Areas of Knowledge

Areas of Knowledge

SCIENCE

Science

“ For thousands of years humans have had a miserable existence. A short life characterised by cold, hunger, disfiguring diseases and eventually a premature and painful death. In the last 100 years or so we have largely be spared this. People suffer less and live longer. In general people are better educated and can now live meaningful lives. This is not a miracle – it is due to Science.”

Simon Porter

What is a scientist?

Draw and/or describe your typical scientist

Google thinks they look like this:

And can be defined like this:

• A person who has studied science, especially one who is active in a particular field of investigation.www.mdanderson.org/patients_public/about_cancer/display.cfm

• a person who uses observation, experimentation and theory to learn about a subject (Biologists, physicists, chemists, geologists and astronomers are all scientists.)education.jlab.org/beamsactivity/6thgrade/vocabulary/index.html

• a person that knows a great deal about a branch of science. An ornithologist is a scientist that specializes in the study of birds.www.inhs.uiuc.edu/chf/pub/virtualbird/glossary.html

• a person with advanced knowledge of one or more sciences wordnet.princeton.edu/perl/webwn

What features did you identify?

What are the ideal characteristics of a scientist?

• Collaborative

• Observant

• Creative

• Open-minded

• Risk-taking

• Methodical

• Analytical

• ??

How about being a believer?

Being perseverant?

Being ethical?

CSI

• Series 1 episode 10Whilst watching this episode – fill in the

sheet.

Learn the Truth card game• Each group offers a card, which the Mr Porter takes or rejects according to an unknown rule• Work out what the rule is to win a point for your team• No random guessing – your group may only propose a theory once it has been discussed and agreed in the group.• You can only suggest the answer when it is your turn

Let’s go!

The first three rules were:

1. Red, black, red, black, red…2. Spade, heart, club, diamond, spade, heart, club,

diamond…3. Odd, even, Odd, even, Odd, even…

It may have been hard to distinguish the first two patterns, because 2 is a specialised form of 1.

They look the same, & once stuck in a theory you may have succumbed to confirmation bias

What was needed to distinguish them?

Experimenting, esp: falsification

The processes you are using:

• Observing

• Reasoning

• Intuiting

• Decision making

• Teamwork

• Cooperating and competing

• Pattern spotting• Guessing the rule• Testing the rule

=• Empirical observation• Forming an inductive, reasoned hypothesis• Testing by falsification

Which is the most important part of the process?

Your processes refined:

Let’s try some more complex patterns

Try these patterns:

4. P, not P, P, not P, P, not P…5. Card given by boy, girl, boy, girl…6. Accepted if given from left hand, right hand, left

hand…7. Accepted if offered with a bribe…

Simple rules, but hard to discern because:You were looking for the wrong thing: you looked

in the cards, not in the circumstances. You made assumptions without realising. Paradigms were not the whole story.

What did this have to do with ToK?

• The teacher was “Nature”• You were scientists, trying to understand “Nature”’s

workings & rules• You cooperated & competed in order to succeed• You observed• You hypothesised, by using inductive reasoning &

intuition• You tested, most successfully by falsification• You modified your theories• Simple appearances hid complex patterns, and vice

versa• Your paradigms got in the way of knowledge

Just like SCIENCE and scientists!

What is the scientific method?

How do scientists gain their knowledge?

Remember the characteristics of scientists

• Collaborative

• Observant

• Creative

• Open-minded

• Risk-taking

• Methodical

• Analytical

• ??

• Pattern spotting• Guessing the rule• Testing the rule=• Empirical observation• Forming an inductive, reasoned

hypothesis• Testing by falsification

Remember the processes used in the card game

Key elements must be:

• observation of empirical and measurable evidence,

• experimentation (esp falsification, the process by which we eliminate failures and falsehoods), and

• Logical, rational and coherent theoretical explanations

Draw and label a diagram or flow-chart

of the model scientific method

How does your model compare with this one?

Experimental data or

observation

Inductive hypothesis

Prediction and experimental

testing

Theory confirmed and publishedas knowledge

Theory is falsified and discarded

What are the problems or issues with this model?

• Paradigms and perception problems with observation (see next slide)

• Subjectivity rather than objectivity in observations

• Confirmation bias (Millikan’s oil drop – following slide))

What are the problems or issues with this model?

What is the essential component of the scientific method?

The extra chromosomes!

• “The Bizarre Case of Chromosomes that Never Was” by Robert Mathews is a fascinating article that explores the human nature of conformity. In 1932, the American zoologist Theophilus Painter, published a study where he claimed that they are 24 pairs of chromosomes in the human body. Painter did so fully confident in his findings. As other scientist repeated Painter’s study they claimed to also find 24 pairs of chromosomes. However there were a few scientists who claimed to see as few as 19 and others 23. These scientists then thought their findings were just wrong because they knew that there was went to be 24. That is until 1956, when scientist finally discovered a way to place cells on microscope slides, which helped separate the chromosomes clearly. When scientists did this they found that there was in fact only 23 chromosomes in the human body. Researchers even went back to textbooks and looked at the photographs of chromosomes. They found that the photograph clearly showed 23 pairs of chromosomes, however the caption stated that there were 24 pairs.

Charge on an electron

• Robert Millikan performed a ground breaking experiment between 1900 and 1913 to measure the change on an electron. There is some controversy over the use of selectivity in Millikan's results raised by the historian Gerald Holton. Holton (1978) pointed out that Millikan disregarded a large set of the oil drops gained in his experiments without apparent reason.

models of scientific change: Karl Popper

http://en.wikipedia.org/wiki/Karl_Popper

• Each theory builds progressively on the theories preceding it

32

1

• Paradigms encompass some parts of previous theories, but reject other parts

models of scientific change: Thomas Kuhn

http://en.wikipedia.org/wiki/Thomas_Samuel_Kuhn

1 2 3

• Theories have little to do with previous theories, and are incoherent or inconsistent.

models of scientific change: Paul Feyerabend

http://en.wikipedia.org/wiki/Paul_Feyerabend

1

23

It could be argued that the scientific method itself has been

developed over time, ‘scientifically’!

An example – quantum physics

Atomic spectra

When a gas is heated to a high temperature, or if an electric current is passed through the gas, it begins to glow.

cathode anode

electric current

Light emitted

Low pressure gas

Emission spectrum

If we look at the light emitted (using a spectroscope) we see a series of sharp lines of different colours. This is called an emission spectrum.

Absorption Spectrum

Similarly, if light is shone through a cold gas, there are sharp dark lines in exactly the same place the bright lines appeared in the emission spectrum.

Some wavelengths missing!Light source gas

Why?

Scientists had known about these lines since the 19th century, and they had been used to identify elements (including helium in the sun), but scientists could not explain them.

Rutherford

At the start of the 20th century, Rutherford viewed the atom much like a solar system, with electrons orbiting the nucleus.

Rutherford

However, under classical physics, the accelerating electrons (centripetal acceleration) should constantly have been losing energy by radiation (this obviously doesn’t happen).

Radiating energy

Niels Bohr

In 1913, a Danish physicist called Niels Bohr realised that the secret of atomic structure lay in its discreteness, that energy could only be absorbed or emitted at certain values.

At school they called me “Bohr the

Bore”!

The Bohr Model

We say that the energy of the electron (and thus the atom) can exist in a number of states n=1, n=2, n=3 etc. (Similar to the “shells” or electron orbitals that chemists talk about!)

n = 1

n = 3

n = 2

The Bohr Model

We can show the energy levels on a diagram

n = 1 (the ground state)

n = 2

n = 3

n = 4n = 5

High energy n levels are very close to each other

Energy eV

-13.6

0

Electron can’t have less energy than this

Atomic transitions

If an electron is a level above the ground state, it can make a transition to a lower state. Thus an atom in state n = 2 can go to n = 1 (an electron jumps from orbit n = 2 to n = 1)


n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

electronWheeee!

Atomic transitions

Every time an electron makes a transition, a single photon of light is emitted ( a little “packet” of light energy)


n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

electron

Atomic transitions

The energy of the photon is equal to the difference in energy (ΔE) between the two states.


n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

electron

ΔE

The Lyman Series

Transitions down to the n = 1 state give a series of spectral lines in the UV region called the Lyman series.


n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

Lyman series of spectral lines (UV)

The Balmer Series

Transitions down to the n = 2 state give a series of spectral lines in the visible region called the Balmer series.


n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

UV

Balmer series of spectral lines (visible)

The Pashen Series

Transitions down to the n = 3 state give a series of spectral lines in the infra-red region called the Pashen series.


n = 2

n = 3

n = 4n = 5

-13.6

Energy eV

0

UV

visible

Pashen series (IR)

Emission Spectrum of Hydrogen

Which is the emission spectrum and which is the absorption spectrum?

The emission and absorption spectrum of hydrogen is thus predicted to contain a line spectrum at very specific wavelengths, a fact verified by experiment.

Limitations of the Bohr Model

1. Can only treat atoms or ions with one electron

2. Does not predict the intensities of the spectral lines

3. Inconsistent with the uncertainty principle (see later!)

4. Does not predict the observed splitting of the spectral lines

Light as particles and waves

In 1905 Einstein showed that the photoelectric effect could be understood if light were thought of as a stream of particles (photons). This seemed to contradict some other experiments that shows light travels as waves.

I got my Nobel prize for that.

Louis de Broglie (in 1923)

If light can behave both as a wave and a particle, I

wonder if a particle can also behave as a wave?

Louis de Broglie

I’ll try messing around with some of Einstein’s formulae and see what I can come up

with.

I can imagine a photon of light. If it had a “mass” of mp, then its momentum would be given by

p = mpc

where c is the speed of light.

Now Einstein has a lovely formula that he discovered

linking mass with energy (E = mc2) and he also used Planck’s

formula E = hf. What if I put them equal to each other?

mc2 = hf

mc2 = hf

So for my photon

mp = hf/c2

So if p = mpc = hf/c

p = mpc = hf/c

Now using the wave equation, c = fλ (f = c/λ)

So mpc = hc/λc = h/λ

λ = h p

So you’re saying that a particle of momentum p has a wavelength

equal to Planck’s constant divided by p?!

Yes!

λ = h/pIt will be known as the de Broglie wavelength

of the particle

Confirmation of de Broglie’s ideas

De Broglie didn’t have to wait long for his idea to be shown to be correct.

In fact in 1929 I received a Nobel prize for my

prediction of the wave nature of the electron.

Confirmation of de Broglie

De Broglie’s hypothesis was confirmed independently by Clinton Davisson (USA) and George Thomson (UK) in 1927

Ironically my Dad (J.J.) had won a Nobel prize for demonstrating that

the electron was a particle!

The “electron in a box” model!

☺

Hi! I’m Erica the electron


• Imagine an electron is confined within an atom of diameter L.

☺

L


• According to de Broglie, it has an associated wavelength λ = h/p

☺

L

L


• Imagine then the electron wave forming a stationary wave in the atom.

L


• Therefore we have a stationary wave with nodes at x = 0 and at x = L (boundary conditions)

The “electron in a box” model!• The wavelength therefore of any stationary

wave must be λ = 2L/n where n is an integer.

L


• The momentum of the electron is thus

• P = h/λ = h/2L/n = nh/2L


• The kinetic energy is thus = p2/2m = (nh/2L)2/2m = n2h2/8mL2


• Ek = n2h2/8mL2

• The energy depends on n2

☺

L

Energy states

This can be thought of like the allowed frequencies of a standing wave on a string (but this is a crude analogy).

Erwin Schrödinger

The many problems with the Bohr model were corrected by Erwin Schrödinger, an Austrian physicist.

http://www.youtube.com/watch?v=IOYyCHGWJq4&feature=related

I like cats!

d2Ψ/dx2 = -8π2m(E – V)Ψ/h2

The Schrödinger equation

Erwin Schrödinger

Schrödinger introduced the wave function, a function of position and time whose absolute value squared is related to the probability of finding an electron near a specific point in space and time.

I don’t believe that God

plays dice!

Erwin Schrödinger

In this theory, the electron can be thought of as being spread out over a large volume and there are places where it is more likely to be found than others! This can be thought of as an electron cloud.

Rubbish!

Wave function

Ψ = (2/L)½(πnx/L) where n is the state, x is the probability of finding the electron and L is the “length” of the orbital.

From this we also get the energy to be

EK = h2n2/8meL2

Beware!This wave function is only a mathematical model that fits very well. It also links well with the idea of wave particle duality (electron as wave and particle).

But it is only one mathematical model of the atom. Other more elegant mathematical models exist that don’t refer to waves, but physicists like using the wave model because they are familiar with waves and their equations. We stick with what we are familiar!

.

I’m used to the idea of waves, so

I like using Schrödinger’s

model

Heisenberg Uncertainty Principle

• http://www.youtube.com/watch?v=gS1dpowPlE8&feature=relmfu

Heisenberg Uncertainty Principle

• It is not possible to measure simultaneously the position AND momentum of a particle with absolute precision.

ΔxΔp ≥ h/4π

Also ΔEΔt ≥ h/4π

A few videos to try and explain!http://www.youtube.com/watch?v=Q_h4IoPJXZwhttp://www.youtube.com/watch?v=_riIY-v2Ym8&feature=endscreen&NR=1

The great Richard Feynmanhttp://www.youtube.com/watch?v=kekayfI8Ii8&feature=related

What does ‘wrong’ mean?

Newton versus Einstein

Newton’s law of gravity

• Newton said that anything in the Universe that has mass, has a property of attraction for any other mass in the Universe.

• This attraction is a force that wants to pull masses together. The size of the pull depends on how big the masses are, and how far apart they are.

Newton’s law of motionBasically, Newton’s Laws of Motion say three things.

• To change momentum a force must be applied.• The applied force is proportional to the change in

momentum.• Every force that is applied produces a resisting force,

equal and in opposite direction to the applied force.

It is possible to create a mathematical formula from the Second Law:

F=mawhere F is the applied Force, m is the mass being

accelerated and a is the acceleration.

Using Newton’s laws

• NASA uses them – for all the spacecraft that have visited the outer reaches of the Solar System.

• The calculated trajectories are highly accurate in every case. One Voyager even passed through a small gap in Saturn's rings, without incident. And that was using Newton's laws of motion over a distance of more than 1,280,000,000 km (800,000,000 miles).

Einstein and Newton

• Einstein showed that Newton’s laws break down when velocities approached that of light.

• Einstein showed that Newton's Law of Gravitation was also only approximately correct, breaking down in the presence of very strong gravitational fields.

Was Newton Wrong?

• Newton's laws are ‘wrong’ in certain circumstances.

• Einstein took the ideas and made them better.

• We should probably describe Newton’s ideas as limited.

• Are theories being put forward today that could prove Einstein ‘Wrong’?

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Areas of Knowledge