Quantum - Booklet - Student 8.2

Richard Howland Page 1 of 60 22 May 2013

PHYSICS

AS

Unit 1 Quantum Phenomena

Student Copy

Name: __________________________

Physics Group: _____________________


Contents

Lesson Page Number Contents

Lesson 1 3 11 The Photo-electric Effect

Lesson 2 12 - 15 Stopping Potential

Lesson 3 16 - 25 Energy Levels

Lesson 4 26 - 30 Emission and Absorption Spectra

Lesson 5 31 - 38 Wave-Particle Duality

Lesson 6 39 - 42 Fluorescent Tubes

Lesson 7 43 - 48 This is only REAL if it is observed

Appendix 1: Specification (Quantum Phenomena) p. 49

Appendix 2: Conversions of Units p. 50

Appendix 3: Prefixes p. 51

Appendix 4: Is light a Particle or Wave? pp. 52 54

Appendix 5: The Ultra-Violet Catastrophe pp. 55 59

Appendix 6: The Electron-Volt p. 60


Lesson 1: The Photo-electric Effect

Point 1: Discovery of the Photo-electric Effect

In 1887, the physicist Heinrich Hertz discovered that a spark (discharge of

electrons) moved more easily if Ultra-Violet light was shining on the

electrodes.

A year later (1888), the physicist Wilhelm Hallwachs (assistant to Hertz) did

additional research and stated that:

Negatively Charged Zinc Plates lose their charge when illuminated by Ultra

Violet light but there is no effect if the plates are Positively Charged.

He concluded that UltraViolet light causes the plates to emit negative

charges.

In 1899, physicist Philipp Lenard showed that negative charges in the Photo

Electric Effect are electrons.

Point 2: Understanding the Photo-electric Effect

Electromagnetic Radiation carries energy from one place to another (a progressive

wave). When the EM Radiation is shone onto the SHINY Zinc Plate, the electrons

absorb the energy. According to Classical Physics (pre 1900), the electrons should

continuously absorb energy from the EM Radiation until they have enough energy to

leave the Zinc Plate.

In other words, given enough time, the electrons would have absorbed enough energy

to escape the metal. They would also need some extra energy (in the form of Kinetic

Energy) to actually move away from the Zinc Plate.

UltraViolet light


The Equation for this process is:

Where:

E = The Energy absorbed from the EM Radiation.

= Work Function (this is the Minimum Energy needed to escape from the Zinc).

KEmax = the extra energy the electrons need to actually move away from the metal

(There is a range of Kinetic Energy since the electrons can lose energy in

collisions while trying to leave the metal. The Maximum KE is where the

electron doesnt lose any energy in trying to leave.)

In this experiment the following variables were changed (one at a time)

The Intensity of EM Radiation (Intensity is Power per Unit Wavelength per

Unit Area).

The Frequency of EM Radiation.

The Work Function is always the same for Zinc since it is a property of Zinc and not

the electrons or EM Radiation. So Lenard measured the Maximum KE of the emitted

electrons (since this was the dependent variable).

If the laws of Classical Physics are correct, then the following results would be

expected:

The more time that elapses, the more EM Radiation is absorbed.

Eventually electrons should be released.

The Maximum KE of the electrons should depend on the Intensity of the EM

Radiation (more EM Radiation means more Energy absorption and since the

Work Function is constant, only the KE of the electrons will vary).

The Maximum KE of the electrons should not depend on the frequency of the

EM Radiation (in Classical Physics, frequency is not a factor of the EM

Radiations energy).

E = + KEmax


Point 3: The actual results of the Photo-electric Effect

In 1902 Philipp Lenard published his results and they astounded the world of Physics.

The passage below is the experimental results obtained by the physicist Philipp

Lenard in 1902 (awarded the Nobel Prize in 1905).

The electrons were only emitted when UV Radiation was shone on the Zinc

Plate and they were emitted instantly.

The electrons were not emitted for any Intensity of Visible Light regardless to

how long it was shining.

The Maximum KE of the electrons was independent of the Intensity of UV

Radiation.

The Maximum KE of the electrons was dependent on the frequency of the UV

Radiation.

Number of electrons emitted is proportional to the Intensity of UV Radiation.

The Photoelectric effect defied the laws of physics for the following reasons:

It suggested that the colour of light determined its energy.

Energy was not continuously absorbed it was instant or never happened.

The intensity of UV light only affected the number of emitted electrons and

not their Kinetic Energy.

KEY POINTS

Lenard showed with real data that the known laws of physics did not work.

The Photoelectric effect defied the laws of Classical Physics since it suggested

that the colour of light determined its energy in Classical Physics all EM Radiation

had the same energy.

This experiment is showing that the FREQUENCY of EM Radiation determines its

energy.

It also tells us that there is no continuous absorption of energy otherwise the

electrons would eventually gain enough energy to leave the Zinc.


Point 4: Einsteins solution to the Photo-electric Effect

The Solution came from Albert Einstein. He proposed the use of Max Plancks

equation E = hf. This may not seem like a giant leap in Physics, but it was

The equation E = hf states that light isnt continuously absorbed; instead it is either

absorbed in one chunk (called quanta) or not at all.

For instance, if you ate a bar of chocolate

In the Classical World of Physics, you would eat the chocolate piece by piece

(or if you were really hungry/greedy all at once). Your body would then break

the chocolate down into individual atoms and molecules and process them.

In the Quantum World of Physics, you would eat the chocolate and instantly

have all the atoms and molecules exactly where they should be. No time would

be required for this to happen. It would be instant or you would never be able

to eat the chocolate.

The Equation for Photoelectric Effect

In 1905, Einstein used the Equation E = hf and put it into the Photo-electric

equation:

Becomes:

Where:

E = hf = the Energy of the EM Radiation

= Work Function = the Minimum Energy required to emit the electron from the metal

KEmax = the Maximum excess energy of the electron when it leaves the metal

E = + KEmax

hf = + KEmax


Point 5: To find h and

Using the form:

y = mx + c

y = KEmax

x = f

c = m = h

Photoelectric Effect Graph

KEY POINTS

The Gradient is always Planks constant, h (6.63x10-34 Js)

The intercept on the x-axis, f0 is the Fundamental Frequency (the MINIMUM

frequency required to emit electrons).

The intercept on the y-axis (below Zero) is the Work Function, (which is the MIMIMUM energy required to emit electrons).

hf = + KEmax

Rearrange the

equation

KEmax = hf

f / Hz

KEmax / J

f0

Gradient = y / x = h

f0: Fundamental Frequency


Point 6: Questions

Question 1

Define the following:

a) Quanta:

b) Photon:

c) Work Function:

d) KEmax:

Question 2

The frequency of the incident radiation = 1.8x1015 Hz, Maximum KE of electrons = 3.3

eV. Calculate the Work Function of the Metal (in Joules and eV).

[6.6x10-19 J,4.1 eV]

Question 3

The frequency of the incident radiation = 6.2x1014 Hz, Work Function of the Metal =

2.4 eV. Calculate the Maximum KE of the emitted electrons (in Joules and eV).

[3.0x10-20 J,0.2 eV]


Question 4

The Work Function of the Metal = 4.8 eV. Calculate the minimum frequency of the

incident EM Waves to release the electrons. [1.2x1015 Hz]

Question 5

Each photon has the same energy (frequency is constant). So why is there a range of

Kinetic Energy (up to a maximum)? [Hint: Where is the energy going?]

Question 6

The wavelength of the incident radiation = 700 nm, the Work Function of the Metal =

7.1x10-19 J. By performing a calculation, explain why electrons would not be emitted

from the material. [2.84x10-19 J]

If the classical wave theory was correct, then after a period of time, the electrons

would have continuously absorbed enough energy to be released. If the light was

shone onto each atom of the metal at a rate of 2 photons per second, how long would

it take (through continuous absorption) for the electrons to get enough energy to

leave the metal? [1.25 s]


Question 7

Explain why the Classical Laws of Physics do not explain the Photo-Electric Effect

but the Quantum Laws of Physics (E = hf) do explain the Photo-Electric Effect.

(Your answer should also include the key observations of the experiment).


Point 7: The Problem with Classical Physics (pre 1900)

So what exactly is the Big Deal with the Photo-electric Effect?

Example- Cooking a Chicken in an oven

Classical Physics:

Controls: Temperature and Time.

Set the temperature and then wait an appropriate amount of time for the

chicken to cook.

The higher the temperature you set, the more waves are sent into the oven and

the chicken will cook faster.

The longer you leave the chicken in the oven, the more waves of energy that

are absorbed and the more the chicken is cooked.

But the Chicken isnt cooking.

No matter how long the chicken is left in the oven, nothing happens.

No matter how hot the oven is, nothing happens. Ever!

Quantum Physics: The controls are the Frequency of the EM Waves.

Controls: Frequency of the EM Waves.

Below a certain FREQUENCY, the chicken never cooks no matter how long it is

in the oven.

Once a certain (THRESHOLD) FREQUENCY is reached, the chicken cooks

INSTANTLY!


Lesson 2: Stopping Potential

Point 1: The Problem

To verify Einsteins view of the Photo-electric effect, we need to measure the

Maximum Kinetic Energy of the emitted electrons. That would mean measuring their

mass and velocity as they leave! This would be an extremely difficult task today so it

would have been impossible in 1905.

A different approach is needed. We need to know the electrons Maximum Kinetic

Energy by any method. And the following is the method used to do just that.

Point 2: The Solution

Rather than finding the Kinetic Energy of the Electrons as they leave the Zinc, a

circuit is set up like this:

As the electrons leave the Cathode, they hit the anode and create a Current. The

Potential Difference generated between the Cathode and Anode can be measured.

- -

- -

cathode anode

- +

Ultraviolet

Power

Supply

A DIODE

Electrons can

only flow this

way


The technique used is to apply a REVERSE Potential Difference. If the same size

reverse Potential Difference is applied, no electrons will move, so the Current will be

zero. We can record the value of this reverse voltage (Stopping Potential) and from

this find the Work Function, Fundamental Frequency and a value for Plancks

constant. We want the REVERSE Potential Difference to JUST STOP the electrons.

Point 3: Stopping Potential

The definition for the Volt is:

1 Volt = 1 Joule per Coulomb of Charge

If we re-arrange the equation:

1 Joule = Charge on 1 electron x 1 Volt

From this, we can say that:

Energy gained by an electron = Charge on 1 electron x Potential Difference

In symbols:

E = eV

The Stopping Potential is the Voltage needed to JUST STOP the electrons from

moving. When this is multiplied by e (charge on an electron) we have the Kinetic

Energy of the electrons (in Joules).

So: eV = KEmax

So all we do is multiply the Voltage reading on the Power Supply by the charge on 1

electron.

For example, if the Voltage (Stopping Potential) is 1.2 V,

Then the Maximum Kinetic Energy is 1.2 eV

Or, 1.2 x 1.6x10-19 J = 1.9x10-19 J


Point 4: Questions

1) Which part of the EM Spectrum causes the Photo-electric Effect?

2) Why wont visible light work?

3) Why must the Zinc be SHINY?

4) Why is a DIODE placed in the circuit?

5) Why will a REVERSE Potential Difference reduce the current?

6) What is the definition of Stopping Potential?

7) If the Reverse Potential Difference is larger than the energy supplied by the

UV photons, will the electrons travel in the opposite direction in the circuit?

Explain your answer.


Point 5: Graph

frequency / 1015 Hz Stopping Potential / V

1.05 0.03

1.10 0.24

1.15 0.44

1.20 0.65

1.25 0.86

1.30 1.06

1.35 1.27

1.40 1.48

1) Plot a graph of Frequency (x-axis) against Stopping Potential (y-axis).

2) What is meant by the term Fundamental Frequency?

3) From your graph, obtain a value for the Fundamental Frequency.

4) Find the gradient of your graph.

5) How can you use this value for the Gradient to obtain a value for Plancks

Constant? Clearly show your working.

6) How does your value for Plancks constant compare to the published value?

7) What is meant by the term Work Function?

8) Use your graph and calculated values to obtain a value for the Work Function

of the metal (in J and eV). Clearly show your working.


Lesson 3: Energy Levels

Point 1: The origin of atom

The following is taken from: http://en.wikipedia.org/wiki/Atom

The earliest references to the concept of atoms date back to ancient India in the

6th century BCE. The Nyaya and Vaisheshika schools developed elaborate theories of

how atoms combined into more complex objects (first in pairs, then trios of pairs).

The references to atoms in the West emerged a century later from Leucippus whose

student, Democritus, systemized his views. In approximately 450 BCE, Democritus

coined the term tomos, which means "uncuttable" or "the smallest indivisible particle

of matter", i.e., something that cannot be divided. Although the Indian and Greek

concepts of the atom were based purely on philosophy, modern science has retained

the name coined by Democritus.

Summary

Everything is made up of an indivisible particle: the atoma

Point 2: Alchemy

The following is taken from: http://en.wikipedia.org/wiki/Alchemy

The best-known goals of the alchemists were the transmutation of common metals

into gold (called chrysopoeia). Certain Hermetic schools argue that the transmutation

of lead into gold is analogical for the transmutation of the physical body (Saturn or

lead) into Solar energy (gold) with the goal of attaining immortality. This is described

as Internal Alchemy. Starting with the Middle Ages, Arabic and European alchemists

invested much effort in the search for the "philosopher's stone", a legendary

substance that was believed to be an essential ingredient for either or both of those

goals. Alchemists were alternately persecuted or supported through the centuries.

Summary

The key for alchemists was that they believed that you could chemically change one

element into another because they believed that everything was made of the SAME

ELEMENT. Even Sir Isaac Newton tried this (for a while) and failed. No-one was able

to change one element into another through chemical change.


Point 3: The Dalton view of atoms The following is taken from: http://en.wikipedia.org/wiki/Atom

In 1803, English instructor and natural philosopher John Dalton used the concept of

atoms to explain why elements always react in a ratio of small whole numbers: the

law of multiple proportions, and why certain gases dissolve better in water than

others. He proposed that each element consists of atoms of a single, unique type, and

that these atoms can join together to form chemical compounds.

Summary

There are different types of atoms. Gold is made from Gold Atoms and Silver is made

from Silver atoms. This explained why the Alchemists had failed to turn one element

into another.

Point 4: The JJ Thomson view of atoms

The following is taken from: http://en.wikipedia.org/wiki/Atom

The physicist J. J. Thomson, through his work on cathode rays in 1897, discovered

the electron and its subatomic nature, which destroyed the concept of atoms as being

indivisible units. Thomson believed that the electrons were distributed throughout

the atom, with their charge balanced by the presence of a uniform sea of positive

charge (the plum pudding model).

Summary: The Plum Pudding Model

The atom has a large positive charge and electrons are stuck on top of this object.

Large centre of

positive charge

Small Negative charges

stuck on the positive charge

Gold Silver


Point 5: Rutherfords Alpha Scattering Experiment

In 1909, Ernest Rutherford published results on work that his team of researchers

had been doing at the Physics Laboratories at Manchester University. The team fired

alpha particles at a piece of Gold Leaf and then measured how many alpha particles

were detected at different places around the Gold Leaf.

The results showed something that was completely unexpected:

Result: The Majority of the Alpha Particles went straight through.

Explanation: Most of the Gold Leaf is empty space: so the Atoms must be far apart.

Result: A few of the Alpha Particles were deflected.

Explanation: Centre of the Atoms was the same charge as Alpha Particles (Positive).

Result: 1 or 2 Alpha Particles came straight back.

Explanation: High concentration of material in the Nucleus.

This meant that the Plum Pudding Model of the atom had to be wrong. The alpha

particles couldnt travel through the atoms if atoms were solid!

Tiny positive charge

(about 10-15 m in diameter)

Tiny negative charge at a

distance of 10-10 m away

from the nucleus


Point 6: The problem the Atom shouldnt work!

In 1862, James Clerk Maxwell published (the now famous) Maxwell Equations of

Electromagnetism. These equations unified (joined) the equations and laws of

Magnetism, Electricity and Electromagnetism.

From these equations, there are 2 key points that are important for understanding

why this new model of the atom shouldnt work:

Opposite charges attract, like charges repel

Accelerating charges emit or absorb energy

With J.J. Thomsons Model

The charges are touching each other, so none of the 2 laws of electromagnetism are

broken.

With Rutherfords Model

The 2 opposite charges are separated. Both these charges are attracted to each

other, so they should move towards each other. But that would mean that they cant

stay apart which is what every experiment was showing.

Large centre of

positive charge

Small Negative charges

stuck on the positive charge

Tiny positive charge

(about 10-15 m in diameter)

Tiny negative charge at a

distance of 10-10 m away

from the nucleus


Point 7: A solution that shouldnt work

An obvious idea is that the electrons could orbit the nucleus in the same way that

planets orbit the sun. The opposite charges are attracted to each other but because

they are in orbit, they never touch.

However

Accelerating Charges

We know from Maxwells Theory on Electromagnetic Waves that if a charged

particle accelerated, it emitted or absorbed Energy.

If the electron is orbiting, then it is constantly changing its direction, so it is

constantly changing its velocity, so it is accelerating.

From Electromagnetism, if a charged particle accelerates, it emits

electromagnetic radiation.

Electromagnetic Radiation contains energy.

If the charged particle emits Electromagnetic Radiation, it is losing energy.

If it loses energy, it will slow down, and so it will fall closer to the atom since it

isnt going fast enough.

The charged particle will fall towards the nucleus.

The time taken for this is about 10-7 seconds.

Electrons cant Orbit

The new model of the atom doesnt work.

Electrons cant orbit the nucleus.

But there is no other mechanism for two oppositely charged particles to stay

apart other than to orbit each other.

But charged particles cant travel in circles without losing energy.

Electrons cant orbit.

Orbiting electrons are unstable.

But clearly, the electrons are 10-10 m away from the nucleus otherwise there

wouldnt be chemical reactions.

And we do know that electrons have set positioning (Shells).

Acceleration

Electromagnetic radiation


Point 8: Niels Bohrs Solution for Rutherfords Experiment

Electrons cant orbit!

And they cant stand still!

In a desperate attempt to solve this problem, many physicists looked at the data of

the frequencies of emitted photons to try and find patterns. In 1911, a physicist

called Niels Bohr added to Rutherfords model of the atom by suggesting that

electrons orbit the nucleus but ONLY in CERTAIN PLACES.

He noticed that the different frequencies of emitted photons could be written as

multiples of E = hf. So he proposed that the emitted photons were governed by the

equation E = hf From this, he produced his theory and new model of the atom. He

received the Nobel Prize in 1922 for his contribution to this work.

Point 9: The Niels Bohr View of the Atom

Electron Shells

Electrons can orbit a nucleus only if they go in a certain place.

When electrons move from one place to the other, they release or absorb a

photon which contains 1 Quantum of Energy.

So when electrons moved from one place to another, a Quantum of energy

was released or absorbed.

The Niels Bohr Atom

Electrons orbit the nucleus in Electron Shells.

The Shells are Discrete and not Continuous.

Shells are also referred to as Orbitals and Energy Levels.

Electrons are only ever found in these places and

for some unknown reason (an answer came many years

later) they can orbit the nucleus and not emit

energy.


Point 10: Energy Levels in Atoms

Energy Levels in the Hydrogen Atom

Ground State

Excited States

Ionisation

13.6 eV

3.4 eV

1.5 eV

Electron is in the next Energy Level

it has gained energy (E = hf = 10.2 eV)

(Energy values are for Hydrogen).

Ground State (n = 1)

Excited States (n = 2, 3, 4 )

Ionisation ( n = )

13.6 eV

3.4 eV

1.5 eV

Electron is in the lowest Energy Level



At ionisation, there is no attraction between the nucleus and freeelectron

(within the atom) so the energy between them is ZERO.

The numbers are negative since you gain energy to go up an Energy Level, and

the final energy has a value of ZERO.

Absorption of Energy

When Electromagnetic Radiation is absorbed by the electron, it can do so only

by following the equation E = hf.

An electron can be raised to ANY Energy Level (shell) provided that it

corresponds to the equation E = hf.

Emission of Energy

When Electromagnetic Radiation is emitted by the electron, it can do so only

by following the equation E = hf.

An electron can be lowered to ANY Energy Level (shell) provided that it

corresponds to the equation E = hf.

Ground State

Excited States

Ionisation

13.6 eV

3.4 eV

1.5 eV

Electron is Ionised it has gained energy (E = hf = 13.6 eV)



Point 11: Questions

1) An electron is in the Ground State in a Hydrogen atom and absorbs a photon. It

is now in the 1st Energy Level (n = 2). What was the frequency of the absorbed

photon? [f = 2.5x1015 Hz]

2) An electron is in the 2nd Energy Level (n = 3) of a Hydrogen atom. It eventually

falls down to the Ground State. Deduce the 2 different mechanisms for falling

to the ground state and the frequencies of the photons released in each of the

possible processes. [f = 2.9x1015 Hz, f = 4.6x1014 Hz & f = 2.5x1015 Hz]

3) A photon is absorbed by an electron in the Ground State of a Hydrogen atom.

If the Hydrogen is just ionised, calculate the wavelength of the absorbed

photon. [ = 9.1x10-8 m]

4) Why are Energy Levels written with a - sign?


5) How many Energy Levels are there between the Ground State and Ionisation?

What can you say about the Energy Gap between these levels as you approach

Ionisation?

6) When the electrons are given or lose energy (in the form of an absorbed or

emitted photon), how does the electron actually get from one Shell to another

if it is not allowed to exist between Shells?

7) Explain how a light bulb shines when electricity is passed through it. Also

explain why the light bulb appears white.


Lesson 4: Emission and Absorption Spectra

Point 1: The Emission Spectrum

When an electron drops down an energy level, a single photon is released.

A Spectrum means that a range of frequencies of different photons are

released this requires many electrons to be falling which means many atoms

have to be present.

The Spectrum produces many single lines each line corresponds to an electron

that has fallen down an energy level.

Photons are then emitted in any (random) direction.

Point 2: The Continuous Spectrum

Technically, a CONTINUOUS VISIBLE SPECTRUM does not exist.

This is every frequency of Visible Light.

Although there are an infinite number of Energy Levels in any atom, only

certain drops correspond to visible radiation.

This means that there is a limited amount of Energy drops available which

produce Visible light photons.

Hot objects not only emit light (through electrons falling down energy levels)

but their atoms vibrate vigorously this means that as the photons are

emitted, they are Doppler shifted.

This Doppler Effect means that individual emission lines are broadened.

Objects which produce Continuous Spectrums are called Black Bodies.


Point 3: Questions

1) What is meant by the term Spectrum?

2) Explain (in full detail) how an Emission Spectrum is produced.

3) Which direction are photons released?

4) What (exactly) is a Continuous Spectrum?

5) Why (in reality) can a Continuous Spectrum not exist?

6) What are the (theoretical) objects called that emit a Continuous Spectrum of

Photons?

7) Name an object that (almost) produces a Continuous Spectrum.


Point 4: Spectral Lines

Each material/atom produces a unique set of Spectral Lines.

This is used to identify unknown elements and compounds through a process

called Spectroscopy.

The element Helium was first discovered by using Spectroscopy on sunlight

the name Helium is derived from Helios (the Sun God).

The following is a series of photographs taken from a variety of elements that are

emitting photons.

Website link: Strasbourg Astronomical Observatory

http://astro.u-strasbg.fr/~koppen/discharge/index.html

Hydrogen

Carbon

Oxygen

Sodium

Iron

Silicon

You can clearly see that each element has its own unique bands of emission lines.

Sodium has a very distinctive YELLOW line which can be clearly seen with older

street lamps.

Hydrogen has distinctive Purple, Cyan and Red lines which can be clearly seen in

Nebula in space.

When you see a fireworks display, all the different colours correspond to

different metallic elements which have their electrons excited. When the

electrons jump down Energy Levels, photons with the above colours are emitted

in random directions.


Point 5: The Absorption Spectrum

This occurs through a combination of a Continuous Spectrum passing through a

material and that material producing an Emission Spectrum.

If a stream of photons from a Black Body Source passes through a material,

the electrons in the atoms of the material will absorb certain photons of a

particular frequency and jump up Energy Levels.

Some time later, these electrons will jump back down and emit photons.

These photons are emitted in different directions randomly.

The amount of photons that pass straight through the material (without being

absorbed) is far greater than the number of emitted photons from the

material.

As a result, these emitted photons appear as darker lines in the resultant

spectrum that passes through the material.

Important note

These lines are darker and not black! There are photons there, but far less than

non-absorbed photons from the rest of the continuous spectrum.

This diagram is taken from: Oglethorpe University

http://www.oglethorpe.edu/faculty/~m_rulison/Astronomy/Chap%2004/Light%20an

d%20Matter%20II.htm

A hot source is an object

where the atoms are vibrating

enough to excite electrons to

higher energy levels.

So stars, light-bulbs, &

flames are hot sources


Point 6: Questions

1) Explain how an Absorption Spectrum is produced.

2) Explain why:

a. A star produces a Continuous Spectrum

b. A glowing (hot) Gas Cloud produces an Emission Spectrum

c. A stream of photons passing through a cold Gas Cloud produces an

Absorption Spectrum


Lesson 5: Wave-Particle Duality

Point 1: What are Waves and Particles?

Wave Behaviour Particle Behaviour

Non-Localised

(not fixed in a particular place)

Localised

(In a fixed position)

No mass (Can) Have mass

No charge (Can) Have charge

Interference & Superposition

(Can pass through each other)

Collisions

(Cant pass through each other)

Diffraction

(Waves spread-out after passing

through a gap)

No Diffraction

(Objects stays fixed in shape)

Polarisation

(Transverse waves only) N/A

As can be seen from the table, Wave behaviour and Particle Behaviour are exactly

opposite.

Point 2: Louis de Broglie

After considering the fact that Electromagnetic Waves can behave like particles (in

the form of photons), Louis de Broglie considered the idea that objects considered to

be particles could behave like waves.

He applied equations from Special Relativity (by Einstein) and combined them with

Plancks equation: E =hf to produce:

/ m: The associated wavelength of the object.

h / J s: Plancks constant (6.63 x 10-34 J s).

p / kg m s-1: momentum of the particle (p = mass x velocity).

His interpretation was that every moving particle has an associated wave. He called

this a MATTER-WAVE. From this, a new branch of physics emerged: Quantum

Mechanics. De Broglie received the Nobel Prize in 1929 for his contributions to

Quantum Physics.

= h / p


Point 3: Questions

For the following particles, calculate the associated wavelength of the matterwave:

1) Mass of electron = 9.11x10-31 kg, velocity = 3.00x107 m s-1

[ = 2.43 x 10-11 m]

2) Mass of electron = 9.11x10-31 kg, velocity = 2.60x108 m s-1

[ = 2.80 x 10-12 m]

3) Mass of proton = 1.67x10-27 kg, velocity = 3.00x107 m s-1

[ = 1.32 x 10-14 m]

4) Mass of atom = 1.00 x10-26 kg, velocity = 1000 m s-1

[ = 6.63 x 10-11 m]

5) Mass of a person = 64.5 kg, velocity = 1.00 m s-1

[ = 1.03 x 10-35 m]

Point 4: What does this mean?

Since h is so small (6.6x10-34 Js) we dont notice the effect of the matter-waves on

everyday objects because the associated matter-waves are too small to detect

(but they are still there).

However, in the atomic world, the associated matter-waves are much larger and of a

comparable size to the space in which these particles exist.

On the atomic level, we cant ignore the matter-waves and the WAVE-PARTICLE

DUALITY ALWAYS has to be considered!


Point 5: What if Plancks constant was 100 Js?

For a typical person: Mass = 70 kg, Velocity = 1 m s-1 (walking pace)

New h = 100 J s

= h / p = 100 / (70 x 1) = 1.4 m

The associated wave would have a wavelength of 1.4 m. This is about the width of a

corridor.

So if you walked through a corridor and someone else walk towards you, you would

pass through each other and the result would be the addition of your heights!

Point 6: The Electron Diffraction Experiment

If matter-waves are real, then particles should show wave behaviour under the

right conditions. And experiment can be done to validate this idea of wave-particle

duality.

Particle Behaviour

If the electron behaves like a particle throughout the experiment, then it will hit the

screen in any location. If we record the position that the electron hits the screen

then the majority should hit the screen opposite each gap.

Wave Behaviour

If the electron behaves like a wave, then it will interfere with itself and there will be

an interference pattern produced on the screen. The electron will not appear on some

parts of the screen because it will destructively interfere. There will be a series of

light and dark patches on the screen corresponding to a Double-Slit interference

pattern for waves.

Electron

going into 1

gap of the

Double Slit

Electron hits

the screen


Point 7: The Hitachi Experiment

The Hitachi Coporatation have designed and built equipment to test this theory.

The weblink is: http://www.hitachi.com/rd/research/em/doubleslit.html .

This is a diagram of the equipment used by Hitachi:

This is a time-lapse recording of their results:


Point 8: Electron Diffraction What does this mean?

As can be clearly seen, there is an INTERFERENCE PATTERN on the screen. This can

ONLY be created by WAVE BEHAVIOUR. This means that the electrons must be

behaving like waves at some point during the experiment.

At the Double-Slits

The electron has to enter through one of the slits. This is particle behaviour since

the electron is localised (in one position/location).

At the Screen

The electron hits one part of the screen. This is particle behaviour.

Between the Double-Slits and the Screen

Since an Interference Pattern is created on the screen, the electron must be

behaving as a wave between the Slits and the Screen. This is the only explanation for

producing the interference pattern.

This experiment demonstrates and proves that electrons can behave like particles

and waves! (Not at the same time).

This is known as WAVE-PARTICLE DUALITY.

This experiment has also been done for protons and neutrons both show Wave-

Particle Duality. Scientists have also been able to show Wave-Particle Duality for

small numbers of Sodium Atoms.

The world is not as it appears to be!

Point 9: Waves and Particles

This experiment (and the Photo-electric Effect) shows that there is no such thing as

waves or particles. There is Wave Behaviour and Particle Behaviour but

Electromagnetic Radiation, electrons, protons, neutrons, nuclei, atoms, etc cant be

pigeon-holed into the categories of wave or particle.

Sometimes they behave like waves and at other times they behave like particles.


Electron Diffraction Experiment

Particle

behaviour

Particle

behaviour

Wave

behaviour

Electron hits the

screen and

releases a photon

Electron going

into 1 gap of the

Double Slit


Point 10: Exam Question

1) Explain how the Double-Slit experiment for electrons demonstrates Wave-

Particle Duality. (You must clearly state what the evidence is and whether this

indicates particle or wave behaviour).

2) Explain the Dual nature of EM Radiation (in terms of Wave-Particle Duality)


Point 11: The Quantum World

The equation E = hf indicates that energy and interactions are QUANTISED. This

means that these interactions are DISCRETE (only specific values are allowed).

In the world of Classical Physics (before the equation E = hf was realised) all

interactions were CONTINUOUS (every value was allowed).

The Atom

The difference between Discrete and Continuous is important. For the atom,

electrons only exist on Energy Levels not in-between. This means that they have to

(somehow) instantaneously disappear and reappear in a different position.

Then there is the issue of PROBABILITY. In the atom, when an electron drops down

an Energy Level a photon is emitted in a RANDOM direction. There is no way to

determine (in advance) which direction the photon will travel. In Classical Physics, we

would always be able to work out where the photon would go in advance.

Also, if the electron is able to fall down more than one Energy Level, there is no way

to predict the method that it will use to (eventually) reach the Ground State. Nor

how long it will take to perform this task.

The Electron Diffraction Experiment

In the Electron Diffraction experiment, the electrons have to interfere with each

other to produce the Interference Pattern. But, the electrons are sent through one

at a time.

So what are they interfering with, if there is only 1 electron in the experiment?

Can the electron really be in two places at the same time?

Classical and Quantum Worlds

In the world of Classical Physics, the equations/laws give you an exact set of answers

to a problem.

In Quantum Physics, the equations/laws give you a probability of an answer occurring.

And it is the probability issue that EINSTEIN hated. He refused to believe that

events only had a probability and that nothing was ever certain.

Think about it it means that if you run into a wall, there is only a probability that

you will bounce back! You could appear at the others side! Or in Paris!


Lesson 6: Fluorescent Lamps

Point 1: The Fluorescent Tube

The central part of a fluorescent lamp is a sealed glass tube.

The tube contains a small bit of mercury and an inert gas (typically argon). This inert

gas is kept under very low pressure to avoid too many internal collisions with free-

electrons (the free-electrons need to get from one end of the tube to the other).

The tube also contains a phosphorus 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 is hooked up to an alternating current (AC) supply.


Point 2: Producing Ultraviolet photons

When you turn the lamp on, 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.

These free-electrons will collide with the liquid Mercury and transfer energy. This

energy changes some of the Mercury in the tube from a liquid to a gas.

As electrons and charged atoms continue to move through the tube, some of them will

collide with the gaseous mercury atoms. These collisions excite the atoms, bumping

electrons (of the gaseous mercury atoms) up to higher energy levels.

When the electrons return to their original energy level, they release photons. The

electrons in mercury atoms are arranged in such a way that they mostly release

photons in the Ultra-Violet wavelength range.

Point 3: Producing Visible Photons

Phosphors are substances that give off light when they are exposed to Ultra-Violet.

When an Ultra-Violet photon hits a phosphorus atom, one of the phosphorus'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 (Infra-Red).

In a fluorescent lamp, the emitted light is in the visible spectrum: the phosphor gives

off white light (range of frequencies) we can see. Manufacturers can vary the colour

of the light by using different combinations of phosphors.

Point 4: Questions

1. Why does a current flow across the electrodes in the tube?

2. Which inert gas is usually placed inside the tube?


3. Give 2 reasons why this gas is in the tube.

4. Why is the gas kept at a low pressure?

5. Why is the mercury a liquid at the start of the process?

6. Why does the mercury turn into a gas?

7. What happens to the electrons in the gaseous Mercury atoms when the free-

electrons hit them?

8. What happens next in the mercury atoms?

9. What happens to the electrons in the phosphorus atoms when Ultra-Violet

photons hit them?

10. What two types of photons are being (mainly) emitted when the electrons

return to the ground state? How do you know this?


Point 5: Longer Exam Question

You are going to explain why the Classical Wave Theory does not explain the

observations of the Photoelectric Effect but the Photon Model of Light does explain

the observations.

[To answer this question thoroughly, the following KEY WORDS must be in your

explanation: Ultra-Violet Photons, Shiny Zinc, Maximum Kinetic Energy, Work

Function, Electrons, Continuous Absorption, Intensity, Quanta, Photons,

Instantaneous].

Part 1 What is the physics of the Photo-electric Effect?

Part 2 Why does Classical Physics FAIL to explain the observations?

Part 3 Why does Quantum Physics explain the observations?


Lesson 7: This is only REAL if it is observed

If you do; you dont.

If you dont; you do.

Understand; that is!?

Point 1: The Atom

1) Instantaneous jumps.

When an electron absorbs a photon, it is not allowed to travel from one Energy

Level to another. It has to instantaneously vanish from its current Energy Level

and then appear in its new Energy Level.

So if you were an electron, and the seats in the room where Energy Levels, you

wouldnt be able to move until a photon arrived with the EXACT energy required to

move you from your existing seat to another. You then absorb that photon and

instantly teleport to another seat.

2) What are you looking at?

To see an atom, an electron jumps down Energy Level(s) and emits a photon. That

photon is then detected by your eye. You dont see atoms or electrons. The

photon is the result of the electron losing energy. You dont see anything.

Look at your hand. The photons that come from your hand are from electrons

falling down Energy Levels.

You never see anything!

3) How do electrons wave?

How can electrons be waves? What is waving?

You are made of electrons are you a wave?

And if protons, neutrons and everything else can behave as waves, what exactly

are all these particles that we are made of?


Point 2: The Electron Diffraction Experiment

1) Can electrons be in 2 places at once?

In the Electron Diffraction experiment, an interference pattern appears on the

screen. But this is only possible if the electron wave interferes with another

IDENTICAL electron wave. But the electrons are sent through one at a time. So

what is the electron wave interfering with?

Can the electron be in 2 places at the same time?

You could argue that the electron waves are SPREAD OUT. So when the electron

passing through the Double-Slit it is spread out across both slits hence

producing 2 Electron-Waves.

Unfortunately, when the electron passes through the slit it is acting as a particle

since this is a localised event. So it would need to pass through both slits at the

same time!

2) Electrons know you are looking at them!

We are PHYSICISTS!

Lets do an experiment!

Lets find out if electrons can go through 2 slits at the same time!

The experiment is simple:

Experiment 1: Observe the electrons passing through the slits (and see which slit

they go through) and then observe the pattern on the screen.

Experiment 2: DO NOT observe the electrons passing through the slits and then

observe the pattern on the screen.

Results:

Experiment 1: The interference pattern disappears the electrons behave as

particles at all times.

Experiment 2: The interference pattern appears.

The electrons only behave as waves when you DO NOT look at them!

How do electrons KNOW that you are looking at them?


3) Electrons know what you are going to do before you do!

Again, we are physicists how can electrons know that you are looking at them?

This is nonsense. Lets do a new experiment.

Lets put the screen much closer to the Double-Slits and then move the

experiment much further away. This now means that the electrons will hit the

screen BEFORE a photon will travel to us to tell us which Slit the electron passed

through.

This means that the electron will have passed through the Double-Slit and hit the

screen before we know which slit the electron passed through.

Now lets catch them out!

We can randomly open and close our eyes so that we randomly choose to look at

which Slit the electrons pass through.

And we do this after the electrons have hit the screen.

Surely we can now find out how the electrons are doing this?!

Well, no.

The electrons will ALWAYS produce an interference pattern if we DO NOT

LOOK and not produce and interference pattern if we do.

ALWAYS!

This means that the electrons would have to know whether or not we are going to

look at them before they hit the screen. That means that they know if we are

going to RANDOMLY look at them before we do!

The electrons know what we are going to do before we do!

What happened to FREE WILL?


Point 4: Observation

1) What is a wave anyway?

The Wave Equations for particles involve the MATHEMATICAL letter i. This is

a COMPLEX NUMBER i is the IMAGINARY SQUARE ROOT of -1!

This means that Matter-Waves are Imaginary and not real. And you are made of

these matter-waves! So what are we?

2) What is the difference between a Particle and a Wave?

The key is OBSERVATION. If an observation takes place, then you have

PARTICLE behaviour. If there is not an observation, you have WAVE behaviour.

3) I have no friends what am I?

If no-one observes you then you will be a wave. The reality is that you are made of

many particles so the chances are that in any given time some observations will

take place. But if you dont find friends soon then you will always be a wave. And

then you could re-appear anywhere at any time! (Unless you can observe

yourself).

4) Psychic electrons they know what the other is thinking

In a Helium atom, 2 electrons orbit in the first Energy Level. Each electron has a

property called SPIN. Each electron must have the opposite spin to the other. So

one has an UP SPIN and the other has a DOWN SPIN.

If you then bash this atom and both electrons fly off into space, neither electron

is SPIN UP or DOWN until they are OBSERVED. And when ONE of them is

observed, the other INSTANTLY takes the opposite value even though there is no

time for a message to be passed between them!

5) Schrdingers Cat

Schrdingers created a thought experiment to highlight the absurdity of the

Wave-Particle situation.

A cat, radioactive isotope, a Geiger Detector and a poison are placed inside a box

(as you do). If any particles decay from the isotope, the Geiger Detector will

detect it and the poison will be released which will then kill the cat (a bit harsh

but thats life really).


The question is: After 1 half-life (time for HALF the particles to decay), is the

cat dead or alive?

Since the decay of a nucleus is governed by probability, then you cannot say that

the cat is DEAD or ALIVE until you OBSERVE it. Until then, the cat is a wave and

is neither DEAD or ALIVE.

6) If a tree falls in a wood, does it make a sound?

For many years this philosophical question kept some people occupied in

intellectual debates. And physicists just said Yes.

But now we realise that unless there is an observer, then all that exists is a

Probability Wave and no answer is real. Once an observer arrives, then the

Probability Wave collapses to a single answer yes or no. Until that point

there are no answers.

7) What is an Observer?

An Observer is something that makes the Probability Wave collapse to a single

value. In other words, it causes the Wave behaviour to change to Particle

Behaviour.

8) When did the Universe become real?

This is a difficult question, and it depends on what is allowed for an Observer. If

an Observer is ANYTHING, then the Universe became REAL once an observation

took place. If an Observer has to be a Conscious Being then the Universe only

became REAL once the Conscious Being observed it!

9) Orbitals Why can electrons break laws of physics in Orbitals?

When an electron absorbs or emits a photon, there is an interaction this is

particle behaviour. When the electron is on its own there is no observation so it

behaves like a wave. If we plot where the electron is observed each time, then we

trace out the path of an orbital.

The question: How can electrons travel in circles without losing energy? is the

wrong question. Between observations, the electron behaves as a wave and isnt

travelling or moving its an imaginary wave. Its only when it is observed that it

has an actual place. Electrons dont orbit or stand still they simply appear when

observed!


10) Quantum Tunnelling

Ever wanted to get out of a room without moving? Well you can! If no-one

observes you, then you behave like a wave. This wave extends to infinity. When

someone observes you, the imaginary wave collapses to a single value particle

behaviour. You just need someone to observe you outside the room!

Think this is nonsense!? Well it isnt. All the electronic gadgets that you own (e.g.

iPod, mobile phones, XBOX 360) contain micro-chips and they use electrons. Since

electrons behave as particles or waves (depending on observation), the micro-chips

have to be designed to treat the electrons as particles and waves!

11) Many Worlds theory

If an object is not observed, it behaves as a wave. These waves are imaginary and

extend to infinity. When an observation takes place, this wave collapses (vanishes)

and the object is located in a single position. But why that particular value?

It is all governed by probability. There is a probability that the object will be

found in a certain place. But how was that place chosen?

This has led to some scientists to consider the Many Worlds Theory. It

considers the idea that when the (imaginary) wave collapses to ONE value every

possible value occurs but in a NEW UNIVERSE. Each Universe is created

PERPENDICULAR (not Parrallel!) to this one. This would mean that every

observation (anywhere, anytime) creates an infinite number of universes 1 for

each possible outcome.

Point 5: Are you making this up?

No. Einstein hated the consequences of Quantum Physics and always refused to

believe (interesting choice of words for a scientist commenting on a scientific theory)

that the universe was governed by probability. Einstein famously stated God does

not play Dice!

Heisenberg and Bohr realised that the only way to solve the experimental data was

using the mathematics of probability and statistics which meant that nothing was

ever certain. Every outcome had a probability and this was given by the WAVE

EQUATION. A solution (mathematically speaking) occurs when the equation is

operated on in PHYSICS we call that an observation (or interaction).


Appendix 1 Specification (Quantum Phenomena)

The Photoelectric Effect

Work function , threshold frequency f0,

photoelectric equation h f = + EK

the stopping potential experiment is not required.

Collisions of electrons with atoms

The electron volt.

Ionization 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

levels in atoms.

h f = E1 E2

Wave particle duality

Candidates 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

required.

de Broglie wavelength, = h m v

where m v is the momentum.


Appendix 2 Conversions of Units Distance

1 km = 1000 m

1 cm = 0.01 m

1 mm = 0.001 m

Mass

1 tonne = 1000 kg

1 gram = 0.001 kg

Time

1 year = 365.24 days

1 year = 3.16 x 107 seconds

1 milli-second = 0.001 seconds

Area

1 cm2 = 1 cm x 1 cm

= 0.01 m x 0.01 m

= 10-2 m x 10-2 m

= 10-4 m2

1 mm2 = 1 mm x 1 mm

= 0.001 m x 0.001 m

= 10-3 m x 10-3 m

= 10-6 m2

Volume

1 cm3 = 1 cm x 1 cm x 1 cm

= 0.01 m x 0.01 m x 0.01 m

= 10-2 m x 10-2 m x 10-2 m

= 10-6 m3

1 mm3 = 1 mm x 1 mm x 1 mm

= 0.001 m x 0.001 m x 0.001 m

= 10-3 m x 10-3 m x 10-3 m

= 10-9 m3


Appendix 3 Prefixes

You need to know the symbols for 10-9 to 109 and how to use them.

Name Symbol Standard Form

Yotta Y 1024

Zeta Z 1021

Exa E 1018

Peta P 1015

Tera T 1012

Giga G 109

Mega M 106

kilo k 103

100

milli m 10-3

micro 10-6

nano n 10-9

pico p 10-12

femto f 10-15

atto a 10-18

zepto z 10-21

yocto y 10-24


Appendix 4 Is light a Particle or Wave?

Point 1: What are Particles and Waves?

Waves can pass through each other, they are not localised (not positioned in one

place), they have no mass, and no charge.

Particles cant pass through each other, they are localised (they are in one place),

and they can have mass, and can have charge.

An object cant be a wave or a particle at the same time since they are exact

opposites.

Point 2: Is Light a Wave or a Particle?

1621 Snells Law of Refraction

Snell finds derives the relationship between wave speeds in different mediums.

1665 Dispersion of Light Francesco Grimaldi

Grimaldi did experiments that showed that light could spread out if passed through

a very narrow slit.

1666 Light is a Particle Sir Isaac Newton

Newtons theory of light was particular (this was the accepted view in England). The

supporting evidence for this was:

The existence of Shadows. Fine edges indicated particles since waves can bend

around objects.

Light can travel in a vacuum. Particles can do this but at this time (1660s) no

wave could do this.

Dispersion was explained by the idea of white light being made up of 7

different coloured particles which split.

1678 Light is a Wave Christiaan Huygens

Huygens proposed that Light is type kind of wave motion. Light can pass through

other light and emerge without being affected. This is a wave characteristic.

Newtons Particle Theory was the accepted view. Also discovered polarisation of

light polarisation is a (transverse) wave property only. (Published in 1690).


1704 Optiks Sir Isaac Newton

Splitting of Light through a prism was explained by Newton in terms of corpsicules

hitting the side of the slit and reflecting to a different place.

1768 Colour of Light Leonhard Euler

Euler suggested that the wavelength of light determines its colour.

1801 Interference of Light Thomas Young

Young proposed that Colours produced by thick films could only be explained if light

were a wave. He even measured the wavelength of Visible Light.

1816 Mathematics of Light Waves Jean Fresnel

Fresnel did a lot of mathematics and demonstrated that we didnt see the diffraction

of light because it has a much smaller wavelength than the object.

1850 The Speed of Light Jean Foucalt

Fouclat measured the speed of light in air and water. He found that the speed of

light in water was slower than the speed of light in air. A particle theory of light

suggests the opposite to this result. A wave theory of light predicts this.

1873 Light is Electromagnetic Radiation James Clerk Maxwell

Maxwell describes (with equations) that light is a type of Electromagnetic Radiation.

Year Scientist Is light a wave or particle?

1666 Isaac Newton

1678 Christiaan Huygens

1704 Isaac Newton

1768 Leonard Euler

1801 Thomas Young

1816 Jean Fresnel

1850 Jean Foucalt

1873 James Clerk Maxwell

In the year 1899, was light considered to be a particle or a wave?


Point 3: The Electro-magnetic Spectrum

1800 The Sun William Herschel

Herschel discovers that the Sun has an InfraRed region.

1801 Ultra Violet Radiation Johann Wilhelm Ritter

Discovery of Ultra Violet Radiation.

1865 Electromagnetic Waves can travel through a Vacuum James Clerk Maxwell

Maxwell did a lot of mathematics and proved that Electromagnetic Waves could

travel through a vacuum and that they all travelled at the Speed of Light.

1867 Fluorescent Lamp Becquerel

Becquerel invents the Fluorescent Lamp (emits Ultra Violet).

1887 Discovery of Radio Waves Heinrich Hertz

This was the first demonstration of the existence of Electromagnetic Waves. Hertz

also calculated the speed of these Radio Waves using c = f and found the value of c

agreed with Maxwells theoretical value.

1895 X Rays Roentgen

Roentgen discovers X Rays (which he called Roentgen Rays)

Year Scientist Part of the EM Spectrum

Discovered / Discovery

1800

1801

1865

1873

1887

1895

In 1899, what does the EM Spectrum contain? What is missing?


Appendix 5 The Ultra-Violet Catastrophe

Point 1: The Ultra-Violet Catastrophe

Blackbody Radiation

1862 Gustav Kirchoff

A Black Body absorbs all the radiation that falls onto it.

Black bodies radiate energy which is only dependent on their temperature.

The radiation emitted from a Black Body is called Black Body Radiation.

From experiment, a graph of Black Body Radiation can be plotted.

Black Body Radiator

Wavelength / m

Intensity

(Power per

Unit Wavelength

per Unit Area)

EM Radiation enters the Cavity (Box) and

is reflected. Given enough time, it will be

absorbed by the walls of the box. The

absorption of energy will increase the

Cavitys temperature.


Classical Physics The Theory

From Classical Physics Theories (Electromagnetism and Statistical Mechanics)

an equation was derived to predict the behaviour of a Black Body Radiator.

The equation (known as the RayleighJeans Law) was very successful at low

frequencies but did not work for high frequencies.

The Black Body Theory

A simplified version of the theory is as follows:

Every possible frequency of radiation can exist inside the walls of the Cavity.

These EM Waves will be continuously reflected inside the Cavity and will

interfere with themselves.

Following the laws of the Interference of Waves, Standing Waves will be

generated inside the Cavity.

Clearly, the shorter the wavelengths (higher frequencies) the more modes

(think of nodes and anti-nodes) that can fit inside the Cavity.

It was believed that each mode carried energy, so the more modes, the more

energy in the standing wave.

Clearly, the higher the frequency of the EM Waves, the more modes so the

more energy it contained.

From this scientists Rayleigh and Jeans formulated an equation to calculate the

Intensity of the EM Waves being released.

The RayleighJeans Law

I is Intensity

2, ,c,k are all constants

T is Temperature

is the Wavelength of the Radiation

If the Temperature rises, the Intensity of the Radiation given out rises

(makes sense the hotter something is the more heat energy it gives out).

If EM Waves have a wavelength of less than 1 metre, the Intensity will

increase, and as the wavelengths approach 0 metres, the Intensity approaches

INFINITY!

I = 2ck T / 4


Comparison to Theory

From the Rayleigh-Jeans law:

Objects emit electromagnetic radiation at all wavelengths and the Intensity of

the radiation depends on its wavelength.

The shorter the wavelength the more energy it emits.

Therefore, the graph for a Black Body would look something like this

RayleighJeans Radiator

At short wavelengths, any object would be emitting an infinite amount of

energy

So as you go towards the short wavelength end of the spectrum (the Ultra

Violet end as it was known at the time) the energy emitted is infinite and

clearly, no object in the world around you is emitting an infinite amount of

energy

Wavelength / m

Int

ens

ity

(Pow

er

per

Uni

t W

avele

ngth

per

Uni

t A

rea)

Area under the graph is

the total Energy emitted

by the object.

This is infinite!

Exponential rise towards

infinity


Black Body Radiator (from experiment)

The Catastrophe

According to all the Classical laws in Physics, the RaleighJeans law should

work, but clearly it cant and doesnt.

It is called the UltraViolet Catastrophe because any object would emit an

infinite amount of electromagnetic radiation at any time.

No object emits an infinite amount of energy.

So clearly, the Classical Laws of physics are wrong.

And the understanding in Classical Physics is wrong.

Point 7: The Breakdown of Classical Physics (it doesnt work!)

Quantisation of Energy

1900 Max Planck

In an attempt to solve the Black Body Radiation problem, Max Planck tried to

derive an equation for a Black Body Radiator.

The only way he could get the physics to make sense was to state that energy

is emitted in packets.

In other words, energy is not given out in a continuous stream but is given out a

little bit at a time.

The Latin word for packet is QUANTA.

He also found that the energy of each Quanta depends on the frequency of the

radiation.

Wavelength / m

Int

ens

ity

(Pow

er

per

Uni

t W

avele

ngth

per

Uni

t A

rea)

Intensity goes to

zero

Area under the graph is the total

Energy emitted by the object

This is finite


E = hf

Since the Energy of radiation is dependent on its frequency, then:

E = Energy in Joules, J

h = Plancks constant = 6.626 x10-34 J s

f = frequency in Hertz, Hz

Black Body Radiation

The implications are that on the atomic scale, Classical Physics can not be

applied.

On the atomic scale, Energy is quantised.

This means that in the Atomic World things will work in a completely different

way to the Macroscopic World.

This was the birth of QUANTUM PHYSICS.

The Ultra-Violet Catastrophe

By using E = hf in the same theory for the Black Body Radiator, Planck derived a

different equation:

And this works!

E = hf

2hf3 I =

c2 ehf/kT - 1

1


Appendix 6 The Electron-Volt

If an electron is passed through a Potential Difference of 1 Volt, it gains the

energy of 1 Electron Volt or 1 eV.

For example, in a cell of 1 V, the electron would gain energy equivalent to 1

electronvolt.

The value of 1 eV = 1.6 x 10-19 J.

This is the energy that an electron would actually have.

Since the number 1.6 x 10-19 J is so small, the unit eV is used.

Energy in an atom or in Particle Physics is given in eV.

Another way to think of the Electron-Volt is from ELECTRICITY:

Potential Difference = Work done per Coulomb of Charge

In Symbols: V = E / Q

Re-arranging: E = Q V

Since: Q = charge on 1 electron = e = 1.6x10-19 C

Then: E = 1 eV = 1.6x10-19 C x 1 V = 1.6x10-19 J

Hence: 1 eV = 1.6x10-19 J

1 eV = 1.6 x 10-19 J

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Quantum - Booklet - Student 8.2