Basic Knowledge and Understanding

Particles and Waves

This section will last for 40 hours , covering 7 areas.

The Standard Model , Forces on charged particles , Nuclear Reactions , Wave Particle Duality , Interference and Diffraction , Refraction of light and Spectra

The course is outlined in more detail later . Each area is divided into subsections . You can use this information to check your understanding. The statements are broad therefore it is essential that you read your summary sheets and keep all your work up to date throughout the course.

Assessment

A 40 minute NAB must be passed . This will cover knowledge and understanding and test your skills ;

Outcome 1

Demonstrate and apply knowledge and understanding of subatomic physics and waves

Performance Criteria

(a) Make accurate statements about subatomic physics and waves facts, concepts and relationships.

(b) Use relationships to solve subatomic physics and waves problems.

Outcome 2

Demonstrate skills of scientific experimentation, investigation and analysis in the field of subatomic physics and waves

Performance Criteria

(a) Use a range of data-handling skills in a scientific context.

(b) Use a range of skills related to experimental design.

For Outcome 2, PC(a), candidates are required to demonstrate that they can use a range of data-handling skills. These skills include selecting, processing and presenting information. Information can be presented in a number of formats including: line graphs, scatter graphs, bar and pie charts, tables, diagrams and text.

For Outcome 2, PC(b), candidates are required to demonstrate they can use a range of skills associated with experimental design. These skills include planning, designing and evaluating experimental procedures.

For Outcome 2, PC(c), candidates are required to demonstrate they can use a range of skills associated with the evaluation of scientific evidence. These skills include drawing valid conclusions and making predictions.

The 7 key areas in which the skills and knowledge and understanding are developed are outlined below. For each key area a broad outline of the key facts is given, this is what you will be examined on.

1 The Standard Model

a) Orders of magnitude.

The range of orders of magnitude of length from the very small (sub-nuclear) to the very large (distance to furthest known celestial objects).

b) The Standard Model of Fundamental Particles and Interactions.

The evidence for the sub-nuclear particles and the existence of antimatter.
Fermions, the matter particles, consist of Quarks (6 types) and Leptons (Electron, Muon and Tau, together with their neutrinos).
Hadrons are composite particles made of Quarks.
Baryons are made of three Quarks and Mesons are made of two Quarks.
The force mediating particles are bosons (Photons, W and Z Bosons, and Gluons).
Description of beta decay as the first evidence for the neutrino.

2 Forces on charged particles

a) Electric fields around charged particles and between parallel plates.

Examples of electric field patterns include single point charges, systems of two point charges and the field between parallel plates. No calculation of electric field strength required.

b) Movement of charge in an electric field, p.d. and work, electrical energy.

The relationship between potential difference, work and charge gives the definition of the volt.
Calculating the speed of a charged particle accelerated in an electric field.

c) Charged particles in a magnetic field.

A moving charge produces a magnetic field.
The direction of the force on a charged particle moving in a magnetic field should be described for negative and positive charges (right hand rule for negative charges). No calculations required.

d) Particle accelerators

Basic operation of particle accelerators in terms of acceleration, deflection and collision of charged particles.

3 Nuclear Reactions

a) Fission and fusion.

Nuclear equations to describe radioactive decay and fission and fusion reactions.
Mass and energy equivalence, including calculations.
Coolant and containment issues in nuclear fusion reactors.

4 Wave Particle Duality

a) The photoelectric effect and wave particle duality.

Photoelectric effect as evidence for the particulate nature of light.
Photons of sufficient energy can eject electrons from the surface of materials.
The threshold frequency is the minimum frequency of a photon required for photoemission.
The work function is the minimum energy required to cause photoemission.
The maximum kinetic energy of photoelectrons can be determined.

5 Interference and diffraction

a) Conditions for constructive and destructive interference.

Coherent waves have a constant phase relationship and have the same frequency, wavelength and velocity.

b) Interference of waves using two coherent sources.

Constructive and destructive interference in terms of phase between two waves.
Maxima and minima are produced when the path difference between waves is a whole number of wavelengths or an odd number of half wavelengths respectively.
Investigations which lead to the relationship between the wavelength,
distance between the sources, distance from the sources and the spacing between maxima or minima.

c) Gratings

Monochromatic light can be used with a grating to investigate the relationship between the grating spacing, wavelength and angle to the maxima.
A white light source may be used with a grating to produce spectra.
Compare the spectra produced by gratings and prisms.

6 Refraction of light

a) Refraction.

Refractive index of a material as the ratio of the sine of angle of incidence in vacuum (air) to the sine of angle of refraction in the material.
Refractive index of air treated as the same as that of a vacuum.
Investigations should include situations where light travels from a more dense to a less dense substance.
Refractive index as the ratio of speed of light in vacuum (air) to the speed in the material. Also as the ratio of the wavelengths.
Variation of refractive index with frequency.

b) Critical angle and total internal reflection

Investigating total internal reflection, including critical angle and its relationship with refractive index.

7 Spectra

a)Irradiance and the inverse square law.

Investigating irradiance as a function of distance from a point light source.
Irradiance as power per Unit area.

b)Line and continuous emission spectra,

Absorption spectra and energy level transitions
The Bohr model of the atom.
Electrons can be excited to higher energy levels by an input of energy.
Ionisation level is the level at which an electron is free from the atom.
Zero potential energy is defined as equal to that of the ionisation

level, implying that other energy levels have negative values.

The lowest energy level is the ground state.
A photon is emitted when an electron moves to a lower energy level and its frequency depends on the difference in energy levels.
Planck‘s constant is the constant of proportionality.
Absorption lines in the spectrum of sunlight as evidence for the composition of the Sun

Waves

A wave allows energy to be transferred from one point to another without any particles of the medium travelling that distance: e.g. Consider the water waves below:

Energy is transferred from points A to B where the boat feels the effect but the water does not move this distance. The energy in Radio and TV Waves (and all other members of the Electromagnetic Spectrum) are also transferred via this method though they do not require a medium.

Transverse Waves

A transverse wave is one in which the particles vibrate at 90o to the direction of motion of the energy.

Amplitude (m)crest

y

time (s)

trough

The particles of the medium vibrate along the direction X to Y whereas the energy is transferred along X - Z

The wavelength is the distance between similar points on adjacent waves eg. peak to peak (measured in metres - m)

The frequency is the number of waves that pass a point in 1 second and is measured in Hertz - Hz.

The amplitude is the distance from the line of zero amplitude to a peak or trough (A), this gives an indication of the amount of energy transferred.

The speed of a wave can be calculated via 2 equations:

v = d/t and v = f.

The PERIOD of a wave motion is the time for 1 wavelength to pass a point. As the frequency is the number of waves that pass a point in 1 sec then the period, T, must equal 1/frequency.

T = 1 / f

Example

Light of wavelength 4.5 x 10-7 m is reflected off a mirror. Calculate:

(a)the frequency of the light(6.67 x 1014 Hz)

(b)the Period of the wave motion and(1.5 x 10-15 s)

(c)the time it takes the light to travel 1.5m(5 x 10-9 s)

Wave Properties

Any wave motion can be REFLECTED e.g. light signals travelling down a Fibre Optic cable via total internal reflection but particles can also be reflected eg. a ball bouncing on a road.

All wave motions can be REFRACTED eg. light waves being focused onto the retina of an eye by a lens but particles can also be refracted e.g. a car travelling along the road shown below will change speed and direction when the wheels enter the mud.

AIR GLASSTARMUD

MOTION

Diffraction in waves can be illustrated by radio signals ‘bending’ into a valley yet particles can also exhibit diffraction.

When two or more COHERENT waves (same frequency, amplitude and phase difference remaining constant) overlap the phenomenon of INTERFERENCE is observed. It is extremely difficult to get 2 Coherent waves from 2 sources therefore a single source is used to split the waves up as shown:

We looked at two cases of interference: CONSTRUCTIVE and DESTRUCTIVE interference. For constructive interference to take place the waves must be Coherent and in Phase i.e. If we consider 2 coherent sources A and B then a crest from A arrives at exactly the same time as a crest from B and similarly 2 troughs arrive together:

CONSTRUCTIVE INTERFERENCE

DESTRUCTIVE INTERFERENCE

For destructive interference the waves are 180o out of phase i.e. a crest from A arrives at the same time as a trough from B and vice-versa. The two waves cancel each other out and the resultant is a dark band (no light).

In all cases, the displacements from the equilibrium line of each wave is added to give the displacement of the resultant wave, bearing in mind that displacement is a vector (so direction is very important). Destructive interference is the ‘test for a wave motion’ .

Young’s Slits

When we use light (or any other electromagnetic radiation) that is monochromatic, i.e. of one colour, it has the same frequency and wavelength throughout.

No particles can exhibit DESTRUCTIVE interference and so this is the test for a wave motion.

Applications

1)Some cars are fitted with a microcomputer and speakers that emit sounds 180o

out of phase with the road/engine noise so canceling them out and making the inside

of the car extremely quiet.

2)Holograms are basically interference patterns formed from a reference beam and

reflected beam.

Reference beam

Laser photo plate

3)Some birds’ feathers cause white light to be reflected and as some of the colours are out

of phase destructive interference occurs and the feathers appear to be coloured.

A thin film gives reflection at both surfaces and destructive interference occurs for some

wavelengths and so the remaining spectrum is seen. This is commonly seen in soapbubbles and a layer of petrol lying on a puddle.

5)Radio/T.V. Waves can be reflected off passing aircraft to a house antenna and thus

cause a flicker on the screen.

Radio/ TV transmitter

PATH DIFFERENCE

Consider the 2 coherent wave sources A and B, the waves meet at point X , obviously the waves from B travel a greater distance than those from A i.e. BX > AX.

The difference between the two

BX - AX is called the path difference (p.d.)

For constructive interference the p.d. must be a whole number of wavelengths and for destructive interference the p.d. = a half of no. of wavelengths:

for MAXIMA p.d. = mm = 0,1,2,3……

for MINIMA p.d. = (m + 0.5) 

Example

The two loudspeakers A and B, 1 m apart are connected to an oscillator of frequency 1700 Hz. A microphone is moved along the line RT and the first maxima is detected at T, 0.5 m from S. Calculate the speed of sound. (340 m/s)

Diffraction Grating

A DIFFRACTION GRATING is a large number of close parallel equidistant slits ruled on glass or metal. Typically the spacing, d, between each slit is of the order 1 x 10-6 m or of the same order as the wavelength as visible light.

If monochromatic light is shone onto a diffraction grating then the pattern below is obtained:

ie. a Principal maximum is obtained with less intense maxima either side of it. As the number of slits is increased the maxima become sharper. The maxima either side of the principal are called 1st order, 2nd order, 3rd order maxima......

(A C.D. acts as a diffraction grating when white light is shone onto it and it splits the light up into its spectrum)

The maxima are caused by constructive interference and the minima result from destructive interference.

Directly opposite the grating there will be a bright central maximum since the path difference is the same for all the waves ie. constructive interference .

At some angle  each wave is ahead of the next by 1 wavelength and so if these waves are brought together constructive interference occurs and a bright maxima is formed.

For the 1st order maxima light from slit 1 travels 1 wavelength further than that from slit 2 and so on for slits 3, 4, 5......

At other angles destructive interference takes place and dark bands (minima) are formed

Suppose aX and bY represent 2 diffracted rays then we can see that the path difference (p.d) between them is represented by bC.

Look at the right angled triangle acb and you can see that the length bc = d.sin 

(sin  = bc/d)

For constructive interference the p.d. = m

ie. m = d.sin

 = wavelength of light (m)

d = slit separation (m)

m = order of spectra

 = Angle of diffraction of light rays (degrees)

Example

Calculate the angle between the 1st order maxima on either side of the principal when violet light of wavelength 410 nm is shone onto a grating with 1.0 x 104 slits per cm. ( = 48.4o)

Calculate the maximum order of interference pattern viewed. (2nd)

Dispersion of White Light

White light is made up from a complete mixture of the various colours of the spectrum ie.

This splitting of white light into its spectrum is called DISPERSION and takes place as the different frequencies of light are refracted by different amounts at the air/glass and glass/air boundaries.

Colour of lightWavelength (nm) 1nm = 1 x 10-9m

Red660

Orange610

Yellow580

Green550

Blue470

Violet410

If a diffraction grating is used to split the white light up the spectrum is still obtained but the colours are ‘swapped’ around as shown above. We can see that the red end of the spectrum is diffracted more than the blue end whereas the reverse is true of the prism, ie. the blue end is refracted more than the red end.

Refraction of Light

Another example of dispersion occurs in Rainbows, in which refraction by water droplets give rise to colours. Rainbows are often seen when a storm is departing, if we look at the departing rain with the sun at our backs. When white light enters a spherical raindrop as shown below, light of each colour is refracted by different amounts. The light is reflected of the back surface of the drop and refracted again as it passes into the air again. Although each water drop disperses the light into its full spectrum we only see one colour from each drop since the one colour of light travels in the correct direction for our eye to see it. Of course we see all the colours as there are millions of drops of water at different elevations .

sunlight

Violet

Red

When a light ray leaves water and enters air it is REFRACTED. This makes the pond look shallower than normal ie.

To eye

Light rays from the fish travel to the surface where refraction occurs and the light is bent away from the normal. When these light rays enter the eye they appear to come from point A. ie. at a point actually above the real position, this is called a VIRTUAL image.

Expts. have shown that when light passes from one medium to another it is refracted ie. it changes speed

Light travels at 3 x 108 m s-1 in a vacuum and for our purposes we assume it travels at this speed in air (note that nothing with mass can travel faster than this) and so when the light enters eg. glass it slows up and bends towards the normal. On leaving the glass the light speeds up again and bends away from the normal.

Our expts. have shown that:

sin i / sin r = a constant

This constant is called the ABSOLUTE REFRACTIVE INDEX

ie. sin i / sin r = n1

The subscript 1 refers to the material e.g. ng is the refractive index for light passing from air/vacuum into glass.

ng can also be expressed as (speed of in air/speed in glass)

thus ng = sin i / sin r = vo/vg

Frequency and Refraction

We know that different colours of light are refracted by different amounts and so we can see that the refractive index of a material depends on the frequency of light used. We also know that different colours of light have different frequencies and so we should really quote frequency when talking about refractive indices.

ColourFrequency (x 1014 Hz)Refractive Index (Diamond)

Red4.542.410

Orange4.922.415

Yellow5.172.417

Green5.452.426

Blue6.382.444

Violet7.322.458

Air Glass