Particles and Waves - WordPress.com...Fermions are named after Enrico Fermi, pronounced fermi‘ons, and bosons are named after Satyendra Nath Bose, pronounced bose’ons. Fermions

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Farr High School

HIGHER PHYSICS

Unit 2

Particles and Waves

Pupil Booklet Based on booklets by Richard Orr, Armadale Academy

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Section 1

The Standard Model

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The Standard Model

A Greek philosopher, Democritus, came up with the idea of a fundamental

particle, the atom. This word comes from the Greek for indivisible

‘atmos’. He wondered if he could keep breaking an object in half

indefinitely. He came to the conclusion that eventually you would get

something that couldn’t be split.

Next came John Dalton. He used his data from chemistry experiments to propose that not

only were substances made of atoms, the atoms of an element were identical . Different

elements had different types of atom.

By the end of the 1800’s J.J. Thomson had discovered the electron, so now physicists knew atoms

were actually made of smaller component parts. This started a race to find out what the smaller

parts were.

The Rutherford scattering experiment

At the beginning of the 20th century, atoms were treated as semi-solid spheres with charge

spread throughout them. However, a new experiment by Ernest Rutherford in 1909 would

soon change this.

Rutherford directed his students Hans Geiger and Ernest Marsden to fire alpha particles at a

thin gold foil. This is done in a vacuum to avoid the alpha particles being absorbed by the

air.

The main results of this experiment were:

Most of the alpha particles passed straight through the foil, with little or no

deflection, being detected between positions A and B.

A few particles were deflected through large angles, e.g. to position C, and a very

small number were even deflected backwards, e.g. to position D.

Rutherford was so surprised by this second result in particular that he described it as being

like firing a cannonball at tissue paper and having it bounce back. Alpha particles were

known to be relatively heavy and fast moving, and if they were encountering the spread-out

charge and matter of the Thomson model there would be nothing solid enough for them to

bounce off.

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Rutherford interpreted his results as follows:

The fact that most of the particles passed straight through the foil, which was at least

100 atoms thick, suggested that the atom must be mostly empty space.

In order to produce the large deflections at C and D, the alpha particles must be

encountering something of very large mass and a positive charge.

Rutherford suggested that the atom

has a small positive nucleus, which

contains most of the mass of the

atom and is small compared to the

size of the atom. The remaining

space is taken up by the electrons

orbiting the nucleus. He estimated

the diameter of the atom to be

about 10,000 times the diameter of

the nucleus.

After Rutherford came a list of

distinguished physicists who prodded,

poked and probed matter to find out

more about the constituent parts of an

atom.

Niels Bohr, Wolfgang Pauli, Louis de Broglie, Paul Dirac,

Erwin Schrödinger, Werner Heisenberg, James Chadwick, Hideki Yukawa, Richard Feynman, Murray

Gell-Mann

This is not by any means a comprehensive list. More history can be found by accessing the web site

below.

http://www.nobeliefs.com/atom.htm

How do you examine a particle to see if it is actually made from more fundamental particles? You smash it up!! As particle accelerators became more powerful, more and more types of particles were being discovered. This led to a fairly messy group of over 100 particles. Physicists felt that there had to be a simpler way of describing these particles that they had to be made from the same basic building blocks. The Standard Model developed from this premise.

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Orders of Magnitude

It would be useful to get an idea of scale to better understand how sub-nuclear and

astronomical dimensions compare with those in our everyday life. You can see how we fit

into the grand scheme of things by watching the film at the link below.

http://www.powersof10.com/film

Some of the important objects are given in the table below.

Smaller than a human

Particle

or object Neutrino Proton

Hydrogen

atom Dust

Human

being

Order of

magnitude ~10–24 m 10–15 m 10–10 m 10–4 m 100 m

Larger than a human

Particle

or object Earth Sun Solar

system

Nearest

star Galaxy

Distance

to a

quasar

Order of

magnitude 107 m 109 m 1013 m 1017 m 1021 m 1026 m

When we get into the world of the very small or very large it is difficult to get a picture of scale in our minds. A distance of 10-15 m for instance, how many of these protons would fit on the point of a pencil? Assuming the pencil point was 1mm across, there would be 1 000 000 000 000 protons. The world population at the time of writing was 7 100 000 000 people.

Distance to a quasar, 1026 m. This would take light, travelling at 3 x 108m/s, 10 000 000 000 years to get from Earth to the quasar.

So if you feel a ‘sair heid’ coming on thinking about these numbers, don’t worry it’s the same for everybody!

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The Standard Model of Fundamental Particles

The standard model was developed in the early 1970’s in an attempt to tidy up the number of particles being discovered and the phenomena that physicists were observing. All particles are classified as either fermions or bosons.

Fermions are named after Enrico Fermi, pronounced fermi‘ons, and bosons are named after

Satyendra Nath Bose, pronounced bose’ons. Fermions

At present physicists believe that there are 12 fundamental mass particles (fermions) split into two

groups, leptons and quarks. The fundamental fermions are summarised in the table below.

Family Quarks (Charge) ~Mass Leptons ~ Mass

First Up u (+2/3) 0.004 Electron e 5 × 10–4

Down d (–1/3) 0.008 Electron neutrino νe <10–8

Second Charm c (+2/3) 1.5 Muon μ 0.1

Strange s (–1/3) 0.15 Muon neutrino νμ <10–4

Third Top t (+2/3) 176 Tau τ 1.8

Bottom b (–1/3) 4.7 Tau neutrino ντ <10–2

Fermions – leptons

The six leptons are - the electron, the heavier muon and tau, together with the associated

neutrinos.

Fermions – quarks

Protons and neutrons are made from even smaller particles called quarks.

There are six types of quark: up, down, charmed, strange, top and bottom, which are

denoted by u, d, c, s, t and b. The quarks have a non-integral charge (see table). There are

six corresponding anti-quarks with charges of opposite sign. They are denoted by a bar

above the letter eg. ū is an anti-up quark.

Individual quarks have not been isolated. All the particles we observe are made of combinations of quarks. Particles made from combinations of quarks are called hadrons. Baryons are made from 3 quarks and mesons are made from 2 quarks. For example, a proton is a baryon with a charge of +1. It is made up of two up quarks and a down quark. + 2/3 + 2/3 – 1/3 = +1 A neutron is also a baryon with a charge of 0. It is made up of two down quarks and an up quark. The force holding quarks together increases with distance (over its short range). Hence, attempting to pull quarks apart would strongly increase the force between them, forcing them back together.

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Bosons Bosons are force-mediating particles. The bosons you need to know about are photons, W bosons, Z bosons and gluons.

Photons are associated with the electromagnetic force. Photons have zero mass. W bosons and Z bosons are responsible for the transfer of the weak nuclear force that holds electrons in atoms. (Masses are ~80 × proton mass for W and ~90 × proton mass for Z.)

Gluons are associated with the strong nuclear force that acts between quarks, holding

nucleons (neutrons and protons) together in the nucleus.

Other force-mediating particles include:

The Higgs particle is a massive particle, predicted by the standard model and possibly

recently observed. Experimental detection of the Higgs could help to explain the mass of

particles.

Gravitons are thought to carry the gravitational force through the universe. Gravi tons have

not yet been detected but are thought to have zero mass.

The table below summarises the fundamental particles:

fermions bosons

quark

s

u up

c charm

t top

photon

forc

e c

arrie

rs

d down

s strange

b bottom

Z Z boson

lepto

ns

e

electron neutrino

muon

neutrino

tau

neutrino

W W boson

e electron

muon

tau

g gluon

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The table summarises the nature of the forces discussed:

Force Range

(m)

Relative

strength Particle Example effects

Strong nuclear 10–15 1038 gluon Holding nucleons in the

nucleus

Weak nuclear 10–18 1025 Z boson Y

boson Holding electrons in atoms

Electromagnetic ∞ 1036 photon Beta decay; decay of

unstable hadrons

Gravitational ∞ 1 graviton Holding matter in planets

and stars

Why do nuclei exist? In the nucleus of every element other than hydrogen, there is more than one proton. The charge on each proton is positive, so why don’t the protons repel each other and fly apart, breaking up the nucleus? There is a short range force that exists that holds particles of the same charge together. This force is stronger than the electrostatic repulsion that tries to force the particles apart. We call it the STRONG force. This force acts over an extremely short range [~10-15m], of the order of magnitude of a nucleus. Outside of this range the strong force has no effect whatsoever. If a proton was placed close to a nucleus it would be repelled and forced away. The particle responsible for carrying the strong force is called the gluon.

nucleus

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Beta decay and the neutrino When physicists were investigating beta decay, they came up with a possible problem - the law of conservation of momentum appeared to be being violated. The nucleus recoils to the left as the electron is ejected to the right. There was a discrepancy in the measured momenta for these two particles. The thinking was that there must be some other particle that wasn’t seen moving to the right; this would make the conservation law work. It was a particle that would have no charge and almost zero mass so it was not easy to confirm it actually existed! It took many years before experimental evidence for the existence of this particle was obtained. Enrico Fermi came up with the name neutrino (small one) for this particle. We now know that in beta decay a neutron decays into a proton and an electron. Only the weak force can cause such a change. The electron is forced out at high speed due to the nuclear forces. Positron Emission Tomography (PET) Scanners A positive emission tomography (PET) scan is used to produce a detailed, three-dimensional picture of the inside of the body. How it works Before the scan takes place, a radioactive substance, known as a radiotracer, is passed into the patient’s body either by injection, through an inhaler, or in the form of a small tablet or capsule.

The tracer gives off particles called positrons that in turn release gamma rays, which are then detected by the PET scanner. By tracking the movement of the tracer, the scanner can build up a detailed image of a number of the body’s functions, as well as highlighting areas of the body that have been affected by disease.

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Questions 1. Sketch a diagram of an atom. Clearly label the nucleus, protons, electrons and neutrons. 2. Complete the table to show the prefixes commonly used to represent large and small numbers and the corresponding orders of magnitude:

Prefix Letter Order of magnitude

pica p

n 10-9

10-6

m

kilo

mega 106

G

T 1012

3. Put these in order, starting with the smallest: diameter of the Sun height of Ben Nevis diameter of a nucleus size of a dust particle your height diameter of a proton distance to Moon diameter of a hydrogen atom 4. If the symbol p is used to represent a proton, write down the symbol used to represent a) a neutron b) an up quark c) an antineutrino d) an antielectron e) a muon neutrino e) an antistrange quark 5. Compare a baryon to a meson. 6. The following table gives the names of some hadrons and the types of quark which make them up. Complete the last column showing the charge on the hadron.

Hadron Composed from … Charge

lambda uds

charmed sigma uuc

xi dss

Charmed lambda udc

7. Name the boson responsible for the strong force between nucleons.

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Section 2

Forces on Charged Particles

+ - + +

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Electric Fields The idea of a field should be familiar to you. A gravitational field and an electric field are two examples of the same type of phenomena. In an electric field a charged particle will experience a force in the same way as a mass experiences a force in a gravitational field.

An electric field will exert a force on any charged object within the field. The shape of the field depends on the shape of the charged object.

Note that the direction of an electric field is always from positive to negative and the closer together the field lines are, the stronger the field is. The potential difference between two points is the work done in moving one coulomb of charge from one point to the other against the electric field i.e. from the lower plate to the upper plate. The work done in moving a charge from the lower plate to the upper plate is

Work done = Q x V This means that if a charged object is in a uniform electric field, parallel plates, then it will experience a force causing it to accelerate. The kinetic energy of the object will change. The change in kinetic energy will depend on the charge on the object and the potential difference across the plates.

Ek =

2

mv2 = QV

This allows us to calculate the speed of an object accelerated across a uniform electric field.

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Example Consider an ink droplet of mass 2 x 10-5kg and a charge of +2 x 10-6C being accelerated across a p.d. of 3000V in a printer. What is the velocity of the droplet when it reaches the 0V plate?

Movement of charged material in electric fields has many industrial applications as well as the ink jet printer. If a car body is given a positive charge and the paint a negative charge then paint wastage in spray painting can be reduced. The cathode ray tube (CRT) was invented in the 1800s but formed the basis of the majority of the world’s new television technology until the mid-2000s. In the CRT an “electron gun” fires electrons at a screen. Electrons, excited by heat energy from the filament, are emitted by the cathode and then accelerated forwards through a large potential difference towards the anode. The electrons pass through the cylindrical anode and a beam is formed. Potential differences applied to pairs of parallel plates are used to deflect the electron beam to different points on the screen.

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In electrostatic precipitation solid or liquid particles can be removed from a gaseous carrying medium by giving them an electric charge and then precipitating them on to a suitable receiving surface in an electric field. This process is used to remove "fly-ash" from power station flues.

Xerox machines (photocopiers) also make use of electrostatic techniques.

Example

An electron is accelerated (from rest) through a potential difference of 200 V.

Calculate: (a) the kinetic energy, Ek, of the electron

(b) the final speed of the electron.

Ew = work done in Joules = Ek

Ew = QV = 1.6 x 10-19 x 200 = 3.2 x 10-17 J

Ek = 3.2 x 10-17 J = ½ mv2

v2 = 2 x 3.2 x 10-17 so v = 8.4 × 106 m s–1

9.1 × 10–31

Questions

1. A proton is accelerated from rest across a p.d. of 300V. Calculate the final speed of the

proton.

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Charged particles in a magnetic field. Things now get a wee bit more complex. A moving charge produces its own magnetic field. If the moving charge is then placed in another magnetic field, it will experience a force. The direction of the force can be determined if you know the sign on the charge and the direction of the magnetic field. Magnetic field by definition runs from north to south. For negative charges in a magnetic field use the right-hand motor rule.

For the movement of a positive charge in a magnetic field, use Fleming’s left-hand motor rule.

× × × × × × × × × × × × × × × The motor rules are also used to determine the direction of spin of the coil in an electric motor.

motor effect – right hand

first finger – direction of the magnetic

field

second finger – direction of the electron

flow current

thumb – direction of motion

thumb -

motion first finger -

magnetic

field

second finger -

electron flow

current

motor effect – left hand

first finger – direction of the magnetic

field

second finger – direction of the

conventional current

thumb – direction of motion

thumb -

motion first finger -

magnetic

field

second finger -

conventional

current

v

F

magnetic field

perpendicularly

into the page

negative

charge

path of

negative charge

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Particle Accelerators There are three main types of accelerators:

Linear

Cyclotron

Synchotron Regardless of whether the particle accelerator is linear or circular, the basic parts are the same:

a source of particles (these may come from another accelerator)

Accelerators using electrons use thermionic emission in the same way as a cathode ray tube. At

the Large Hadron Collider (LHC) at CERN the source of particles is simply a bottle of hydrogen

gas. Electrons are stripped from the hydrogen atoms leaving positively charged protons. These

are then passed through several smaller accelerator rings before they reach the main beam pipe

of the LHC.

beam pipes (also called the vacuum chamber)

Beam pipes are special pipes which the particles travel through while being accelerated. There is

a vacuum inside the pipes which ensures that the beam particles do not collide with other atoms

such as air molecules.

accelerating structures (a method of accelerating the particles)

As the particles speed around the beam pipes they enter special accelerating regions where there

is a rapidly changing electric field. At the LHC, as the protons approach the accelerating

region, the electric field is negative and the protons accelerate towards it. As they move

through the accelerator, the electric field becomes positive and the protons are repelled away

from it. In this way the protons increase their kinetic energy and they are accelerated to almost

the speed of light.

a system of magnets (electromagnets or superconducting magnets as in the LHC)

Newton’s first law states that an object travels with a constant velocity (both speed and

direction) unless acted on by an external force. The particles in the beam pipes would go in a

straight line if they were not constantly going past powerful, fixed magnets which cause them to

travel in a circle. There are over 9000 superconducting magnets at the LHC in CERN. These

operate best at temperatures very close to the absolute 0K and this is why the whole machine

needs to be cooled down. If superconducting magnets were not used, they would not be able to

steer and focus the beam within such a tight circle and so the energies of the protons which are

collided would be much lower.

a target

In some accelerators the beam collides directly with a stationary target, such as a metal block.

In this method, much of the beam energy is simply transferred to the block instead of creating

new particles. In the LHC, the target is an identical bunch of particles travelling in the opposite

direction. The two beams are brought together at four special points on the ring where massive

detectors are used to analyse the collisions.

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The first accelerator was conceived and built by John D. Cockcroft and E.T.S. Walton in 1930 at the Cavendish Laboratory in Cambridge. They used a potential of up to 800kV to accelerate proton down an eight foot long vacuum tube. This gave the proton energy of 800keV. This was a linear accelerator and used electrostatics only.

It was quite cumbersome and other developments led to the design known as the cyclotron. This made use of both magnetic and electric fields to accelerate a particle in a spiral path. They produced particles of energy 10MeV. Synchrotrons were the next step up in increasing energy, they used electric and magnetic fields to accelerate particles around a ring, the ring diameter increasing as new technology and techniques were developed. Energies of up to 28GeV were produced at CERN in 1959. The Large Hadron Collider can now accelerate protons to an energy of 7TeV, this is around 1,000,000,000 times more energy than Cockroft and Walton’s original accelerator.

Cyclotrons are used in medicine in various ways, they can be used to accelerate particles to be used in radiotherapy, they can also be used to generate radioactive isotope that can then be used as tracers. The accelerators can be used to produce high energy protons for use in cancer treatment; these protons allow doctors to be more accurate in their administering treatment. The latest development is in neutron therapy for cancer treatment.

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Section 3

Nuclear Reactions

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Atomic Structure Atoms consist of three types of particles: electrons, protons and neutrons. Neutrons are electrically neutral, but protons have a relative charge of +1, while electrons have a relative charge of -1. Protons and neutrons are found in the small, central nucleus of an atom. Electrons are arranged in energy shells around the nucleus. It is the number of protons in an atom which determine which element it is. All atoms of the same element have the same number of protons. However, they may have a different number of neutrons (ISOTOPES). We can write a shorthand description of a nucleus shown below:

Sc – element symbol 21 – Number of protons in nucleus [Atomic Number] 45 – Number of protons + neutrons in nucleus [Mass Number] The number of neutrons in the nucleus can be determined by the calculation:

Mass Number - Atomic Number Nuclear Radiation There are three types of nuclear radiation, alpha (α), beta (β) and gamma (γ). The diagram shows the penetrating power of the types of radiation.

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The table shows the nature of the types of radiation:

Type of Radiation Symbol What is this radiation? Charge

Alpha α Helium nucleus ie 2 protons and 2 neutrons

2+

Beta β Fast-moving electron 1-

Gamma γ Short wavelength em radiation

0

Radioactive Decay

AAllpphhaa ddeeccaayy iiss tthhee eemmiissssiioonn ooff aa hheelliiuumm nnuucclleeuuss..

IInn aallpphhaa eemmiissssiioonn,, tthhee mmaassss nnuummbbeerr ddeeccrreeaasseess bbyy 44 aanndd tthhee aattoommiicc nnuummbbeerr ddeeccrreeaasseess bbyy 22..

BBeettaa ddeeccaayy iiss tthhee eemmiissssiioonn ooff aa hhiigghh ssppeeeedd eelleeccttrroonn.. TThhee eelleeccttrroonn ccoommeess ffrroomm tthhee nnuucclleeuuss ooff tthhee

aattoomm bbyy tthhee bbrreeaakkddoowwnn ooff aa nneeuuttrroonn iinnttoo aa pprroottoonn aanndd aann eelleeccttrroonn.. TThhee eelleeccttrroonn iiss eemmiitttteedd ffrroomm

tthhee nnuucclleeuuss bbuutt tthhee pprroottoonn rreemmaaiinnss..

IInn bbeettaa eemmiissssiioonn,, tthhee mmaassss nnuummbbeerr rreemmaaiinnss ccoonnssttaanntt aanndd tthhee aattoommiicc nnuummbbeerr iinnccrreeaasseess bbyy 11..

GGaammmmaa rraayyss aarree nnoott ppaarrttiicclleess lliikkee aallpphhaa aanndd bbeettaa rraaddiiaattiioonn..

TThheeyy aarree eelleeccttrroommaaggnneettiicc rraaddiiaattiioonn wwiitthh aa hhiigghh ffrreeqquueennccyy..

GGaammmmaa ddeeccaayy iiss tthhee eemmiissssiioonn ooff eenneerrggyy ffrroomm tthhee nnuucclleeuuss ooff aann aattoomm.. TThhee mmaassss aanndd pprroottoonn nnuummbbeerrss

ooff tthhee aattoomm rreemmaaiinn uunncchhaannggeedd..

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Fission and Fusion If the nucleus of an atom breaks up into smaller constituent parts then we say that nuclear fission has taken place. Fission of a nucleus may be spontaneous, that is, it may happen at random due to internal processes within the nucleus. Fission can also be induced by bombarding a nucleus with a neutron. Induced fission is used to generate nuclear power. Neutrons are usually released when fission takes place. Alpha decay of Thorium-227

Nuclear fission of uranium nucleus

There is another group of reactions where the mass of the product is greater than that of the reactants. These reactions are known as fusion reactions.

In the examples above there are certain rules that must be obeyed.

The total of atomic numbers must be the same on both sides of the arrow

The total of mass numbers must be the same on both sides of the arrow This allows us to identify any missing elements in a given reaction. The mass number gives an indication of the mass of a nucleus; however it is a fairly crude measurement of the actual mass.

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In the example given for the uranium nucleus the actual masses each side of the arrow are: LHS: 391.875 x 10-27kg RHS: 391.550 x 10-27kg This gives a mass loss of 0.325 x 10-27kg The conservation of mass is a fundamental principle within physics, so where has the mass gone? Strange, but true, it has changed into energy, heat in this example.

E = mc2 where E = energy, m= mass, c = speed of light Einstein’s famous equation links mass and energy directly, they are in fact one and the same thing!! To find the energy given out in a nuclear reaction:

Calculate the total mass before the reaction.

Calculate the total mass after the reaction.

Calculate the mass loss.

Calculate the energy released using E = mc2

Example Calculate the energy released during this fission reaction.

92

235

56

137

42

97U + n Ba + Mo + 2 n + energy0

1

0

1

Mass before fission (kg) Mass after fission (kg) U 390.2 × 10–27 Ba 227.3 × 10–27 n 1.675 × 10–27 Mo 160.9 × 10–27

___________________ 2n 3.350 × 10–27

391.875 × 10–27 _________________________ 391.550 × 10–27

Decrease in mass = (391.875 – 391.550) × 10–27

= 0.325 × 10–27 kg Energy released during this fission reaction, using E = mc2

E = 3.25 × 10–28 × (3 × 108)2 = 2.9 × 10–11 J This is the energy released by fission of a single nucleus. Note the need to work with six significant figures for mass due to the small difference. Questions 1. Identify element X, it’s mass number and it’s proton number in the alpha decay shown below: 2. Identify element Z, it’s mass number and it’s proton number in the beta decay shown below:

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Applications of fission and fusion Fission reactions have been used for some time to generate energy. The U.K. currently has 10 nuclear power stations in operation. Legislation was passed in November 2009 for the development of 10 further plants in England and Wales. These power stations use the heat produced by the fission reaction to generate steam, which in turn powers turbines just as in a conventional thermal power station. Advantages of nuclear power:

• Unlike conventional power stations, however, nuclear power stations do not release carbon dioxide, so they do not contribute to global warming while in use.

• There is enough uranium left to produce nuclear power for thousands of years. • About 2 million times more energy is released per kilogram of uranium compared to a

kilogram of coal or oil. Disadvantages of nuclear power:

• Nuclear waste stays radioactive for hundreds of thousands of years and so there is a big problem with storing nuclear waste safely.

• There is a danger of nuclear accidents in which radioactive substances can be released into the atmosphere. These can cause damage to health.

The fuel rods in a nuclear reactor are made of uranium oxide. Uranium oxide is not naturally abundant on earth so after it is mined it needs to be enriched. Each time a uranium nucleus splits up it releases energy and three neutrons. These neutrons can then go and induce fission in other uranium atoms. This chain reaction must be controlled. To control the energy released in the reactor moveable control rods are placed between the fuel rods. These control rods are made of boron which absorbs some of the neutrons so fewer neutrons are available to split uranium nuclei. The control rods are raised to increase and lowered to decrease the number of free neutrons. Most of the neutrons produced in a fission reaction are fast-neutrons and move too quickly to be ‘captured’ by uranium nuclei. The graphite moderator slows down the neutrons in order for them to collide with uranium atoms and so allow the fission process to continue.

heat

exchanger

turbine

generator

reactor core

control rods

fuel elements

containment

vessel

coolant

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The coolant removes the heat produced during the nuclear reactions. The coolant is usually carbon dioxide gas. The CO2 absorbs the heat as it passes through the core. The heat is then transferred to water and the water turns to steam to drive a turbine. The containment vessel must be secure and able to absorb the radioactivity produced within the core. The temperature of the reactor core must be maintained at a safe level. This is achieved by a combination of the control rods and the coolant. Nuclear reactors are also used to power submarines and ships. The first nuclear powered submarine was USS Nautilus, which was launched in 1955. Using fusion to generate energy is a much more attractive prospect. Practically all of the energy we use at present comes from nuclear fusion. Unfortunately the nuclear reactor is around 150 000 000 km away from us [the commute is murder!!]. It is of course the Sun, and much of the energy we are using was stored by plants and animals millions of years ago, fossil fuels.

The Joint European Torus (JET), in Oxfordshire, is Europe’s largest fusion device. In this device,

deuterium–tritium fusion reactions occur at over 100 million kelvin. Even higher temperatures are

required for deuterium–deuterium and deuterium–helium 3 reactions.

To sustain fusion there are three conditions, which must be met simultaneously:

plasma temperature (T): 100–200 million kelvin

energy confinement time (t): 4–6 seconds

central density in plasma (n): 1–2×1020 particles m–3 (approx. 1 mg m–3, i.e. one millionth of the density of air).

The problem is that the plasma produced during the fusion reaction is at a temperature of around 100 million °C. This would vaporise any material it came into contact with. The diagram opposite shows how the plasma is contained within the torus by magnetic fields. Currently the energy required to contain and maintain a fusion reaction is greater than the energy released in the reaction itself.

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Section 4

Wave Particle Duality

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What is Light? This question has troubled scientists since the time of the ancient Greeks. Aristotle considered that light was a disturbance in the air, i.e. a wave. Democritus, who originally proposed the concept of atoms, thought that light is made up of ‘corpuscules’ or tiny particles. At various points in history one view has held sway over the other as new experimental evidence came to light. For many of the properties of light it doesn’t actually matter which view we take. Both theories can describe light as rays which travel in straight lines.

However, experiments carried out by Thomas Young and Christiaan Huygens in the 19th

century seemed to finally sound the death knell of the particle theory. They made

observations of light that it would be impossible to explain using particles.

Then, within 20 years, Heinrich Hertz had observed that electromagnetic radiation could

knock electrons off the surface of a metal plate in what came to be known as the

photoelectric effect. This in itself didn’t pose any problems to the wave theory of light,

but after the turn of the century more detailed study of this effect by Philipp Lenard

showed that the speed of the ejected electrons did not depend on the intensity of the light

but its frequency. This could not be explained using a wave view of light.

At the same time Max Planck was studying a seemingly separate problem called black body

radiation. This is the radiation emitted by any hot object. It requires the introduction of

quantisation, i.e. the idea that electromagnetic energy comes in tiny packets called quanta

or now more commonly photons. The energy of these photons is directly proportional to

their frequency and the constant of proportion is now known as the Planck constant (h).

The size of these packets is far too small for us to easily observe in everyday life. A relatively simple experiment can be conducted in class. Light is shone onto a zinc plate on top of a charged electroscope. It is found that the electroscope will only discharge if it is charged negatively AND the incident light is of a sufficiently high frequency. This is a pivotal experiment in light theory. The explanation of this effect was impossible using the then, current wave theory of light. Einstein came up with a new theory, the particulate nature of light, to explain the effect. This was what he was awarded his Nobel Prize for.

incident light

Zinc

Plate

26

The Photoelectric Eeffect Some basic principles:

Light behaves as a particle – a package of light with an associated frequency – a photon

The energy of a photon depends solely on its frequency. [E = hf]

Electrons are held onto a metal surface, the energy required to release them depends on the type of metal.

The energy to release an electron is known as the work function. [E = hf0] A photon is incident on a metal plate. In order for an electron to permanently leave the plate the plate must be negatively charged. If the photon has sufficient energy, an electron will be ejected from the surface of the metal. If the incoming photon does not have sufficient energy then no electrons will be ejected, no matter how intense the beam of photons or how long the beam is incident on the metal. It was this fact that meant a new theory had to be introduced. http://web2.uwindsor.ca/courses/physics/high_schools/2005/Photoelectric_effect/index.html Relationships The energy of a photon is calculated using the expression E = hf E = photon energy (J) h = Planck’s constant = 6.63 x 10-34Js f = photon frequency (Hz) Think of the nasty end of the E.M. spectrum UV, X-rays and gamma, all high frequency, high energy and high danger. The incoming photon has energy, hf. The electron requires energy of hf0 to release it. The difference in energy is transferred to the electron as kinetic energy, EK.

EK = hf – hf0

27

Wave Particle Duality This now throws up the dilemma, is light a wave or is it a particle? The answer is yes; light is a wave or a particle!!! It depends on how you look for light. If you look for light as a wave, by producing an interference pattern, then you find it’s a wave. If you look for light as a particle, by producing the photoelectric effect, then you find it’s a particle. The phenomena of interference cannot be explained in terms of particles. So light must be a wave. The photoelectric effect cannot be explained in terms of waves. So light must be a particle. What if we pass UV light through a grating then use one of the maxima to cause the photoelectric effect?

If you think your head is hurting now, just wait until you discover quantum mechanics! Example Gold has a work function of 7.84 x 10-19 J. (a) Calculate the threshold frequency of gold. (b) Gold foil is illuminated with radiation of frequency 1.7x1015Hz. Calculate the maximum kinetic energy of the ejected electrons. (a) W = hfo

fo =W/h = 7.84 x 10 -19/6.63 x10-34 = 1.18 x 1015 Hz

(b) Ek = hf - hfo

hf = photon energy = 6.63 x10-34 x 1.7x1015 = 1.13 x 10-18 J so Ek = 1.13 x 10-18 - 7.84 x 10 -19 = 3.43 x 10-19 J

28

Section 5

Interference and

Diffraction

29

Wave Properties A longitudinal wave – eg. a sound wave

A transverse wave – eg. light

The speed of a wave is the distance travelled per unit time by the wave. The unit of speed is the metre per second, ms-1. The speed, frequency and wavelength of a wave are linked by the following relationship: v = fλ The frequency (f) of a wave is the number of complete waves passing a point per second. Frequency is measured in Hertz (Hz). The periodic time (the time for one wave to be produced) (T) is found by T = 1/f

30

Interference and diffraction In order for waves to interact with each other they must have the same wavelength and frequency. This is why radio stations putting out the same station from different transmitters do it on different frequencies. If they did not then the signals would cause interference. Phase: This is a measure of how ’in step’ waves are. For interference to occur two waves must combine at a point in space. The waves must have the same wavelength and frequency as well as having a fixed phase difference. This is known as COHERENCE. How the waves are configured at the point where they meet will determine how they combine. The phenomena of interference can only be explained in terms of waves. Interference can be thought of as a test for waves. If we can produce an interference pattern we must have a wave.

31

Producing Interference Two coherent waves can be produced by having identical signals emitted from two separate sources. This can only be done easily with sound waves. Two loudspeakers can be connected to one output of a signal generator. As you move around the lab you will hear the volume of the sound vary. There will be points where the sound is louder [constructive interference] and points where the sound is quieter [destructive interference]. The waves that meet at your ear, away from the centre line, will have travelled different distances from each loudspeaker. The difference in distance is known as the Path Difference (pd). When trying to produce interference patterns with sound it is impossible to produce completely constructive and destructive interference in a lab due to reflections from walls, floor and ceiling. When dealing with light or microwaves we need to find some other method of producing interference. Two lamps cannot be used as the phase of the light from a light source changes at random ~ every 10-9s. To get around this problem we can place a single source behind two slits. Each slit behaves as an individual source. These sources are coherent since the waves are coming from the same single source. If we measure the path difference to a max or min then it is possible to determine the wavelength of the source. For a maximum:

pd = m (where m is the number of the maximum from the centre line, m = 1,2,3,…….) For a minimum:

pd = (m + ½ ) (where m is the number of the minimum from the centre line, m = 1,2,3,…….) Obviously this method depends on the source having a wavelength that is of the order of cm or greater.

32

Example Microwaves with a wavelength of 2.8cm are incident on a double slit. The third maximum on one side of the straight-through position occurs 13cm from the closest slit. How far is the maxima from the other slit?

Solution: For constructive interference

Path difference = mλ

= 3 x 2.8

= 8.4cm

Distance to farthest slit = 13 + 8.4

= 21.4cm

33

Diffraction Diffraction occurs whenever a wave passes an edge, passes through a narrow gap or goes past an object. The wavelength, frequency, period and speed are same before and after diffraction. The only change is the direction in which the wave is travelling. When a wave passes through a gap the diffraction effect is greatest when the width of the gap is about the same size as the wavelength of the wave.

Diffraction Gratings If we wish to measure the wavelength of visible light, say, then we would have to be able to measure a path difference accurate to ~ 10-7m. This is an unattainable level of accuracy within a school laboratory. It is possible to determine the wavelength of visible light using a diffraction grating. This is a slide which has a series of uniform lines etched onto it. The spacing of these lines is typically of the order of 10-6m. When monochromatic light is passed through a grating the light produces an interference pattern. In order to determine the wavelength of the light the measurements that must be made are

The angle between the central [zero order] maximum and the maximum under

consideration (θ) [tanθ =

D

x ]

The spacing between the lines on the grating (d) The relationship that links these measurements to the wavelength is

m= dsinθ

34

If white light is shone through a grating a series of spectra are produced on the screen. This is due to the different wavelengths of light that constitute white light diffracting by different amounts. Similarly if we observe a white light source by looking at it through a grating we see a series of spectra either side of a white central image of the source. A spectrum can also be produced by passing white light through a prism. There are differences in the spectra produced by gratings and prisms.

Prism – single spectrum, grating – multiple spectra

Prism – red refracted least, grating – blue diffracted least. Example Monochromatic laser light is shone onto a diffraction grating which has 300 lines per mm. The second order maximum is formed at an angle of 23o. What is the wavelength of the laser light? d = 0.001/300 = 3.3 x 10-6m dsinθ = mλ λ = dsinθ = 3.3 x 10-6 x sin23 n 2

= 6.51 x

10-11m

= 651nm

white

light

prism

grating

white

light

35

Section 6

Refraction of Light

36

Refraction of Light When light passes from one medium to another there is a change in speed. The ratio of these speeds is known as the refractive index(n).

nmed =

medium in speed

(air) vacuum in speed =

med

airv

v

Strictly speaking the relationship is

air

medn

n =

med

airv

v

but, we take the refractive index of air to be 1. If we wish to determine the refractive index of a medium experimentally in the lab we would have difficulty measuring the speed of light. Fortunately we can use another relationship to determine the refractive index. In order to do this we must have a ray of light meet the air – medium boundary at a non-normal angle. The diagram below shows a ray passing from air into a medium. The path of the ray in the opposite direction would be the same. The relationship between the refractive index and the angles is

nmed =

med

airsin

sin

The frequency of a wave does not change when the wave undergoes refraction. This means that if the velocity does change then there must also be a change in wavelength. We now have three relationships that can be used to determine the refractive index of a medium.

nmed =

med

airsin

sin

=

med

airv

v =

med

air

37

Lenses Lenses work by refracting light. The thickness of the glass determines how much the light will be bent. Lenses have many applications, including correcting vision defects, telescopes and binoculars. Critical Angle As the angle of incidence of a ray of light shining onto a surface increases, the amount the light bends also increases. Eventually the angle becomes such that the light is not refracted out of the material but is reflected back inside it. The angle at which this first occurs is called the critical angle. The angle in air is always going to be greater than the angle in the medium. This leads to a situation where an angle in the medium will result in a 90° angle in air. The angle in the medium for this situation is known as the critical angle. (θC) If the angle in the medium is greater than the critical angle then the ray is totally internally reflected. There is a relationship between the critical angle and the refractive index for a medium.

nmed =

med

airsin

sin

=

csin

09sin

=

csin

1

The greater the refractive index the smaller the critical angle. Experts can analyse the way light passes through gemstones to identify, for instance, fake diamonds.

You may have seen the scientists on CSI immerse glass fragments in oil to determine the refractive index and hence identify the source of the glass. They do this by altering the temperature of the oil to change its refractive index. When the indices match the glass disappears from vision.

38

Total Internal Reflection Total internal reflection (TIR) occurs at a boundary where light tries to travel from an optically denser material into one of lower density. Glass prisms are used in binoculars and SLR cameras to reflect light.

In an optical fibre, light is totally internally reflected inside the fibre. An optical fibre is as thin as a hair and is very flexible. It is made of a narrow core made of very pure glass surrounded by a cladding of very pure glass with a different refractive index to the core. It has a protective coat around the outside. Examples The diagram shows a ray of monochromatic light incident along the normal to side AC of a glass block. (a) What happens to the direction, speed, frequency and wavelength of the light as it enters the glass block? (b) What is the angle of incidence on the side AB? (c) The refractive index of the glass is 1.48. Calculate the critical angle for the light in the glass. (d) Complete the diagram to show the path of the ray of light after it has been incident on side AB. (a) Direction remains same, speed slows down, frequency unchanged and wavelength decreases. (b) 45o

(c) nglass =

csin

1

so sin Θc = 1/1.48 so Θc = 42.5o

(d)

39

Section 7

Spectra

40

Irradiance When you are out in the sun you can feel the heat energy that is hitting your skin. Some days the sun feels stronger than others. The irradiance changes. Irradiance is a measure of how much power is incident on the area of a surface.

I = A

P

We must consider the component of the power that is perpendicular to the surface. The further we move from a point source of energy the smaller the irradiance. The diagram shows that as the distance increases, the power is spread over a bigger area so the irradiance decreases. The relationship between the distance (d) and the irradiance (I) is:

I1d12 = I2d2

2 Example A light meter is placed 20cm away from a lamp and it measures a value of 24 Wm-1. What will the reading on the meter be at a distance of 40cm from the lamp? I1d1

2 = I2d22

24 x 0.22 = I2 x 0.42 I2 = 24 x 0.04 = 6 Wm-1

0.16 ie. If the distance increases by a factor of 2, the irradiance falls by a factor of 22 = 4. Questions 1. A light meter is placed 10cm away from a light bulb and it measures an irradiance of 64 Wm-1. The meter is moved away from the lamp until it reads 16 Wm-1. How far is it away from the lamp now? 2. Why is it better to put a black cloth over the work bench when carrying out irradiance experiments?

I = Irradiance W/m2

P = normal component of power W

A = surface area m2

41

Emission Spectra A line spectrum is emitted by excited atoms in a low pressure gas. Each element emits its own unique line spectrum that can be used to identify that element. The spectrum of helium was first observed in light from the sun (Greek - helios), and only then was helium searched for and identified on Earth. A line emission spectrum can be observed using either a spectroscope or a spectrometer using a grating or prism.

As with the photoelectric effect, line emission spectra cannot be explained by the wave theory of light. In 1913, Neils Bohr, a Danish physicist, first explained the production of line emission spectra. When the structure of the atom had been determined a problem arose. If electrons orbited around the nucleus then they should lose energy. Moving in a curved path meant that they were accelerating and consequently would emit energy. This means that their orbit would eventually decay and they would fall into the nucleus and the atom would essentially have no volume. We couldn’t exist!! Now since we clearly do exist there had to be some other explanation. This is where Niels Bohr came in; he proposed a model where electrons existed in discrete energy levels around a nucleus. De Broglie further extended this theory.

vapour lamp

spectroscope

vapour lamp

collimator

grating

telescope

42

If you look at a cadmium discharge lamp through a grating a series of individual separate colours are seen. This is quite different from looking at an extended light source such as a filament lamp where a complete spectrum is seen. How do we explain the existence of these discrete lines? Consider the diagram below; it is a representation of the energy levels for an atom. E0 is known as the ground state and is the lowest energy level. As an electron moves to energy levels further away from the nucleus, the energy of the electron will increase. If an electron gains sufficient energy it can escape from the atom completely - the ionisation level. By convention, the electron is said to have zero energy when it has escaped the atom. Therefore the energy levels in the atom have negative energy levels. The ground state is the level with the most negative energy. . Electrons can be promoted to higher energy levels if the atom absorbs energy. When an electron falls from a higher to a lower energy level energy is released in the form of a photon. The diagram below shows the first five the energy levels for a hydrogen atom.

discharge lamp filament lamp

E0

E1

E2

E3

E4 -0.864 x 10-19 J

E3 -1.360 x 10-19J

E2 -2.416 x 10-19J

E1 -5.424 x 10-19 J

E0 -21.76x 10-19 J

43

The transition shown represents an electron falling from E2 to E1. Transition E2 E1

ΔE = E2 – E1 ΔE = [-2.416-(-5.424)] x 10-19 J

= 3.008 x 10-19 J

f =

h

E

= 34-

19-

10 x 6.63

10 x 3.008

= 4.537 x 1014 Hz This is the frequency of red/orange light and a red/orange line is seen. Continuous Spectra A continuous visible spectrum consists of all wavelengths of light from violet (~400 nm) to red (~700 nm). Such spectra are emitted by glowing solids (a tungsten filament in a lamp), glowing liquids or gases under high pressure (stars). In these materials the electrons are not free. The electrons are shared between atoms resulting in a large number of possible energy levels and transitions. Absorption spectra An electron may also make a transition from a lower energy level to a higher energy level. The electron must gain energy corresponding to the energy level gap. It can do this by absorbing a photon of exactly the correct frequency. If white light passes through a vapour containing discrete atoms the electrons in those atoms will absorb light of frequencies corresponding to the energy level differences in the atoms.

excited state

electron

photon

white

light

source

glowing vapour

spectrometer

44

When the light is observed there will be voids in the white light spectrum corresponding to the frequencies of light absorbed by the atoms. When white light is passed through a colour filter, a dye in solution or a glowing vapour, the frequencies of light corresponding to the energy level gaps are absorbed. This gives dark absorption lines across the otherwise continuous spectrum.

The fact that the frequencies of light that are absorbed by the glowing vapour match exactly those emitted can be demonstrated by the fact that a sodium vapour casts a shadow when illuminated with sodium light. Absorption Spectra in the Sun By examining the lines in the Sun’s spectrum it is possible to identify elements present in the upper atmosphere of the Sun. The white light produced in the centre of the Sun passes through the relatively cooler gases in the outer layer of the Sun’s atmosphere. After passing through these layers, certain frequencies of light are missing. This gives dark lines (Fraunhofer lines) that correspond to the frequencies that have been absorbed. The lines correspond to the bright emission lines in the spectra of certain gases. This allows the elements that make up the Sun to be identified.

45

Example The diagram below shows two energy transitions within an atom. (a) Determine the energy of the photons emitted during transitionsA and B. (b) Calculate the frequency of the emission line produced by transition A. (c) Determine the wavelength of the remaining spectral line due to transitions between these energy levels.

(a) A:ΔE = (−11·5 10-19) – (−3·6 10-19) = −7·9 10-19 J

energy of photon A = 7·9 10-19 J

B: ΔE = (−11·5 10-19) – (−7·3 10-19) = −4·2 10-19 J

energy of photon B = 4·2 10-19 J (b) E = hf

7·9 10-19 = 6·63 × 10−34 × f f = = 1·2 × 1015 Hz

(c) ΔE = (−7·3 10-19) – (−3·6 10-19) = −3·7 10-19 J

E = hf so f = = 1·09 × 1015 Hz

v = fλ so λ = = 2·75 × 10−7 m

−3·6 10-19 J

−7·3 10-19 J

−11·5 10-19 J

A B

7·9 10-19

6·63 × 10−34

3·7 10-19

6·63 × 10−34

3·0 108

1.09 × 1015