AN INTRODUCTION TO… MODERN PHYSICS Maxwell’s – Good to the last…. In 1873, James Clerk Maxwell summarized in 4 equations everything that was known.

AN INTRODUCTION TO…

MODERN PHYSICS

Maxwell’s – Good to the last….

• In 1873, James Clerk Maxwell summarized in 4 equations everything that was known about EM and EM waves

They state (basically):1. Electric field lines start on a positive

charge and end on a negative charge.2. Magnetic field line form closed loops

and have no beginning or end

Maxwell’s Thoughts cont…

3. An electric field must exist around a changing magnetic field.

4. A changing electric field generates a magnetic field.

These equations were thought to be the “be all and end all” of Physics. They fully explained everything known about electromagnetic waves. They were used to predict the speed of these waves.

Catastrophe!

• The first problem for Maxwell’s eq’ns started with incandescence.

Gustav Kirchoff

I’ve got a bad feeling about this…

James Maxwell

• Incandescence: heating matter until it emits electromagnetic radiation.

• Kirchoff (1824-1887) thought of a “blackbody radiator”

Catastrophe!

According to Maxwell’s eq’ns: PαT4 and fmax α T

• This relationship worked- sort of….• It worked until the frequency of light

emitted was higher than visible light.• This was what was expected:

Catastrophe!

Catastrophe!

• This is what occurred:

Catastrophe!

p

• This was called the UV catastrophe – the top minds of the day couldn’t figure out why this occurred.

Catastrophe!

Enter Max Planck- one of Kirchoff’s grad students

Planck to the rescue…

• Planck came up with a formula to get the curve we saw earlier. It was an empirical model.

The theory behind this model was that ENERGY WAS QUANTIZED! Energy was made up of discrete energy amounts

The Beginning of Quantum Physics

• Planck found that the vibrations of the atoms in the radiator had certain energy levels.

• He found that the energy levels were a constant multiplied by the frequency: E = hf

Finally a constant that’s not a k! That’s OK!

• The energy of the oscillations were found to be: 0hf, 1hf, 2hf, 3hf, …

• So, E = nhf, where n = 0, 1,2,3,…• ‘h’ is called Planck’s constant and is

h = 6.626 x 10 ^-34 Js

The Beginning of Quantum Physics

Planck’s model was purely mathematical and worked only if energy was quantized. The theory behind this was still a mystery.

Shedding light on Problem #2

• Physicists’ understanding of EM was challenged with another experiment: The Photoelectric Effect

In the experiment, light was incident on a metal plate which was attached to a wire. The wire was connected to a galvanometer (a sensitive ammeter).

The Photoelectric Effect

A simulation of the Photoelectric effect

When certain light shines on the metal, current passes through the ammeter. What is happening?

The Photoelectric Effect

It must be that electrons are being ejecting from the metal. But why?

To solve these questions, physicists called on probably the greatest physicist ever…

The Photoelectric Effect

Einstein developed the theory behind this and won the Nobel Prize for it.

The Photoelectric Effect

To fully understand the significance of Einstein’s theory we must look at what physicists expected to happen and then we really did occur during the experiment.

Experiment 1: Changing the intensity of light

The Photoelectric Effect

What we saw was light hitting a metal and electrons from the metal were given off. From now on these electrons will be called PHOTOELECTRONS indicating they were emitted through the photoelectric effect.

When we increased the intensity of the light incident on the metal, we saw……

The Photoelectric Effect

Since light is a wave resonance must be the factor

behind the emitted electrons. Light strikes an electron at the electron vibrates with the frequency of the light ray. As more and more light rays hit this electron, it will gain energy. (Think pushing someone on a swing.) This is possible since resonance can do this…

Example 2

The Photoelectric Effect

So, classical physics explains what we saw initially: more intensity = more current. However, let’s go over the experiment again.

Experiment 2a and b: Introduce a negative voltage to the circuit and increase the intensity of red light.

The Photoelectric Effect

Remember: for a wave I = P/A = E/t/A so I α E. More intense waves carry more energy.

What we see now shows us that

1) the photoelectrons have different energies and this energy is independent on the intensity of the light.

2) the photoelectrons are emitted without delay

3) that the photoelectric effect occurring is independent of the light’s intensity but is dependant on the light’s frequency.

Classical Physics is…

Philipp Lenard also figured out that if you switch the battery poles, you can stop the electrons from hitting the collector plate. But again…why?

The Photoelectric Effect

The Photoelectric Effect

Einstein (who never worked in the lab!) studied these results and came up with the idea that light is a PARTICLE, not a wave.

He took Planck’s idea of energy being quantized and applied it to light. He called a packet of light energy a PHOTON. Each photon of light has a certain energy pertaining to its colour (its frequency).

The Photoelectric Effect

If the photon has the right energy, it can knock the electron off the metal.

Einstein also recalled Lenard’s contribution: reversing the polarity of the battery enables us to control and stop the current.

Einstein realized that what was happening was that these photoelectrons had different energies. That’s why when the polarity was reversed, the current decreases – some of the electrons are “sucked back”.

The Photoelectric Effect

The Photoelectric Effect

When all the electrons are sucked back, the voltage is called the stopping potential. It has enough potential to “use up” the kinetic energy of the most energetic electron.

Remember: qVEQ *

ping Potential

The Photoelectric Effect

This height represents the “stopping potential” of the Frisbee

So the potential energy the Frisbee has here…

equals the kinetic energy it had here!

The Photoelectric Effect

Experiment 3: Finding the stopping potential:

λ = 494nm

I = 100%

V = -0.20V

Unclick Show electrons with max energy only.

The Photoelectric Effect

By measuring the voltage require to stop the photoelectrons from hitting the collector plate, we are calculating ….

We know now the MAXIMUM kinetic energy of a photoelectron for the experiment. Why do photoelectrons have different energies anyways?

The Work Function

Let’s take a close look at the surface of a metal:

The first electron used some of the energy to move to the top of the surface. Then it used some to be ejected off the surface. Its kinetic energy was the left over energy. The second electron was already at the top of the surface so it just lost the energy required to be ejected: the work function! That photoelectron will have the max. kinetic energy.

The Results: Graphically

Threshold frequency

Work Function

The Equation of the Line

As we know the equation of a line is y =mx+b. This graph is no different:

KE(max) = hf - W

A few things to remember:

The KE(max) is calculated by using the stopping potential (V*q)

The threshold frequency, f0, and the work function are related: W=hf0

The KE(max) is measured in eV. 1eV = 1.6 x 10^-19J

The energy of a photon = hf

Examples

Calculate the energy of the green photon and the velocity of the photoelectron (blue incident light)

Photoelectric Effect Problems

1.Calculate the energy of a photon of blue light with a frequency of 6.67 x 1014 Hz. (State in eV) [2.76eV]

2.Calculate the energy of a photon of red light with a wavelength of 630 nm. [1.97eV]

3. Light of wavelength 600nm is directed at a metallic surface with a work function of 1.60 eV. Calculatea. the maximum kinetic energy of the photoelectron. [Ek = 7.6 x 10-20]b. the maximum speed of the photoelectron. [v = 4.1 x 105m/s]c. the stopping potential of the metal. [v0 = 0.48 v]

4. Barium has a work function of 2.48 eV. What is the maximum kinetic energy of the ejected electron if the metal is illuminated by light of wavelength 450 nm? [0.28 eV]

5. When a 350nm light ray falls on a metal, the maximum kinetic energy of the photoelectron is 1.20eV. What is the work function of the metal? [2.3 eV]

Blackbody

a small hole in the side of a large box is an excellent absorber, since any radiation that goes through the hole bounces around inside, a lot getting absorbed on each bounce, and has little chance of ever getting out again. So, we can do this in reverse: have an oven with a tiny hole in the side, and presumably the radiation coming out the hole is as good a representation of a perfect emitter as we’re going to find.