Name:________________________ Regents Physics

Date:________ Mr. Morgante

UNIT 6 MODERN PHYSICS & THE STANDARD MODEL

Dual Nature of Light and the Photoelectric Effect Einstein’s photon theory of light brought up a question that most physicists believed had been answered in the debates between Christian Huygens and Isaac Newton… is light a particle or a wave? You have discussed light as a wave… always. But now serious questions had been raised as to whether or not this was true. Before we decide if light is a wave or particle, let’s examine the properties of the photoelectric effect based on each. “Light is a Wave” To keep one variable a constant, we will assume that we are testing monochromatic light (one color, one frequency). · A higher intensity of light (like a brighter bulb) means a higher amplitude of wave · A higher amplitude means that the wave has more energy. · We would expect that if light is a wave, as the intensity of the light increases more electrons with higher Ek should be ejected. · The frequency should not affect photoelectric effect, since it has nothing to do with the energy of the wave. Example: You’re at the water park at West Edmonton Mall. The wave machine is going so that it is making small waves (small amplitude). You could stand up to your waist in the water all day without getting moved, because the waves just don’t have enough energy to move you. Even if they increase the frequency of the little waves (so that more hit you every second), the waves are still too small to push you around. It’s only when they increase the amplitude (the size of the waves) that you can get pushed off your feet. You represent the surface electrons on the metal, and the water waves are light waves. “Light is a Particle” We will still assume that we are dealing with monochromatic light, but now we assume light is a particle (the photons in Einstein’s theory). · Since E = h¦, monochromatic light will be made up of photons that all have the same energy. · This is the energy that could eject electrons and give the Ek. · The energy of the light will only increase if the frequency of the light increased. · Increasing the intensity of the light only causes more photons of the same energy to hit the surface, so more electrons would drop off, but they all have the same maximum kinetic energy. Example: You are so bored studying physics that you decide to go practice your forehand in tennis. You go to a court that has one of those automatic ball machines that shoots balls at you. Unfortunately the wiring is all fried and it 2

starts shooting balls at you! Getting hit with one ball every ten seconds isn’t too bad, but then it cranks up the frequency and hits you with ten balls every ten seconds… ouch! That hurts! So you run off the court. Even though each ball was still being shot at you with the same velocity (intensity), they were hitting you a lot more frequently. You represent the surface electrons on the metal, and the tennis balls are photons of light. Which model is right? Well, you’ve already seen that Einstein’s use of Planck’s ideas to explain the photoelectric effect depend heavily on the frequency of light, but is there any other evidence that supports the particle theory of light? Millikan performed further experiments with the photoelectric effect in 1913-14 and found that at any frequency less than the threshold frequency (fo) no electrons are emitted, no matter how great the intensity of the light. An increase in the intensity of the light only means more electrons are emitted, but since the energy of each photon hasn’t changed, the maximum Ek of each electron stays the same. So, now we have evidence that light behaves as a particle, at least when it comes to explaining the photoelectric effect. But we still have to recognize that light has some properties (diffraction, interference) that are better explained using a wave model… so both models are right! The current model of light is usually referred to as “wave-particle duality”. We now recognize that light is both a particle and a wave. This means that sometimes a wave acts like a particle!

Photoelectric Effect Late in the year 1900, Max Planck (pronounced “Plonk”) came up with a new idea that might be able to solve the problems everyone was having trying to explain blackbody radiation. to be the source of blackbody radiation) could vibrate at any frequency. any amount of energy. about radiation acting like a wave and Maxwell’s equations). Planck tried to figure out a formula that would fit the experimental data, even if he didn’t have a good theory to back it up. if he assumed that electrons could only vibrate at specific frequencies. energy. of energy of the electrons vibrating at a frequency…

3

E = hf

E = energy of the radiation (J)

h = Planck’s Constant = 6.63x10 - 34 J∙s f = frequency of the emitted radiation (Hz) (or packets of energy called quanta!) You could have 1, 2, 3, …, pieces of radiation, as long as you had a whole number… no fractions! o This sounds like Millikan showing that charges always come in multiples of 1.6x10-19C and Thompson showing that electrons always had the same mass. o Only now we are taking about Electromagnetic Radiation, including light! Planck said that energy is not continuous as shown on the graph, but instead lots of very small points that look like a solid line. This is sort of like when you look at a picture in the newspaper… looks like a continuous picture, but it’s actually made up of little dots that blend together. Quantum. The smallest amount of energy possible at a given frequency (E=hf) is called a quanta of energy. This just means a “piece” of energy. Quanta – singular Quantum – plural The value for Planck’s Constant (h = 6.63 x 10 -34Js) is a universal constant, just like the gravitational constant, G. Example: What is least amount of energy from a light source that emits at a frequency of 4.50 x 1014 Hz? E = hf = (6.63 x 10 -34Js)(4.50 x 1014 Hz) E = 2.98 x 10 –19 J

Einstein Investigates Photoelectric Effect At the beginning of the 1900’s Albert Einstein linked Hertz’ research on the photoelectric effect to the work of Planck. · Remember, Planck said that an object emits energy according to the formula E = hf. · Einstein said that when an object emits light, the object must decrease its energy by that same amount… E= hf. · So light must be released in “packets” of energy… · Wait a second… he saying light is emitted as tiny particles, not waves… · He called these packets of light “photons” To test his theory, Einstein examined the photoelectric effect. A device similar to this one was set up:

4

Einstein ran several different tests with this apparatus. 1. What happens when the voltage source is turned off and the device is in the dark (no UV radiation falls on the plate)? Nothing happens. There are no readings on the ammeter, which is exactly what we would expect. As shown above, this is a broken circuit that (at the moment) has no voltage source. 2.

What happens when the voltage source is turned off and the device is exposed to radiation with a frequency less than UV? Again, nothing happens. This agrees with the original experiment that Hertz performed, since he found that you need frequencies of radiation that were equal or greater than UV before anything happens at the metal plate.

3.

What happens when the voltage source is turned off and the device is exposed to radiation with a frequency equal to or greater than UV? Now a current is shown by the ammeter readings! Einstein hypothesized that there were electrons being “ripped” off of the metal plate (as Hertz had observed). Einstein believed that these electrons then moved towards the electrode and hit it, which completes the circuit. This is why a current is shown on the ammeter.

4.

What happens if the voltage source is turned on, and slowly increased? Notice that the variable voltage source is set up so that the electrode will be negative and the metal plate becomes positive. This voltage should work against the electrons getting all the way from the metal plate to the electrode. Only electrons with sufficient kinetic energy (going fast enough) will be able to get to the electrode. The voltage was slowly increased from zero, and for a while nothing appeared to be changing. But, there came a point when the voltage became too great for electrons to get across the gap. At this point (and for any higher voltages) the ammeter gives a reading of zero. 5

Work Function Einstein believed that to give a single electron this energy to move, a single photon hit the metal surface (destroying itself), and transferred its energy to the one electron. · Since the electron is attracted to the surface of the metal, some minimum amount of energy must be needed just to snap it off. Otherwise, electrons would just be dropping off of atoms all the time. · Einstein called this the work function of the material, since you needed to do work on the electron to break it off. · Since yanking the electrons started to happen at a minimum frequency (usually around UV), he called it the W = work function (J or eV) threshold frequency of the material. h = Planck’s constant · This was all related to Planck’s formula E=hf in the following way… f0= threshold frequency (Hz)

W = hf0 The work function of materials goes as high as about 10eV. Example: What is threshold frequency of a material with a work function of 10eV Since the value for the work function is given in electron volts, we might as well use the value for Planck’s constant that is in eV s. W = h o o = W / h

= (10eV) / (4.14 x 10-15eVs)

o = 4.14 x 10-14 Hz

Photoelectric Effect Formula ·

If the frequency of the incoming light is great enough, there should be enough energy to break off the electron and have some left over to give it some kinetic energy. So… hf = Ek max + W

·

·

·

Which just basically says, if a photon (E=hf) transfers its energy to an electron, the electron has energy to tear away from its surface (W) and energy to move (Ek) This follows the conservation of energy, since the photon’s original energy is equal to the energy it takes to snap off the electron and get it moving. Note: some electrons will need more than the bare minimum W to be released (they might be attracted more strongly), so their Ek is not as great as the maximum. · That’s ok, though, since we’ll only worry about the electrons that came off the easiest and have the maximum kinetic energy. 6

Example: The work function of silver is 4.73eV. Electromagnetic Radiation with a wavelength of 1.20x1015Hz strikes a piece of pure silver. What is the speed of the electrons that are emitted? To figure out the answer you will need to go through a few steps… Calculate the maximum Ek first… hf = Ek + W Ek = hf – W = (4.14x10-15eVs)(1.20x1015Hz) – 4.73eV Ek = 0.238 eV = 3.81 x 10-20J

Then calculate the speed of the electron… Ek = ½ mv2

v = 2.89 x 105m/s Notice that in this example I used the value for Planck’s constant that is given in eVs, rather than Js. This saved me the trouble of changing the work function into Joules. But, it is just as important to realize that this results in an answer in eV which I have to change into Joules before I can use the kinetic energy formula. If you are more comfortable always working with standard units, go for it! If you changed the work function for silver into Joules you’d be doing great. In fact, if you’re ever in doubt, change everything into standard units and go from there. Because eV are so common in this unit.

Compton & deBroglie Einstein For a while Einstein continued research into the photoelectric effect.  He showed (using the photoelectric effect) that even though light had no mass, it still had kinetic energy.  Einstein predicted that we showed see another particle characteristic in light waves… momentum!  Based on his findings he predicted that photons have momentum which could be calculated by the formulas…

and …but at the time he had no way of confirming that these formulas were true.

7

Compton Effect In 1923 A.H. Compton started shooting high frequency x-rays at various materials.  Found that the x-rays scattered after hitting the target (graphite worked really well to cause this effect).  The radiation that was scattered after hitting the graphite had a slightly longer wavelength than the incident x-ray. Remember, longer wavelength = smaller frequency.  Since E = h, the scattered photons had less energy!  

He then found that electrons were being thrown off the target. Compton was able to explain all he was seeing (which became known as the Compton Effect) by using the photon theory of light…  As incident photons collided with the electrons, they transferred some of their energy to them  He applied the conservation of momentum and energy to the experiment, and found the results agreed!  Photons obey the laws of conservation of momentum and energy!  This provided support of Einstein’s theories that EM radiation has momentum.

deBroglie Wavelengths In 1923 Prince Louis de Broglie proposed a new idea…  Could things believed to be particles (like electrons and baseballs) sometimes act like waves?  All the stuff discovered so far has shown that electromagnetic radiation sometimes acts like a particle, so deBroglie just wanted to know if particles could act like waves. 

de Broglie said that since

then it should be easy to substitute p = mv

into the formula…

 

This is the de Broglie Wavelength of a Particle. 8

 

Nobody really took de Broglie seriously until Einstein read his paper and agreed with his ideas. Now the hard part… finding experimental data to support the theory.  The problem was that no one had ever seen a particle diffract or interfere with another particle, which would be proof that the particle was acting like a wave.  Notice that the wavelength of everyday objects would be very small.

Example: What is the de Broglie wavelength of a 0.20kg ball moving at 15m/s?



Remember from Young’s Double Slit experiment that to be able to see the effects of diffraction and measure wavelength, you need slits or objects which are not much larger than the wavelengths being studied.  It is impossible to build a diffraction grating as small as 10-34m! So for large objects we have a problem.  But notice where mass is in the formula… with a really small mass (like an electron), the wavelength gets bigger!



Although this is very small, the spaces between the atoms of a crystal are about this size.  Davisson and Germer shot electrons at a metal crystal and observed a diffraction pattern.  The conclusion: Particles have wave properties! So, the wave-particle duality applies to objects as well as light.

9

EINSTEIN’S E=mc2 MAIN POINTS:  EINSTEIN DISCOVERED THIS THEORY IN 1905.  THE THEORY RELATES THE MASS OF AN OBJECT TO THE AMOUNT OF ENERGY THAT OBJECT CONTAINS. IN OTHER WORDS, MASS AND ENERGY ARE THE SAME, THEY ARE JUST IN DIFFERENT FORMS.  THIS STATEMENT IN EQUATION FORM IS E=mc2. UNITS ARE FOR E ARE JOULES (J), m IS MASS IN kg, c IS THE SPEED OF LIGHT IN A VACUUM (3x108 m/s).  THIS THEORY IS GOVERNED BY THE LAWS OF CONSERVATION OF MASS AND ENERGY.  A SMALL AMOUNT OF MASS CAN PRODUCE IMMENSE POWER, THIS IS THE BASIS FOR NUCLEAR ENERGY AND NUCLEAR WEAPONS. EX. PROB 1: a) 1 kg OF MASS IS CONVERTED INTO HOW MUCH ENERGY? KNOWNS: m=1kg; c=3x108 m/s (FROM REF. TABLE) UNKNOWN: E E=m c2 E=(1kg)*( 3x108 m/s)2 = 9x1016 joules b) HOW MANY MeV IS THIS EQUAL TO? 1Ev = 1.6x10-19 J (FROM REF. TABLE) 9x1016 joules x 1Ev/1.6x10-19 J = 5.625x1035 eV = _________ MeV c) HOW MANY UNIVERSAL MASS UNITS IS THIS EQUAL TO? START W/ REF. TABLE FOR CONVERSION, SHOW ALL WORK. Alpha decay happens in elements further down the periodic table because the strong nuclear forces in the atom are not able to hold a very large nucleus together. daughter nucleus plus the alpha particle is less than the mass of the original parent nucleus. following Einstein’s famous formula E = mc2.

10

Example: How much energy is released when Uranium-238 decays to Thorium234 This is an alpha decay. The reaction for it would be… It is possible to look up the total masses of these atoms in text books. They would be…

There’s 0.0046u unaccounted for after the reaction has occurred. Since 1u = 931.5MeV, the energy released in this reaction is 4.3MeV. This energy is found (mostly) in the kinetic energy of the alpha particle and daughter nucleus moving away from each other.

Fusion Nuclear fusion can result when atoms or subatomic particles combine. Example: Proton + Neutron Mass of p+ = 1.00782 amu Mass of n0 = 1.00866 amu Mass of = 2.01410 amu Add them up and you’ll find the total mass on the left is more than the total mass on the right! This mass didn’t disappear, it was turned into energy according to Einstein’s formula E = mc2 . In the above example the difference in mass (called the “mass defect”) is… 2.01410 – (1.00782 + 1.00866) = 0.00238 amu = 3.95 x 10-30 kg The energy released would be… E = mc2 = 3.95 x 10-30 kg (3.00 x 108 m/s)2 E = 3.56 x 10-13 J This may not seem like a lot of energy, but remember that it came from the fusion of just one proton and neutron. If we could trillions of these reactions going every second the release of energy would be impressive! Also, notice what the product is… not highly radioactive elements like in a fission reaction… here we get good old hydrogen!

11

So why don’t we use fusion instead of fission?  Unfortunately at this stage in our technology we haven’t worked out all the bugs yet.  We can build and run fusion reactors right now, but we end up putting in more energy than we get out. o Fusion reactions require intense heat and pressure to allow fusion to happen.  There is a great deal of research working on “cold fusion”, the ability to cause fusion to happen at lower temperatures.

12

What is Particle Physics? Particle physics is the study of what everything is made of. Particle Physicists study the fundamental particles that make up all of matter, and how they interact with each other. Everything around us is made up of these fundamental building blocks of nature. So, what are these building blocks?

In the early 1900's it was believed that atoms were fundamental; they were thought to be the smallest part of nature and were not made up of anything smaller.

Soon thereafter, experiments were done to see if this truly was the case. It was discovered that atoms were not fundamental at all, but were made up of two components: a positively charged nucleus surrounded by a cloud of negative electrons.

13

Then the nucleus was probed to see if it was fundamental, but it too was discovered to be made up of something smaller; positive protons and neutral neutrons bound together with the cloud of electrons still surrounding it.

Now that these protons and neutrons were found, it was time to see if they were fundamental. It was discovered that they were made up of smaller particles called "quarks", which today are believed to be truly fundamental, along with electrons. Furthermore, electrons belong to a family of fundamental particles, which are called "leptons". Quarks and leptons, along with the forces that allow them to interact, are arranged in a nice neat theory named The Standard Model. The Standard Model

The Standard Model is a theoretical picture that describes how the different elementary particles are organized and how they interact with each other along with the different forces. The elementary particles are split up into two families, namely the quarks and the leptons. Both of these families consist of six particles, split into three generations, with the first generation being the lightest, and the third the heaviest. Furthermore, there are four different force carrying particles, which lead to the interactions between particles. The table below shows this all a little bit more clearly.

14

So, is everything in the world made up of quarks and leptons? Well, not quite. Next stop, Antimatter. What is Antimatter?

An interesting thing that has been discovered about matter particles, is that each one has a corresponding antiparticle. The term "anti" may be a bit deceiving, as it is still real matter. The only difference between a particle and its antiparticle is that an antiparticle has the opposite electrical charge.

15

Think of it as a mirror image. In our experience left and right are the only things to reverse when looking in the mirror. Similarly, in the particle world, charge is what reverses when looking in the "mirror". It's mass, spin, and most (quarks have something called colour charge which is also changed in the "mirror") other properties are the same.

In general, an antiparticle is the particles name with "anti" in front of it. For example, the antiparticle of the proton is the antiproton. An exception to this rule is the electron, whose antiparticle is known as the positron. An interesting fact about antimatter is that the entire universe is made up of matter as opposed to antimatter. This is somewhat of a mystery. On to Quarks. What are Quarks?

To start with, there are six types of quarks (plus their six antiquarks), which are coupled into three pairs. They are the up-down, the charm-strange, and the top-bottom (sometimes known as truth-beauty). Another interesting fact about quarks is that you can never find one by itself, as they are always with other quarks arranged to form a composite particle. The name for these composite particles is "hadrons". Quarks, like protons and electrons, have electric charge. However, their electric charges are fractional charges, either 2/3 or 1/3 (-2/3 and 1/3 for antiquarks), and they always arrange to form particles with an integer charge (i.e. -1, 0, 1, 2...).

16

Flavour

Mass (GeV/c2)

Electric Charge (e)

u

up

0.004

+2/3

d

down

0.08

-1/3

c

charm

1.5

+2/3

s

strange

0.15

-1/3

t

top

176

+2/3

b

bottom

4.7

-1/3

Because quarks join with each other to form particles with integer charge, not every kind of combination of quarks is possible. There are two basic types of hadrons. They are baryons, which are composed of three quarks, and mesons, which are made up of a quark and an antiquark. Two examples of a baryon are the neutron and the proton.

The proton is composed of two up quarks and one down quark. As you can see, when the charges from the individual quarks are added up, you arrive at the familiar charge of +1 for the proton.

The neutron is made up of two down quarks and one up quark. Again, adding the charges from the quarks up, we arrive at zero.

17

An example of a meson is the pion. It is composed of an up quark and a down antiquark. Because mesons are a combination of particle and antiparticle, they tend to be very unstable and decay very quickly.

So we've now talked about quarks, but there is still the other family of elementary particles to talk about, the "leptons", which we will now discuss. What are Leptons?

Like quarks, there are six types of leptons, and again, in three pairs. Electron - neutrino, muon - neutrino, and tau - neutrino (these three neutrino's are different from each other). The electron, muon, and tau each carry a negative charge, whereas the three neutrinos carry no charge. Leptons, unlike quarks, exist by themselves, and, like all particles, have a corresponding antiparticle.

Flavour

Mass (GeV/c2)

Electric Charge (e)

electron neutrino