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Sec 3 Physics and Maths MYE Revision 2018

Sec 3 Physics and Maths MYE Revision 2018

Attention PMC S3 PHYSICS & MATHS students!

What to expect in the next 4 weeks?

You must be aware that the Sec 3 Mid Year Exams is only 4-5 weeks away! So we thought it’s about time we gave you a little sneak peek on what is going on in class…

And in case you were wondering, here’s an overview of essential lesson materials that our students will receive this week:

Term 2 Week 2 – Week 3 (26 March – 8 April)

  1. You will receive a revision DIY package for Measurement and Kinematics. Please complete the questions at home as a timed test. Shade your answers on the OMR answer sheet which you will be given in class to mimic actual examination condition. Mark your answer against the solutions given at the back of the booklet. The worked solutions will be uploaded to your student portal on the following week.
  2. In class, the tutor will go through the Kinematics and Dynamics (structured questions) and you can complete the MCQ questions at home with the OMR answer sheet. The worked solutions will be uploaded to your student portal.

Term 2 Week 4 – Week 5 (8 – 15 April)

  1. There will be a 30 minutes The Physics Cafe MYE Mock Exam in week 4 (16 – 22 April). All students must prepare for the test. Your answer sheet will be collected by the tutor for marking and your score will be published and converted to points (which is cash). The details will be explained in class.
  2. Students who did not do reasonably well for the test will see the tutor for consultation. Parents will receive an update of your results via email. Don’t say we didn’t warn you 😛

Are you attending both Physics and Maths classes in the café?

 Sec 3 Maths revision will commence next week. There will be a Term Test in week 4 – 5. For existing students who are keen to sign up for Physics or Maths classes, do register your interest in the student portal. Registration fee will be waived.

For Parents:

Your child will be receiving a lot of materials coupled with complete worked solutions during this period. Kindly assist to encourage them to complete the home assignments. They can approach the tutor before or after their weekly lessons if they need help.

Tutor Comments:

Finally, everyone seems to be finally aware that the mid year exam is near. (If you aren’t, that’s worrying isn’t it?) School life isn’t all fun and games -a bit of stress now is definitely good to pace the student in the sec 3 academic year. Many will soon realise that while they can easily score well in small tests especially after covering a particular topic, it’s not easy to score well in big exams that integrate more than one topic. The question banks in the booklets aim to prepare students for their exams, and we believe that solving questions is as important, if not more than merely going through notes. The mock paper before the actual exam is important and is usually provides good feedback on whether the student has invested enough time in the MYE preparation. As always, the results you get in the exams should not be a surprise to you. It’s usually an accurate measure of what you understand and what you remember at that point of time. With that, we wish you all the best in your preparation and examinations!

$100 Term Test Challenge

Calling PMC J2 PHYSICS & MATHS students!



How to play?

Come on any of the time slots below in The Physics Cafe Paya Lebar to take either the Physics or Maths Challenge in 60 mins. It’s free, so just turn up to test your concepts and earn cash at the same time.


What are the available timeslots?

17 March, Sat 1.00pm – 2.00pm

17 March, Sat 2.30pm – 3.30pm

18 March, Sun 2.30pm – 3.30pm

18 March, Sun 4.00pm – 5.00pm

*If you are taking both Physics and Maths challenges, you can come for 2 of the timeslots.



The Physics Cafe Flagship Outlet (Besides Paya Lebar MRT)

SingPost Centre Enrichment Zone #01-207



Physics: Oscillations, Waves, Superposition, E field, COE DC

Maths: Integration and Vectors


What is the Prize?

Top 3 students in each subject will win $100 cash each.

*If there are more than 3 top students, all students will share prize money equally.

The Physics Cafe Movie Marathon 2018

Reserve a Seat for the Movie Marathon

This annual event is organised to help students get ready for the first JC2 common test (usually after the march holiday). Existing students and non-existing students are welcome to attend.

You will be watching a video recording of 2017 Live lesson. This is a special, unique digital experience where you can see the tutor, the projector screen, the white board, the students in the classroom and even hear the interaction between them. You will be solving lots of questions together with your peers attending the movie marathon. At the end of the video, you will know everything you need to know for the topic. It will be the most efficient way to get ready for the common test.

What are the movie available for booking?

  • Thermal Physics Crash Course Lesson 1 (2 hours) on 6 Mar 7-9pm (Term 1 Week 10, Tue)
  • Thermal Physics Crash Course Lesson 2 (3 hours) on 9 Mar 6-9pm (Term 1 Week 10, Fri)
  • Electric Field Crash Course (3 hours) on 12 Mar 3-6pm (March Holiday, Mon)


Where will the movie marathon be held?

The movie will be held at The Physics Cafe flagship store @ Singpost Centre beside Paya Lebar MRT.


How much do I have to pay to watch the movie marathon?

There will be a $10 admin fee per video. We will waive off the regular fee of $50 for this movie marathon. Regular fee of $50 will still be applicable for all other digital lessons.


What if I cannot make it for the scheduled movie marathon?

You may register separately to watch the digital lesson at your preferred timing and outlet at  Regular fee of $50 will be applicable.


What are the seats available?

Auditorium Seating Plan

How do I buy a ticket for the movie marathon?

You can buy your ticket here at! There is an admin fee of $10. The fee for the digital lesson is waived for this movie marathon only.


  • Choose your movie.
  • Choose your seat.
  • Pay $10 admin fee to reserve your seat.

What you need to know about Stellar Evolution?

Stellar Evolution


Image result for stellar evolution


Stars form from enormous clouds of hydrogen atoms, pulled together by the force of gravity.  As the cloud collapses, gravitational potential energy is converted to kinetic energy of the atoms (they are all “falling” toward their common center of mass).  If a cloud has enough mass, the pull of gravity will eventually compress these atoms into a tiny enough space that collisions between the fast moving atoms will lead to nuclear fusion.



You can play with simulation of the formation of a solar system here:



Once fusion begins, hydrogen will be converted to helium in a three step process that ultimately forms one He from 4 H atoms, releasing lots of energy in the form of gamma rays, along with some neutrinos and some positrons.



Khan discusses the initiation of fusion here:



The energy that is released streams outward and heats the outer layers of the star so that they glow and give off the visible light that we can see.  The outward flow of energy also exerts some pressure to counter the inward pull of gravity.  Stars exist in a fine balance between the inward pull of gravity and the outward radiation pressure.  If the radiation pressure is larger than the gravitational pull, the star will expand and fusion will slow down, and if the gravitational pressure is larger then the star will compress and fusion will accelerate, so the star can find a stable equilibrium.



Stars that are fusing H to He are called main sequence stars.  More than 90% of the stars are main sequence stars.  They come in a wide variety of sizes.  For a main sequence star, there is a relationship between the luminosity (the power output of the star) and the mass.  The relationship is roughly that luminosity is proportional to mass to the 3rd or 4th power.



Most of main sequence stars are so small that they are called red dwarfs, and most of those will simply live out their lives by fusing H into He until they eventually run out of fuel and become white dwarfs.  These small stars use up their fuel so slowly that very few if any have had time to become white dwarfs yet, since the universe isn’t old enough.



Main sequence stars whose mass is at least 1/4 that of our sun will eventually pass through a red giant phase.  That phase will start when the star has used up about 12% of its hydrogen  You can learn about that process by watching this Khan Academy video:


Becoming a Red Giant or Supergiant



Red giants fuse elements heavier than H.  Relatively small ones will only be able to produce He.  Larger giants will fuse He into C, O, and similarly massive atoms.  Supergiants are large enough to fuse even those elements into heavier elements, up to Fe.  Fe is the most massive atom that can be formed from fusion inside a star because Fe is at the peak of the nuclear binding energy curve (see Atomic Physics to learn why Fe and Ni are the most stable of all the atomic nuclei).



Khan has a video about the evolution of massive stars here:



The star’s mass will determine its fate after it goes through the giant or supergiant phase.  The relatively small ones will become white dwarfs once they run out of fuel.  They will spend the rest of eternity cooling off.  The white dwarf is very dense and hot even though fusion is no longer taking place in its core.



Without fusion, there is no radiation pressure outward, so what is keeping the white dwarf from collapsing?  The answer is “electron degeneracy pressure”.  The laws of quantum mechanics do not permit electrons to be pushed too close together.  Their resistance to further compression creates its own pressure outward, so the star withstands the crushing force of gravity.



Stars whose core (not initial mass) have mass greater than 1.4x the sun are too big to become white dwarfs.  This limit is called the Chandrasekhar limit.  Stars that surpass the limit are destined to become neutron stars or black holes.  But first they will undergo a…





The supernova explosion will shine briefly as bright as an entire galaxy.

Khan has a good video about supernovas, here:

I also like this video by PhysicsGirl which helps illustrate how the supernova produces such a dramatic expulsion of the outer layers of the star’s mass, at up to 1/10th the speed of light:  




Neutron Star or Black Hole?


After the supernova, if the star has a core mass greater than the Oppenheimer-Volkoff limit (around 2 or 3 masses of our sun), the star will become a black hole.  If not, it will become a neutron star.  In a neutron star, the pressure of gravity becomes so great that the electrons, which won’t go closer together because of degeneracy, instead MERGE with protons to form neutrons.  The neutrons then behave like the electrons do in a white dwarf – they refuse to be packed too tightly together, and this neutron degeneracy pressure is what stops gravity from crushing the star any further.  Now we have an incredibly dense star made up entirely of neutrons.  A star larger than the sun now is about the size of Manhattan!



If the star’s mass is large enough, even neutron degeneracy is not enough to stop the collapse, and the star becomes a black hole, virtually disappearing from our universe, detectable only by the gravitational effects it has on the universe around it.



Khan has a video about black holes here:



I have a chart that summarizes what IB students need to know about stellar evolution here



5 reasons students flock to The Physics Cafe

by The Straits Times

  1. The tutors are stars 


Forget social media influencers and music chart-toppers. Follow stellar tutors to clinch A grades on your examination scripts.

Mr Dave Sim, the founder of The Physics Cafe and The Maths Cafe, taught physics for six years at a top junior colleague before going into private tuition in 2010.

He and his dedicated team of tutors conduct O- and A- level mathematics and physics tuition classes.

Last year, more than 80 per cent of students scored A grades at the physics and/or mathematics A level examinations. Nine out of ten students clinched distinctions in the physics and/or mathematics O level examinations.


  1. Convenient locations

Classes are currently conducted at Orange Tee Building near Toa Payoh MRT station and Bukit Timah Shopping Centre near Beauty World MRT station.

Two more branches will be opening soon — SingPost Centre mall near Paya Lebar MRT station and Goldhill Centre near Novena MRT station. 


  1. Develop academic mastery like never before

Students are typically pressed for time with busy schedules — Mr Sim and his team help students learn in a ruthlessly effective manner.

The team works well with comprehensive notes, excellent lesson delivery, timed practices during classes and recorded lessons for students to revisit at their own time.


Inline images 1

Mr Sim helps students learn in a ruthlessly effective manner.


  1. The premises lives up to its name

Why is a tuition centre named a café? The branches have interiors mimicking a café where students perk themselves up with beverages from the free-for-all pantry.

Take a break and challenge your study buddies to a game of foosball.

Other than a well-stocked pantry cum in-house café, each branch has its own lecture theatre, study rooms, vending machine and digital library.


  1. Thrills and frills

Need someone to attend to your administrative queries? Onsite student councillors, who are The Physics Cafe’s ex-students, will help you get what you need.

Get home easily with the shuttle bus services. All branches have shuttle buses ferrying students to the MRT stations of Botanic Gardens, Jurong East, Serangoon and Paya Lebar.


Inline images 3

Fact : About a thousand students enrol in The Physics Cafe and The Maths Cafe yearly.

There will soon be two new branches at SingPost Centre mall near Paya Lebar MRT station and Goldhill Centre near Novena MRT station. 

What do you need to know about Introduction to the Universe?

Introduction to the Universe (IB Option E1)


209 Seconds video showing cosmic scales: 



Powers of Ten video zooming out from earth to edge of universe :




A photo showing why the Milky Way is called that:




A photo showing stars moving across the night sky due to the rotation of the earth :



Where are the Voyager spacecraft now? 

It’s fascinating to look at the real-time measurement of the distance, to 8 decimal places!  Because of the motion of the earth, there are times of year when the distance actually shrinks instead of growing.  It takes light about 18 hours now to reach Voyager 1, which is now outside the solar system.  It is amazing that it is still able to make contact with us.  It has a radio that is about as strong as a refrigerator light bulb, and we are able to pick up the blinking of that light from almost 20 billion km away!


Monty Python’s Galaxy Song:





Lyrics to the Monty Python Galaxy song:


Just remember that you’re standing on a planet that’s evolving

And revolving at nine hundred miles an hour

That’s orbiting at nineteen miles a second, so it’s reckoned

A sun that is the source of all our power

The sun and you and me and all the stars that we can see

Are moving at a million miles a day

In an outer spiral arm, at forty thousand miles an hour

Of the galaxy we call the ‘Milky Way’

Our galaxy itself contains a hundred billion stars

It’s a hundred thousand light years side to side

It bulges in the middle, sixteen thousand light years thick

But out by us, it’s just three thousand light years wide

We’re thirty thousand light years from galactic central point

We go ’round every two hundred million years

And our galaxy is only one of millions of billions

In this amazing and expanding universe

The universe itself keeps on expanding and expanding

In all of the directions it can whizz

As fast as it can go, the speed of light, you know

Twelve million miles a minute and that’s the fastest speed there is

So remember, when you’re feeling very small and insecure

How amazingly unlikely is your birth




What do you need to know about Nuclear Physics and Radioactivity ?

Nuclear Physics and Radioactivity



Radioactivity is spontaneous and random.  The probability that an atom will decay remains constant for the entire life of the atom.  If you think about it, this is really strange.  How can it not matter whether a uranium atom is 1 million years old or 1 billion years old?  Surely the billion year old atom would seem more likely to decay in the near future?


On the other hand, it would also be pretty weird if we were able to distinguish young atoms from old ones, and we would be able to do that if the probability of decay increased with age.  But still, what mechanism could be at work inside that atom that would be immune to the passage of time, so that the decay event would remain completely unpredictable?


The answer is tied to the uncertainty principle.  The protons and neutrons have wavelike characteristics, which means that their positions and their energy levels are not precisely defined.  This allows the particles to remain in a bound up state while still having a probability of becoming unbound.  The particles are constantly jiggling and there’s a fixed probability over time that the jiggling will bounce a particle all the way out of the nucleus.


Khan Academy Videos about exponential decay




My spreadsheet showing simplified mathematics of radioactive decay


Nuclear Fission simulated with ping-pong balls and mousetraps




Nuclear Fission simulator


Alpha decay simulation


Periodic Table with all isotopes


Veritasium videos about radiation



How Damaging is Radiation? 





Radiation vs Radioactive Particles :




How to calculate binding energy:


What do you know about Atomic Physics ?

Atomic Physics


Rutherford Experiment (aka Geiger-Marsden)


Image result for rutherford atomic model



My summary


Rutherford shot alpha particles at a thin film of gold foil

Most of the alpha particles went right through

Some had high angles of deflection

He was shocked when a small number of the alpha particles came zooming back out in the direction they went in

He concluded that the atom must have a nucleus that is


  1. a) very small compared to the total size of the atom.  That’s why most of the alpha particles go right through


  1. b) very dense, with most of the mass of the atom concentrated there.  That’s why some alpha particles can bounce right back


  1. c) positively charged.  That’s why the positively charged alpha particles’ paths are deflected


Simulation of the experiment:


Narrated animation of the experiment:


Discrete emission spectra


Image result for discrete emission spectra


When we heat or pass electricity through a gas, we see different colors of light depending on what element the gas is.


When we pass that light through a prism, we discover that the color is really a blend of a few discrete colors emitted by the gas


Each gas has a unique pattern of emissions

Find a simulator here


Art meets physics


The artist Georges Seurat used discrete dots or “quanta” to make paintings that look continuous.  This was in the late 1800’s, around the same time Max Planck was quantizing his formulas to try to explain the light emitted by heated metals,_Georges_Seurat,_1884.png


Bohr Model


Image result for bohr model



The key idea of the Bohr model is that the electrons orbit around the nucleus in orbits with certain “special” radii

Transitions from one orbit to a lower orbit cause the emission of a photon

The distance of the jump determines the energy of the photon, and the energy determines the frequency

So Bohr has explained why we see discrete emission spectra

But he hasn’t explained why special radii exist

And his model has other shortcomings:



  1. a) It only works for hydrogen


  1. b) It doesn’t explain why some spectral lines are very bright and others are not 


  1. c) It doesn’t explain the fine detail of the hydrogen atom’s emissions




What do you need to know about Thermal Energy?

Thermal Energy Transfer / Greenhouse Effect 


Some Background


IB calls this topic Thermal Energy Transfer, but really it’s about the greenhouse effect and climate change.  Calling it Thermal Energy Transfer it sounds more physics-y.


Image result for greenhouse effect and climate change


Climate change is of course a controversial subject.  Before I started teaching physics, I wasn’t quite sure what to believe about it.  But now that I had learn it well enough to teach it, I understand that the basic physics of the greenhouse effect are irrefutable, and that there is no way that adding CO2 to the atmosphere could NOT have a warming effect.


We still can’t predict with high confidence exactly what the effects will be, but the direction is clear:  the earth has to get warmer.  It has to.  It doesn’t matter whether you think the temperature records of the last few decades demonstrate this or not.  Even if you think the climate hasn’t changed yet, just wait a while longer: it’s going to be warmer in the future than it would otherwise be if we did not pour CO2 into the atmosphere.  Guaranteed.  We have raised the CO2 concentration very fast, but it takes time to warm up something as big as the earth, so the effects of what we’ve already done won’t show their full force for


How much warmer will it get, and how fast?  This is hard to tell. At least a few degrees, and certainly at a rate that is much faster than what the earth has previously experienced from natural causes.  What should we do about it?  That’s a question that goes beyond science to economics, politics, and even morality.


Here’s an excellent video by Veritasium that addresses the most popular misconceptions about climate change:


On to the physics…


A major component of this topic is understanding Black Body Radiation.  Every object emits electromagnetic radiation.  The temperature of the object determines how much power is radiated, and how that power is distributed across the frequency spectrum.  It depends on the color of the object, but a perfectly black object will give you the most radiation for any particular temperature.  Perhaps surprisingly, a lot of objects behave almost like black bodies, including the earth and the sun, so we will use the black-body model for them.



Image result for black body radiation



We have complicated equations that can tell us exactly how much radiation there will be at any particular wavelength or frequency for any temperature of the object.  But we don’t need that level of detail to understand what’s going on, so , we are going to focus on just two ways of describing the power radiated by a black body:


  • The amount of power radiated goes up very fast as temperature goes up, and it gets much smaller as temperature goes down.  The Stefan-Boltzmann equation quantifies that relationship.


  • The wavelength distribution of the radiation changes with temperature.  Cooler temperatures push the peak toward infrared.  Infrared waves are lower energy, lower frequency, longer wavelength.  Hotter temperatures push the peak toward ultraviolet.  UV rays are higher energy, higher frequency, shorter wavelength.  So it makes sense that the peak shifts toward UV as the object gets hotter.  Wien’s Law tells us how to calculate exactly where the peak is on the frequency spectrum.


You can look at how the distribution of the radiation changes with temperature with this excellent simulation of the black-body effect:


Image result for wien's law


Wien’s Law explains why the sun radiates all across the visible spectrum:  the sun’s surface is very hot, about 5000-6000 Kelvin.  Wien’s Law also explains why the earth radiates only in the infrared part of the spectrum:  the earth’s temperature, 288 K, is very cool compared to the sun.  The reason this is important for this topic is that the earth’s atmosphere only absorbs infrared radiation, not visible or ultraviolet light.  This means that most of the sun’s light that does not reflect off the atmosphere will pass all the way through the atmosphere and be absorbed by the earth’s surface.  It also means that when the earth re-radiates that energy, the radiation will all be in the part of of the spectrum that the atmosphere does absorb.  This is the greenhouse effect: light energy comes in easily but can’t get out so easily. We need it, or else the planet would be far too cold for us (about 255 K)!


Stefan-Boltzman tells us what temperature the atmosphere and the earth’s surface have to reach in order for the earth to find an equilibrium where the energy coming into each of them is equal to the energy going out.  That’s when the temperature of each one will be stable.  If more energy is coming into an object than going out, the object’s temperature will rise. Stefan-Boltzmann tells us that rise will cause an increase the power going out, until the energy flows balance again.


When the atmosphere absorbs infrared radiation coming up from the earth’s surface, the atmosphere heats up and radiates more, too. It radiates in all directions, so half of this atmospheric radiation goes out to space, but half of it goes back down toward earth’s surface.  So now earth’s surface has TWO sources of incoming radiation:  the original solar radiation, AND the infrared radiation coming down from the atmosphere.  The earth’s surface has to heat up to restore the balance.  This is the earth’s version of the greenhouse effect: the absorption and re-radiation of infrared energy by the atmosphere.


Image result for why does atmosphere absorb infrared



Why does the atmosphere absorb infrared?  It’s because the atmosphere has gas molecules in it that are very good at absorbing infrared. These include water vapor, CO2, methane, and nitrous oxide.  These come from natural and man-made sources.  The reason these molecules are good at absorbing infrared has to do with the laws of quantum mechanics, but we can understand it in a simplified way by considering that molecules are atoms connected by chemical bonds, and these atoms behave a little bit like masses connected by springs.  Mass/spring systems have resonant frequencies, and the resonant frequencies for the greenhouse gas molecules match the frequency of infrared light.  This makes them good at absorbing photons of light of that frequency, and then re-emitting that energy at the same frequency.  It’s similar to the way a swing will absorb your energy if you pump your legs with the right timing, but you won’t go anywhere if you stick your legs out at the wrong frequency, too rapidly or too slowly.



Light that does not match the resonant frequency of the molecules will not be absorbed and will pass right through.  This is why most of the sunlight reaches the ground but the infrared radiation gets trapped on its way out.



Enhanced greenhouse effect


Image result for greenhouse effect and enhanced greenhouse effect


The greenhouse effect is natural, and we need it to keep the planet warm enough to be habitable.  But by burning fossil fuels, humans are adding large quantities of CO2 into the atmosphere, and this creates an enhanced greenhouse effect, which must result in planet that is warmer than it would otherwise be.  I say “must” because it is just a matter of physics.  We KNOW that earth radiates infrared and why it does that; we KNOW that burning fossil fuels adds CO2 to the atmosphere, and why it does that; we KNOW that CO2 absorbs infrared, and why it does that; we KNOW that when the atmosphere absorbs more infrared the earth has to get hotter, and why that’s the case.  All of this is demonstrable in a laboratory!



If we are adding lots of CO2 to the atmosphere, we should be able to measure that, and we can.  We know that the concentration of CO2 in the atmosphere is now over 400 parts per million.  The norm over the last 800,000 years has been more like 200 or 250.  NEVER has there been this much CO2 in the atmosphere in the last 800,000 years, not even close.  And the amount has never risen at the rate that it has risen over the past 70 years or so.  The earth has “normal” cycles of increases and decreases in CO2, but those occur over tens of thousands of years, not decades.



We know that the CO2 in the atmosphere came from burning fossil fuels because it has the right chemical “signature” (the right blend of isotopes).  We know how much fossil fuel humanity has burned, and that matches up with the increase of CO2 in the atmosphere and oceans.



We also know that over the last 800,000 years, when CO2 has increased, so has the temperature.  Skeptics like to suggest that maybe the temperature causes the CO2 to go up rather than the other way around, and it’s true of course that correlation never proves causality.  But how could more CO2 not cause the temperature to rise?  We know the physics!  When we understand the mechanism of a causal relationship AND we see correlation, then it is silly to continue to pretend the causality might go the other way.



What happens in these cycles is that an initial warming starts a release of previously trapped CO2, and then that released CO2 causes additional warming, in a feedback loop.  In past cycles, there were obviously non-human causes of the initial warming that released CO2.  Most commonly these causes were astronomical, having to do with wobbles in the way the earth orbits the sun.  This time, the cause is human emissions of CO2.  Either way, we know what happens next:  feedback creates additional warming.  That’s what’s happening now.



Here’s a graph of earth’s temperature more recently: 




There are other greenhouse gases besides CO2.  Methane is a much more potent absorber of infrared, but it breaks down in the atmosphere, while CO2 does not.  Water vapor is the most significant greenhouse gas, but when there’s too much water in the air, it rains, and vapor is removed.  But, as the planet warms, the air holds more water vapor, and this additional vapor is an important source of warming – it roughly doubles the warming effect of our CO2 emissions.



The history of earth’s climate


You might wonder how we could possibly know the CO2 concentration and temperature over a period of 800,000 years.  An important source of information about the history of the climate is buried in Antarctic ice.  Every winter, snow falls in Antarctica, and because it is so cold, it never melts.  As more snow falls on top of the older snow, the older snow becomes compressed into ice, and each winter’s snow is recorded as a distinct layer of ice, just as each summer is recorded in the growth rings in a tree’s trunk.  If we dig into the ice, we can count the layers, and we can figure out how old the ice is that way.



Trapped inside each layer of ice are tiny air bubbles.  Eight hundred thousand layers down, there’s air from 800,000 years ago, like an air fossil!  We can extract that air and measure the CO2.  We can also figure out what the temperature was when the air was trapped by comparing the presence of certain oxygen isotopes in the air.



There are other sources of variation of CO2 and temperature besides human activity, of course.  Small variations in the path of earth’s orbit around the sun produce cyclical variations that are clearly evident in the 800,000 year record.  These cycles have a period of about 100,000 years and are responsible for the arrival and end of ice ages.  As the earth emerges from an ice age, CO2 is released from the oceans, and then this CO2 amplifies the warming effect until the earth’s orbit takes it back into a phase of cooling.  These cycles are far too slow to explain any of the CO2 changes or temperature changes we have seen in the past 100 years.  Other sources of temperature variation include volcanic activity and solar activity.  Volcanoes emit much, much less CO2 than humans produce by burning fossil fuels, and solar activity does not track the changes we see happening on earth.



What else IB wants you to know

You should be able to figure out what the intensity of the sun’s radiation is at earth’s distance from the sun.  It’s about 1400 W/m^2, and it’s called the solar constant, S.



You should also be able to explain how 1400 W/m^2 absorbed by a circle whose radius is equal to that of earth becomes 350 W/m^2, or S/4, when it gets spread over the spherical surface of the earth.



You need to know the definitions of albedo and emissivity.


What do you need to know about Quantum Physics?

The sequence of development of quantum mechanics, summed up for IB students, from me:


(1) Hydrogen atoms emit a discrete spectrum of light.  This is our first evidence that energy levels in the atom are quantized.  What a mystery!  Physicists have never seen something like this before.


(2) Balmer comes up with a crazy formula that predicts the wavelengths that come out from hydrogen.  He doesn’t know why it works, it just does.  It is a discrete formula that involves the term n^2.  Why would n^2 be in there?


(3) Einstein in 1905 explains the photoelectric effect by treating light as a particle rather than a wave, overturning 200 years of belief about the nature of light.  His conclusion is particularly surprising in light of Young’s experiment and Maxwell’s equations, which both provide strong support for the idea that light is a wave.   Light refracts, it diffracts, and it can be polarized.  These are all characteristics of waves, not particles. Millikan attempts to disprove Einstein’s particle idea, but instead he confirms Einstein’s predictions with his stopping voltage experiments.  Light is a particle, at least sometimes.  This discovery makes Einstein the father of quantum mechanics, among other things.


(4) Bohr comes up with a quantized model of the atom, in which the electrons orbit at particular radii, but never in between those radii.  He does not know exactly what makes these particular orbits special, but his model explains the discrete emission spectrum, and it fits the Balmer series (by assuming that the angular momentum of the electrons must be quantized).  But why is this quantization happening?


(5) DeBroglie suggests that if waves can be particles, particles can also be waves.  Davisson and Germer confirm by experiment that electrons can be diffracted.


(6) Schrodinger says that the electron in an atom acts not as a particle but as a standing wave.  Bohr’s model, which provided so much insight into the discreteness of energy levels in the atom, turns out to be wrong.  The electrons are not particles in orbit, they are standing waves.  Finally we have an understanding of how discreteness has crept into the atom.  Standing waves can only exist at integer multiples of half-wavelengths.  Furthermore, the energy of these standing waves will be proportional squares of integers.  This is where the n^2 term comes from in the Balmer series!


(7) Max Born sees that Schrodinger’s wave equation needs to be interpreted as a probability distribution.  Einstein hates this idea: God does not play dice!  Schrodinger hates the idea, too!  But there’s no way around it.  This is the end of deterministic physics!  There are some events that just can’t be predicted.  Physicists never thought this could be the case.  But it is.


(8) Heisenberg recognizes that unlike particles, waves do not have a specific location.  They are spread out, rather than local.  And they are continuous, rather than discrete.  This wave nature of all particles means that there are limits to what can be known about the location and velocity of a particle.  This is the Heisenberg Uncertainty Principle and it arises because particles act like waves.   It has nothing to do with insufficient technology to measure locations and positions.  This is the final death blow for certainty in physics.  The science, and our understanding of the universe, will never be the same.


1. Discrete Emission Spectra

My spreadsheet showing the calculation of wavelength using the Balmer formula:


2. Bohr Model


Using classical physics and vectors, plus assumption that angular momentum of electron is quantized, to derive the equation for Bohr model radii.



Using equation for Bohr model radii to draw shell model for n=1 to 3, and calculating the velocity of a ground state electron.



Using classical physics to calculate the energy of electrons in Bohr model. Solving for energy of ground state and more generally for level n.


3. The Photoelectric Effect



Image result for photoelectric effect




A simulator of the effect and of Millikan’s experimental setup to study it

Khan Academy video discussing the effect



What happens in the photoelectric effect:


1) When you increase the intensity but keep the frequency the same, you get more electrons coming out, but the energy of those electrons does not change


2) There is a threshold frequency below which no electrons come out, regardless of how intense the light is.  The threshold frequency is different for different materials.


3) Above the threshold frequency, the energy of emitted electrons increases linearly as the frequency increases, following Planck’s formula E = hf.



Key points IB students need to understand about how the Photoelectric Effect shows light to be a particle rather than a wave:


(1) The energy of a wave is proportional to amplitude squared.  This means more intense light should make electrons come out with more energy.  This does not happen.


(2) If light is a wave, why is there this special threshold frequency?  All frequencies of waves carry energy.  Why are some frequencies too low to make any electrons come out, no matter how intense the light is?


(3) Wave energy takes time to arrive, but energy associated with a particle arrives all at once when the particle arrives.  If light is a wave, there should be a time delay between when the light is turned on and when the first electrons come out, especially if the intensity is really, really low.  There’s no delay.  The electrons come out immediately.


How does Einstein use the idea of photons to explain the photoelectric effect?


Image result for photons to explain photoelectric effect




(a) Electrons are stuck in the metal like balls stuck inside a bucket.  It takes a certain amount of minimum energy (also called the “work function”) to get the electrons released from the surface of the metal.  If a photon doesn’t have at least that much energy, then no electrons will come out.  This explains the existence of the threshold frequency.


(b) Light is a particle, but it is a unique particle whose energy is equal to h*f. When the light particles (photons) hit the electrons, they can knock the electrons loose.  This explains why higher intensity – more photons – leads to more electrons coming out.  It also explains why electrons come out right away.


(c) Energy is conserved when the photon ejects the electron.  The electron uses up some energy to escape from the metal.  Whatever it has left over becomes kinetic energy of the electron.  Surface electrons are the easiest to knock looses, so they come out with the most energy.  Electrons that were deeper in the metal will come out with less energy, or not at all.  This explains why higher frequency results in electrons with higher kinetic energy.   The kinetic energy will be equal to the total energy, hf, minus the escape energy.  KE = hf – work function.


4. Young’s Double Slit Experiment


Veritasium video about the original experiment




Veritasium does the double slit with SINGLE PHOTONS



Richard Feynman talks about a thought experiment using electrons. He says this is THE central paradox of Quantum Physics. Here’s the text of his lecture:


5. Heisenberg Uncertainty Principle


Veritasium demonstration of uncertainty principle with a laser


A musical version of the uncertainty principle:


Quantum Mechanics seems ridiculous!  How can it be right?




Yale lecture about the key experimental results from quantum mechanics



Physicist Brian Greene explains why Einstein hated his “quantum mechanics” child (and he gives you a taste of general relativity, too!)