve lepton number.

Hadrons


ELECTRONS (e)

NEUTRINOS ()

BARYONS(3 Quarks)

MESONS(2 Quarks)

PHOTONS ()

PROTONS (p)

NEUTRONS(n)

PION ()

KAON (K)MUON (-)

TAU (-)

GLUONS

VECTOR BOSONS

(W, Z)

GRAVITON

Hadrons are not fundamental particles and consist of quarks. The word Hadron comes from the Greek word meaning “bulky”. Hadrons interact via all four fundamental forces. Although individual quarks have fractional electrical charges, they combine such that hadrons have a net integer electric charge.

Quarks have been discovered by deep inelastic scattering of electrons. The idea is to accelerate electrons to very high energies, and then allow them to interact with a stationary proton, and investigate what happens. At high energies, the wavelengths associated with the electrons are much smaller than the size of a proton. Hence the electrons can probe distances that are small compared with the proton - that is, DEEP within the proton. However, the high energies tend to disrupt the proton, so that it produces several new particles (hadrons). This means the scattering is INELASTIC because the target has been changed in the process.

Baryons are any hadron which is made of three quarks (see next section). Protons are baryons because they are made of two up quarks and one down quark (uud). So are neutrons (udd). Mesons contain one quark and one antiquark. One example of a meson is a pion (+), which is made of an up quark and a down anitiquark. The antiparticle of a meson just has its quark and antiquark switched, so an antipion ( -) is made up a down quark and an up antiquark.

Because a meson consists of a particle and an antiparticle, it is very unstable. The kaon (K+), which is made of an up quark and a strange anitiquark lives much longer than most mesons, which is why it was called "strange" and gave this name to the strange quark, one of its components. Kaons are assigned a strangeness number of S = 1. There is partial conservation of strangeness – conserved during strong force interactions, but not weak force interactions.

Conservation of Baryon Number

Nature has specific rules for particle interactions and decays, and these rules have been summarized in terms of conservation laws. One of the most important of these is the conservation of baryon number. Each of the baryons is assigned a baryon number B=1. This can be considered to be equivalent to assigning each quark a baryon number of 1/3. This implies that the mesons, with one quark and one antiquark, have a baryon number B=0. No known decay process or interaction in nature changes the net baryon number.

The neutron and all heavier baryons decay directly to protons or eventually form protons, the proton being the least massive baryon. This implies that the proton has nowhere to go without violating the conservation of baryon number, so if the conservation of baryon number holds exactly, the proton is completely stable against decay.

An extremely small part of the mass of a hadron is due to the quarks in it.

Gauge Bosons

These are the exchange particles. An Exchange particle is a virtual particle, which may exists for only a short time, and is the mediator of a force.

When two charged particles interact, they do so by exchanging a virtual photon. The exchange is impossible to detect and hence the term virtual is used to describe the photon involved.

FEYNMAN DIAGRAM The diagram below represents two electrons approaching then repelling each other

e- e-

a photontime


e- e-

space - decay -

+ decay +

p (e-) n (e+)

e e

n W- boson p W+ boson

n p + e- + e p n + e+ + e

Quarks and antiquarks

There are six quarks, but physicists usually talk about them in terms of three pairs: up/down, charm/strange, and top/bottom. (Also, for each of these quarks, there is a corresponding antiquark.) Quarks have the unusual characteristic of having a fractional electric charge, unlike the proton and electron, which have integer charges of +1 and -1 respectively.

There are three quantum numbers associated with quarks: Charge, expressed as the fraction of the electronic charge. 1/3 e

= 5.33 ´ 10-20 C Baryon number Strangeness number, when there are strange quarks. Each antiquark has equal and opposite values of charge, baryon

number and strangeness.

Quark Charge (Q) Baryon number (B) Down (d) -1/3 1/3 Up (u) +2/3 1/3 Antidown (<d>) +1/3 -1/3 Antiup (<u>) -2/3 -1/3 Baryons are made of three quarks; antibaryons of three antiquarks. Mesons are made up of one quark and one antiquark. Gluons bind quarks together; they are subject to the strong

interaction.

Electromagnetic Radiation and Quantum Phenomena

Syllabus extract:

The photoelectric effectWork function , photoelectric equation hf = + Ek

the stopping potential experiment is not required.

Collisions of electrons with atomsThe electron volt.Ionisation and excitation;understanding of ionization and excitation in the fluorescent tube.

Energy levels and photon emission


Line spectra (e.g. of atomic hydrogen) as evidence of transitions between discrete energy levels in atoms.hf = E1 - E2

Wave-particle dualityCandidates should know that electron diffraction suggests the wave nature of particles and the photoelectric effect suggests the particle nature of electromagnetic waves; details of particular methods of particle diffraction are not expected.de Broglie wavelength: λ = h/mv, where mv is the momentum.

The photoelectric effect

Light as a Particle?

Historically there had been a lot of controversy about the wave nature of light, as proposed by the Dutch physicist Hans Huygens, against the corpuscular model as proposed by the headstrong Isaac Newton. The concept of wave-particle duality was the start of modern physics in the middle to late Nineteenth Century.

We know that light shows wave properties such as: · Reflection · Refraction · Diffraction · Polarisation However it can also be shown to have particulate properties as well. Consider this model:

If we spray just a short burst, we get just a few spots on the screen:

The longer we spray, the more spots appear until the whole area is covered in paint:

When using a spray can, we don’t notice any diffraction effects as the particles pass through the stencil. Hardly surprising as the paint droplets are particles, not waves. Now, if we expose a piece of photographic paper to a short burst of light we will see:


The intensity of the image on a photographic plate increases the longer the paper is exposed for. That intensity is determined by the number of silver grains deposited. We see that the pattern of silver grains deposited is random. It seems that the light that deposited the grains was actually made of particles.

The debate raged on until the discovery in the late nineteenth century with the discovery of the photoelectric effect. The Photoelectric Effect.

The concept of wave-particle duality was the start of modern physics in the middle to late Nineteenth Century. We can show the photoelectric effect with apparatus like this:

1. We charge the electroscope with a negative charge.2. We expose the reactive metal to light of a long wavelength, e.g. red. 3. We observe that there is no effect, however bright the light. 4. We then expose the metal to short wavelength light, e.g. UV. 5. This time we see that the gold leaf drops down, showing that the electroscope is losing charge. 6. It does not matter how bright or dim the UV light is. 7. No effect was observed when the electroscope was positively charged.

The results were: Metal X-rays Ultra-Violet Blue Light Red Light Magnesium P O O OZinc P P O OSodium P P P OCaesium P P P P

This led to the conclusion that:


Electrons were being knocked off. Reactive metals have outer shell electrons that can be removed easily. Red light would not show this effect however bright it was. So the amplitude of the light wave was not

important. Red light only worked for caesium, which is a very reactive metal. There was a threshold frequency at which this phenomenon started to occur. Light waves with a

frequency higher than this (shorter wavelength) always showed the effect, whatever the brightness; light waves with a lower frequency never showed it.

The more reactive the metal, the lower was the threshold frequency. This indicated a particle behaviour to light.

These findings led to the notion of light being tiny little packets of wave energy called photons.

Further work by Max Planck in 1900 produced the Photon Model of Electromagnetic Radiation. We can sum this up in the following points:

Light and other electromagnetic radiation is emitted in bursts of energy. We say that it is quantised. The packets of energy, photons, travel in straight lines. When an atom emits a photon its energy changes by an amount equal to the photon energy. The energy changes are discrete amounts or quanta. The frequency of the light and the energy are related by a simple equation:

[E – energy in J; h – Planck’s Constant; f – frequency of the radiation in Hz]

The constant h is Planck’s Constant with the value 6.6 ´ 10–34 Js (joule seconds, NOT joules per second).

We can combine the equation above with the wave equation: E = hf and c = fl

The joule is the SI unit for energy. However atomic physicists find the joule far too big and clumsy. (You would not measure the width of your desk in kilometres.) So they use a unit called the electron volt (eV). The electron volt is the amount of energy used when a charge of electronic charge passes through a potential difference of 1 volt. The charge on an electron is 1.6 × 10-19 C, so 1 eV = 1.6 × 10-19 J.

Collisions of electrons with atoms

Albert Einstein developed the theory further to study how atoms interacted with photons. He produced the notion of quantum physics, in which electromagnetic radiation has a particulate nature. The essential points of quantum theory are:

All electromagnetic radiation is emitted in tiny bursts of energy called photons Photons travel in one direction only and in a straight line When an atom emits a photon its energy changes by the energy of the photon. Energy contained in a photon is given by E = hf.

Details of this experiment are NOT needed for the AQA Module 1 exam. However to understand the results, we need to be aware of what goes on in the experiment:

The photocathode is given a positive voltage, and the photoanode a negative voltage. This means that photoelectrons (electrons released by interaction with a photon. One photon releases one

electron) are repelled from the anode.


E = hf

E = hc l

If the electrons have lots of kinetic energy, they can overcome the repulsive force.

We turn up the reverse voltage until the electrons with the most kinetic energy are just repelled. The voltage is called the stopping voltage. We can see what is happening in this diagram

The totally unexpected result is that the maximum kinetic energy of the photoelectrons is exactly the same regardless of the intensity of the illumination. However dim or bright the light, the maximum kinetic energy is the same.

How can we explain these observations? Look at the diagram

Although the diagram is a simplification as to what really happens, we can see that the photoelectrons are released with a range of kinetic energies. The lowest kinetic energy is where the electron just manages to crawl out. It will be hauled back pretty quickly by the electrostatic forces.

We can summarise these findings in three rules, the laws of photoelectric emission.

1. The number of electrons emitted per second depends on the intensity of the radiation. 2. The photoelectrons have a range of energy, from zero to a maximum value. The maximum value is determined by the frequency of the radiation, not the intensity. 3. A minimum value for the frequency is needed, the threshold frequency. The maximum kinetic energy has the same value in eV as the stopping voltage. This stands to reason. We know that energy = charge × voltage, and that the electron carries a single electronic charge (1e = 1.6 × 10 -19 C). So if that charge moves through a potential difference, that amount of work is done.


The graph shows how the energy of the photoelectrons depends on the frequency (colour) of the light:

There has to be a threshold frequency below which no photoelectrons are emitted, regardless of brightness. Therefore radio waves, however strong, will NEVER affect

A photon with a long wavelength carries less energy than one with a short wavelength. So if the wavelength of a photon is longer than the wavelength suggested by the threshold frequency, photoelectrons will not be ejected.

Einstein’s Photoelectric Equation

When photoelectrons are removed from a metal surface, a certain amount of work has to be done in removing them. Therefore the photoelectrons will lose some of their kinetic energy in order to escape the attractive field of the positively charged nuclei. The work required to remove the photoelectron is called the work function. It is given the physics symbol Φ (Phi - a Greek capital letter ‘Ph’) and is measured in joules, or electron volts.

The energy received from a photon is split into: The work necessary to separate the electron from the metal (the work function) The kinetic energy.

Energy of Photon = work done to remove electron + kinetic energy of the electron

We must note the following:

Ek is the maximum kinetic energy (the charge × stopping voltage), i.e. the kinetic energy of the fastest electrons. We are not interested in slower electrons.

The maximum kinetic energy is dependent only on the frequency, NOT the intensity. A more intense beam produces more photons per second, but each photon has the same energy.

We can work out the work function of any metal by plotting the maximum energy against the frequency


E = Φ + Ek

E = Φ + ½mv2

We find that the gradient of this graph is constant, regardless of the metal. The equation of the graph is:

Ek = hf - Φ So the gradient is Planck’s constant, h. Also

Energy Levels in Atoms

Atoms can interact with photons of lower energy than is required to remove electrons from them. The photons we looked at in the photoelectric effect could remove the electrons from very reactive metals like caesium. Photons can interact with other atoms to give them extra energy, which makes them excited.

When we heat a gas or pass an electric current through it we can make it glow. We have ionised the gas. If we look at the glowing gas through a spectrometer, we see the spectrum of the gas which is distinctive for that gas.

There are three principal types of spectra which appear when the light from an object is broken up into its component wavelengths or "dispersed":

a continuous spectrum or continuum; the emission of a thermal spectrum is one type of continuum.

an absorption spectrum or sometimes an absorption-line spectrum.

an emission spectrum or emission-line spectrum.

An absorption spectrum is produced when a continuum passes through "cooler" gas. Photons of the appropriate energies are absorbed by the atoms in the gas. Although the photons may be re-emitted, they are effectively removed from the beam of light, resulting in a dark or absorption feature. The atmospheres of stars act as a cooler blanket around the hotter interior of a star so that typical stellar spectra are absorption spectra.


Φ = hf0 = hc λ

hf = Φ + Ek

http://csep10.phys.utk.edu/astr162/lect/light/absorption.html

Unlike the spectrum of the Sun, in which we see all the colours of the rainbow, we only see certain colours, while others are absent. We call this kind of spectrum a line emission spectrum. The colours are discrete wavelengths

When a gas is ionised, one or more outer electrons are ripped off. The molecule has become positive. It will recombine with an electron and lose energy, giving that energy in the form of a photon. Other atoms may not have been ionised, but are still in a very excited state. The atoms have interacted with the photon and the electrons have moved to a higher energy level.

About a microsecond later, the electrons lose their energy as a photon and return to the stable state, called the ground state. The important thing to remember is that electrons can only exist at permitted energy levels. It’s like a person standing on a ladder; he can exist at one rung up, two rungs, etc., but NOT at a height of 1.5 rungs.As we consider energy levels in atoms, we will look at hydrogen which fits this model well. (Hydrogen has one electron.) More complex atoms with several electrons do not.

If we look at a spectrum of hydrogen, we find lines at several discrete wavelengths.

Each line represents the energy of a photon as the electron makes a transition from a higher energy level to a lower. This we can show in a diagram below: The electron does a job of work in releasing a photon; it has lost potential energy. Therefore we start at the highest level which we give a value of zero. Therefore the electron falls from the zero point to the –3.41 eV level. The more negative the level, the lower the energy level.

The highest energy level is where ionisation occurs. The lowest level is the ground state.

Electrons can make transitions from any energy level to any other:

These transitions give us photons in the visible spectrum. In fact, the ground state is at –13.6 eV. This is the ionisation energy of hydrogen, the energy required to strip an electron from the atom.

We need to be aware of the following points:

The lowest level (-13.6 eV) is the ground state. This is the normal configuration of the atom. Energy must be put in to raise the electron to other levels.

The highest level is the ionisation energy.


Electron energy levels in Hydrogen

Energy levels are not evenly spaced.

We can quantify this in an equation. If an electron is at an excited level (E1) and makes a transition to a lower level (E2), then the energy of the photon given out can be worked out with the equation:

E = E1 – E2 Since E = hf, we can rewrite this as: hf = E1 – E2

Fluorescent lamps

The central element in a fluorescent lamp is a sealed glass tube. The tube contains a small bit of mercury and an inert gas, typically argon, kept under very low pressure. The tube also contains a phosphor powder, coated along the inside of the glass. The tube has two electrodes, one at each end, which are wired to an electrical circuit. The electrical circuit, which we'll examine later, is hooked up to an alternating current (AC) supply

When you turn the lamp on, the current flows through the electrical circuit to the electrodes. There is a considerable voltage across the electrodes, so electrons will migrate through the gas from one end of the tube to the other. This energy changes some of the mercury in the tube from a liquid to a gas. As electrons and charged atoms move through the tube, some of them will collide with the gaseous mercury atoms. These collisions excite the atoms,


bumping electrons up to higher energy levels. When the electrons return to their original energy level, they release light photons. The electrons in mercury atoms are arranged in such a way that they mostly release light photons in the ultraviolet wavelength range. Our eyes don't register ultraviolet photons, so this sort of light needs to be converted into visible light to illuminate the lamp. Phosphors are substances that give off light when they are exposed to light. When a photon hits a phosphor atom, one of the phosphor's electrons jumps to a higher energy level and the atom heats up. When the electron falls back to its normal level, it releases energy in the form of another photon. This photon has less energy than the original photon, because some energy was lost as heat. In a fluorescent lamp, the emitted light is in the visible spectrum -- the phosphor gives off white light we can see. Manufacturers can vary the colour of the light by using different combinations of phosphors.

Wave Behaviour of Particles

The Belgian physicist de Broglie reasoned that if waves have a particulate properties, it was reasonable to suppose that particles had wave properties. He devised the relationship, which states that particles have wave properties. It is the logical extension of the particulate nature of electromagnetic wave phenomena. He combined the following equations: Energy of photons: E = hf Einstein’s mass equivalence: E = mc2 Therefore hf = mc2

Now f = c/λSo mc = h/λThe term mc is mass X velocity, which is momentum. We give momentum the symbol pWe can rewrite the equation as

λ = h/p or λ = h/mv Therefore every particle with a momentum has an associated de Broglie wavelength, even something as absurd as a car travelling at 20 m/s.

Electrons can be shown to have wave properties by the simple use of an electron diffraction tube. A slice of carbon is placed in a beam of electrons so that the electrons diffract.

We need to note a couple of points: l is the de Broglie wavelength

The wave properties of electrons have led to the development of the electron microscope, which allows magnifications much bigger than was ever possible with the light microscope. A good light microscope can magnify


up to 1000 times. The electron microscope can magnify up to about 1 million times, and can reveal the existence of individual atoms. The electron beams are focused by magnets just like the lenses on a microscope.

Current Electricity

Syllabus extract:

Charge, current and potential differenceElectric current as the rate of flow of charge;potential difference as work done per unit charge.I =ΔQ/Δt, and V = W/Q

Resistance is defined by R = V/I

Current / voltage characteristicsFor an ohmic conductor, a semiconductor diode and a filament lamp;Candidates should have experience of the use of a current sensor and a voltage sensor with a data logger to capture data from which to determine V – I curves.Ohm’s law as a special case where I V.

Circuits (part)Energy E = I V t, P = IV, P = I2R; application, e.g. Understanding of high current requirement for a starter motor in a motor car.

Resistivityρ = RA/LDescription of the qualitative effect of temperature on the resistance of metal conductors and thermistors. Applications (e.g. temperature sensors)Superconductivity as a property of certain materials which have zero resistivity at and below a critical temperature which depends on the material. Applications (e.g. very strong electromagnets, power cables).

Circuits (part)Resistors in series: RT = R1 + R2 + R3 + …Resistors in parallel: 1/RT = 1/R1 + 1/R2 + 1/R3 + …Conservation of charge and energy in simple d.c. circuits.The relationships between currents, voltages and resistances in series and parallel circuits, including cells in series and identical cells in parallel.Questions will not be set which require the use of simultaneous equations to calculate currents or potential differences.

Potential dividerThe potential divider used to supply variable pd e.g. application as an audio volume control.Examples should include the use of variable resistors, thermistors and LDRs.The use of the potentiometer as a measuring instrument is not required.

Electromotive force and internal resistance = E/Q = I(R + r)Applications; e.g. low internal resistance for a car battery.

Alternating currents


Sinusoidal voltages and currents only; root mean square, peak and peak-to-peak values for sinusoidal waveforms only.Irms = Io/√2; Vrms = Vo/√2Application to calculation of mains electricity peak and peak-to-peak voltage values.

OscilloscopeUse of an oscilloscope as a d.c. and a.c. voltmeter, to measure time intervals and frequencies and to display a.c. waveforms. No details of the structure of the instrument is required but familiarity with the operation of the controls is expected.

Current and ChargeThe base electrical quantity is current, the flow of charge. All other electrical quantities are derived from it. Current is measured in ampères, or amps (A). Charge is measured in coulombs (C), which is defined as:

1 coulomb is the quantity of charge carried past a given point if a steady current of 1 amp flows for 1 second.

1 electron carries a charge of 1.6 ´ 10-19 C. 1 coulomb is equivalent to 6.2 ´1018 electrons. Charge and current are linked by a simple formula:

Charge (C) = current (A) X time (s) There are some important multipliers for current:

1 microamp (1µA) = 1 X 10 -6 A 1 milliamp (mA) = 1 X 10 -3 A

Cells and Batteries

Chemical reactions inside a cell help to create a small POTENTIAL DIFFERENCE between the terminals and this makes the electrons flow along any conducting path that connects them.

A current (flow of charge) will flow through an electrical component (or device) only if there is a voltage or potential difference (p.d.) across its ends. The bigger the potential difference across a component, the bigger the current that flows through it.

The conducting path through the bulbs, wire and battery is called a circuit.

Energy from a Cell

The cell is a source of Chemical potential energy. It does work on electrons and the electrons gain Electrical potential energy (we call it just potential energy).

P.D. (Potential difference or Voltage) across battery terminals. The p.d. or voltage across the terminals of the cell indicates the potential energy given to each coulomb (approximately 1018 electrons) of charge.

If 1 Joule of energy is given to 1 Coulomb of electric charge by the battery then we say that the p.d. across the cell is 1 Volt.

When the charges move through the wire they do not lose any of the potential energy they are carrying. When they pass through something that resists their flow, they will have to do work.

Potential Difference


Q = It I = Δ Q Δt

V = w Q

Potential Difference is defined as energy per unit charge. The unit of potential difference is the volt (V). Using the definition, we can define the volt as Joules per Coulomb. 1 V = 1 JC-1 Potential difference is often referred to as voltage.

Resistance

Resistance is defined by the following equation:

Resistance = p.d. across conductor Current through conductor

A conductor has a resistance of 1Ω if a current of 1A flows through it when a p.d. of 1V is applied across its ends.

Potential difference, current and resistance are related as shown:

The current through a resistor (at constant temperature) is proportional to the voltage across the resistor.The resistance of a conductor increases

as the temperature of the conductor increases. as the thickness of the conductor decreases as the length of the conductor increases

Energy and Power in Circuits

When energy changes from one form to another in a resistor, the power indicates the rate (how quickly) at which this takes place.

Suppose a current I flows for t seconds in a component. The charge that flowed led to E joules being dissipated in the component.We know that: Q = It , E = QV

So if we substitute Q out of the second equation, we get: E = ItVNow Power = energy timeSo we can write: P = ItV tThe power output of a cell depends on the p.d. across its terminals and the current it supplies.

Power is measured in watts (W). 1 watt = 1 joule per second


potential difference = current x resistance (volt, V) (ampere, A) (ohm, Ω)

V = I R

Power = energy change time taken

Power = potential difference x current(Watts, W) (Volts, V) (Amps, A)

P = VI

The Heating Effect of a Current

We know that: V = IR and P = IV So we can write: P = I x IR

We know that: I = V/R and P = IV So we can write: P = V x V/R

Ohm’s Law

Resistance is the ratio of the voltage to the current, described in the simple equation R = V/I. In a metallic conductor, we find that if we alter the voltage or the current, the other variable changes in such a way that the ratio remains constant.

This is Ohm’s Law, which states: The current in a metallic conductor is directly proportional to the potential difference between its ends provided that the temperature and other physical conditions are the same. A conductor that obeys Ohm’s Law is called an ohmic conductor.

Voltage Current Characteristics

We can easily measure voltage and current, using the data to plot voltage current graphs. We use the following circuit:

From this circuit we take readings of voltage and current plotting them as a graph called a VI characteristic.

We normally put the voltage on the y-axis and current on the x-axis. This allows us to determine the resistance from the gradient. This is a voltage current graph for an ohmic conductor:

The straight line shows a constant ratio between voltage and current, for both positive and negative values. So when the voltage is negative, the current is negative, i.e. flowing in the opposite direction. Ohm’s Law is obeyed. We call this an Ohmic conductor.

For a filament lamp we see: The resistance rises as the filament gets hotter, which is shown by the gradient getting steeper.

A thermistor (a heat sensitive resistor) behaves in the opposite way. Its resistance goes down as it gets hotter. This is because the material releases more electrons to be able to conduct.

Although it looks similar to the graph above, notice how the gradient is decreasing, indicating a lower resistance. As the current goes up, the thermistor gets hotter. As it gets hotter, it allows more current to flow; therefore it gets hotter and so on.

This is called thermal runaway, and is a feature of many semiconductor components. At the extreme the component will glow red-hot, then split apart.


P = I2R

P = V2/R

Diodes are semi-conductor devices that allow electric current to flow one way only. The diode characteristic graph looks like this:

The diode starts to conduct at a voltage of about +0.6 V. We call this forward bias. Then the current rises rapidly for a small rise in voltage. If the current is reversed (reverse bias) almost no current flows until the breakdown voltage is reached. This usually results in destruction of the diode.

Resistivity

The resistance of a wire depends on three factors:

the length; double the length, the resistance doubles. the area; double the area, the resistance halves. the material that the wire is made of.

Resistivity is a property of the material. It is defined as the resistance of a wire of the material of unit area and unit length.The formula for resistivity is:

Remember: 1 mm2 = 1 x 10-6 m2

Series and Parallel Circuits

Series Circuits In a series circuit, the electrons in the current have to pass through all the components, which are arranged in a line. Consider a typical series circuit in which there are three resistors of value R1, R2, and R3. The values may be the same, or different.

The current throughout the circuit is the same

The voltages add up to the battery voltage.

Therefore: VT = V1 + V2 + V3 From Ohm’s Law we know: VT = IRT;

Thus: IRT = IR1 + IR2 + IR3

Therefore:

By adding resistors in series, the total resistance of the circuit increases. If two or more resistors are connected in series, they give a higher resistance than any one of the resistors by itself.


Resistivity ( Ω m ) = Resistance ( Ω ) x Area ( m 2 ) Length ( m )

RT = R1 + R2 + R3

Parallel Resistors Parallel circuits have their components in parallel branches so that an individual electron can go through one of the branches, but not the others. The current splits into the number of branches there are. Look at this circuit:

In this case, the current will split into three.

The voltage across each branch is the same The currents in each branch add up to the total current.

From this we can write: IT = I1 + I2 + I3 From Ohm’s Law, IT = V/RT , we can write:

V = V + V + V RT R1 R2 R3

By adding resistors in parallel, the total resistance of the circuit decreases. If two or more resistors are connected in parallel, they give a lower resistance than any one of the resistors by itself.

Kirchhoff's Laws

These two simple laws were drawn up in the Nineteenth Century by Gustav Robert Kirchhoff. They explain all observations we see in electric circuits. We can explain everything we have looked at in series and parallel circuits in terms of the two laws. They can also be used to explain more difficult circuits which cannot be explained in terms of simple series and parallel circuits.

Kirchhoff I : The algebraic sum of currents at a junction is zero.This states that the total current flowing into a point is equal to the current flowing out of that point.

In other words, the charge does not leak out or accumulate at that point. Charge that flows away must be replaced. It is conserved.

From this diagram we can easily see that I3 = I1 + I2. Mathematically we can write this as: I1 + I2 + (-I3) = 0

Or Σ I = 0

Kirchhoff II: Around a closed circuit loop, the algebraic sum of the e.m.f.s is equal to the algebraic sum of the p.d.s. The potential differences around a circuit add up to zero.

Provided the charge returns to the same place as it started, the gains and losses are equal, no matter what route is taken by the charge. The battery in this circuit has an emf (electromotive force or open terminal voltage) of ε. The curly ε is the battery voltage.

EMF and Internal Resistance

Batteries (or more strictly speaking cells) convert chemical energy into electrical energy. Generators turn kinetic energy into electrical energy. In doing so, they keep the negative terminal with an excess of electrons and the


1 = 1 + 1 + 1 RT R1 R2 R3

positive terminal with a deficiency of electrons. A battery does a job of work in pumping the electrons around the circuit. Positive charges do not move.

The early day physicists got it wrong when they said that electric current flows from positive to negative. They didn't know about electrons. When the mistake was discovered, they decided to stick to the positive to negative, so all conventional current flows from positive to negative.

A battery is said to produce Emf (electromotive force) which is defined as the energy converted into electrical energy when unit charge passes through the source. (ε) It represents the total energy that can be supplied to a circuit. EMF is a voltage.

A good working definition of emf is the open circuit terminal voltage of the battery, i.e. when there is no current flowing. Although the old text books had a complex method for measuring emf using a metre bridge, nowadays a digital multimeter will give you a good reading as it takes a very small current indeed.

The energy supplied to a circuit by a battery is given by:

Where W is the energy in J Q is the charge in C ε, curly E is the physics symbol for emf.

No circuit at all is 100 % efficient. Some energy is dissipated in the wires, or even in the battery itself.

Internal Resistance All batteries and generators dissipate heat internally when giving out a current, due to internal resistance. A perfect battery has no internal resistance, but unfortunately there is no such thing as a perfect battery. Nickel-Cadmium and Lead-Acid batteries have very low internal resistance, and we can regard these as almost perfect. These batteries can provide very high currents.

Suppose we connect a cell to a high resistance voltmeter. (A perfect voltmeter has infinite resistance. A digital multimeter has a very high resistance, so needs a tiny current; it is almost perfect. An ordinary moving coil voltmeter has a relatively low resistance, so it takes a small but appreciable current.)

In this circuit the voltmeter reads (very nearly) the emf.

Suppose we now add a load. We will assume the wires have negligible resistance.

This time we find that the terminal voltage goes down to V. Since V is less than ε, this tells us that not all of the voltage is being transferred to the outside circuit; some is lost due to the internal resistance which heats the battery up.

Emf = Useful volts + Lost volts

So we can represent the circuit as:

So our cell is now a perfect battery in series with an internal resistor, r. You cannot open up the battery to find the internal resistor; it is part and parcel of the battery.


ε = W Q

ε = Vext + Vlost

We can now treat this as a simple series circuit and we know that the current, I, will be the same throughout the circuit. We also know the voltages in a series circuit add up to the battery voltage.

Emf = voltage across R + voltage across the internal resistance

We also know from Ohm’s Law that V = IR and v = Ir, so we can write:

ε = IR + Ir or ε = I (R + r)

All you have to do is turn the cell with the internal resistance into a perfect battery in series with its internal resistor, and treat it as a simple series circuit.

Alternating Currents

Direct current from a battery moves in one direction only, from positive to negative. In alternating current the direction is changing all the time. The charge carriers are moving forwards and backwards many times a second. In Europe it is 50 Hz (cycles per second); in the USA 60 Hz.

AC and DC are equally good at heating, lighting, or running motors. AC is much more easily distributed than DC. This is because transformers use AC only. So electricity is distributed at very high voltages (275 kV) at relatively low currents. As a result only a small proportion of the transmitted energy is lost as heat in the wires.

The graph below shows the difference between AC and DC. One complete alternation is called a cycle The frequency is the number of cycles per second. Units are Hertz (Hz).

The period is the time taken for one cycle. It is measured in seconds. f = 1/T.

The current follows exactly the same wave form as voltage.

The graph is called a sinusoidal waveform or a sine wave.

These features are shown on the graph:

Root Mean Square Value

The values of voltage and current are constantly changing in AC, unlike in DC in which they are steady. We can measure AC voltages in two ways:


Measure the peak to peak voltage, easily done on a cathode ray oscilloscope (CRO). Measure the root mean square (rms) value, or the effective value.

We use the rms value because its use allows us to do electrical calculations as if they were direct currents.

How Does the Power Vary?

Notice that power varies from a maximum of +2P to a minimum of 0. Therefore the average power is P. We never get a negative power, since that would imply that the component was creating energy.

The Cathode Ray Oscilloscope

The CRO is connected in exactly the same way as a voltmeter, i.e. in parallel with a component. The input resistance is very high and the electron beam acts as a pointer of negligible inertia. It is also robust and not easily damaged by overloading. The CRO can be used as a DC voltmeter. We get a horizontal line or a dot, depending whether the time base is on. If it is used as an AC voltmeter, it will show the sinusoidal waveform

The most important controls that we use are:

The vertical sensitivity or y-gain setting, calibrated in V/cm. The time base, in s/cm.

The CRO is a perfect voltmeter as its input resistance is very high.

Remember:

We measure the voltage on the vertical axis. We can adjust the sensitivity by turning the knob marked y-gain or voltage gain.

The horizontal direction is determined by the time base setting. We can change this by using the time base knob.

As well as analysing the waveform, there are two measurements we can make with the CRO:

We can determine the peak voltage of the AC waveform shown below. We can also read the period, which in turn allows us to work out its frequency.


Irms = I0

√2Vrms = V0

√2

Notice that:

The peak to peak voltage is 12.8 V. Often engineers read the peak to peak voltage off the CRO as the determination of the 0 level is not always easy. The peak voltage is half of the peak to peak voltage.

The root mean square voltage, which we use in electrical calculations, is the peak voltage divided by √2

Therefore the Vrms = 6.4 X √2 = 4.5 V


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Unit 1 PHYA1 Particles, Quantum Phenomena … · Web viewPHYA1 Particles, Quantum Phenomena and Electricity Written Examination . 70 marks, 6 or 7 structured questions 1 ¼ hours