Physics 200 Class #1 Outline



Physics 200 Class #11 Notes October 12, 2005

Reading Assignment Text: Chapter 6 pp. 141-160

• Reminder: The MidTerm Exam is on October 17

• An introduction to The Photoelectric Effect (30 min.)

• Review of the first 5 chapters (60 min.)

We now come to one of the first crucial problems of the early twentieth century.

Three types of Spectra:

1. Continuous (Blackbody Radiation)

2. Line Spectra

3. Absorptiion Spectra

Max Planck and Incandescent Radiation

Incandescent Radiation, Cavity radiation, Blackbody Radiation and Thermal radiation are all the same.

The experimental facts: We plot the power radiated per unit area at each temperature. Note that the temperature must be the absolute temperature in Kelvins. To convert from centigrade, add 273. TKelvin = TCentigrade + 273.

So, 0 degrees C = 273K

and 3727 oC = 4000K

(notice you don't have to use the degrees symbol o for Kelvin)

[pic]

R(λ) is the energy radiated per unit area per unit time. Notice the visible region.

(1) We find that the total power/area over all wavelengths (area under the curve) is given by:

[pic]

In other wards, if we double the temperature, the power radiated increases by 16 times!

(2) The peak of the curves is described by Wien’s Law which says that the product of wavelength and temperature is a constant. This is a very useful relationship, especially in Astronomy.

[pic]

You saw the light bulb change color with different temperatures. Here are some more examples - this is how they tell the temperature of stars!

[pic]

Spectra for actual stars, from zebu.uoregon.edu There's a vertical offset so the spectra don't overlap so you can actually look at them. The top spectrum is for a star with temperature of about 7000K. The temperatures of the stars are lower as you go down, until the bottom spectrum is of a star at about 4000K. The star labeled G12V is "solar like". That means, this is pretty much what the sun looks like. The curves are a bit messy because some light gets absorbed by gasses out in space and around the stars themselves. Note though that the peaks of the curves move to longer wavelengths for cooler stars.

Problem: The peak of the blackbody curve is measured to be at 1000 nm for a temperature of 2900 K. Find the temperature of the surface of the sun if the peak of the solar spectrum is at 500 nm.

And now, the beginning of quantum mechanics:

All attempts to predict the blackbody curve using classical physics failed except for very high wavelengths (ultraviolet catastrophe). Planck was able to predict the curve by making some assumptions about the energies of the atomic oscillators emitting the light.

[pic]

Planck’s Assumption: The energy of the oscillators emitting the light is not continuous but is quantized. If an oscillator is vibrating at a frequency f its energy can only have values given by

[pic]

Where h is a constant that must be determined experimentally. You will do this in Lab #7. The units must be

joule x seconds.

[pic]

With this hypothesis, Planck introduces the notion that the Energy of a system is quantized (comes in discrete fixed sizes). This might be considered one of the beginnings of quantum mechanics.

(Remember the standing waves on a string - only certain frequencies were allowed (f, 2f, 3f, 4f ...). This is the same principle.)

A nice Java Applet on Blackbody radiation:



Chapter 6 The Photon

Is the wave theory of light enough to describe all phenomena in which it participates?

6.2 The photoelectric Effect

Einstein and the Photoelectric Effect

[pic]

1. Collector positive: current flows

2. Collector negative: Current stops at some unique value

Major Problem with Wave Model: There is no time delay between the light turning on and the

ejection of photoelectrons! Classical theory predicts time delays of hours while the energy from

a wave builds up on the electron.

Classroom demonstration of Photoelectric effect!

Key Points:

• No time lag between turning on light and photocurrent.

• Each frequency has a unique stopping voltage.

• Increasing the Intensity of the light does not change the stopping voltage

• There is a threshold frequency below which there is no effect.

The experimental facts are summarized by plotting stopping energy (voltage) versus frequency. Typical curves are shown in the next figure.

[pic]

Interpretation:

1) The stopping voltage is a measure of the maximum kinetic energy of the ejected electrons.

2) The kinetic energy of the electrons is directly proportional to the frequency.

3) The threshold frequency indicates that the incident light must have a minimum energy to eject electrons.

Einstein’s Interpretation:

The light is quantized (photon) and has energy directly proportional to its frequency!

[pic]

[pic]

W is the (Work Function): Minimum energy needed to remove electron from surface. This is a unique value for each metal.

A new energy unit: The electron volt eV

If we measure the stopping voltage in volts, we convert to joules by multiplying by the charge on the electron. One volt is equal to one joule/coulomb. The joule is an inconvenient unit to use in atomic physics.

We usually specify the wavelength rather than the frequency:

[pic]

Quick review of quantitative concepts (Chapters 1-5 only):

General:

v velocity

λ wavelength

f frequency

[pic]

velocity of light in a vacuum: c = 3x108m/s

Sine wave: [pic]

Diffraction: (light bending when moving between different materials)

n index of refraction

n=c/v

(light moves more slowly in materials with a higher index of refraction)

so... velocity of light in material: v=c/n

v=λf

When moving through different materials, frequency stays same but wavelength changes.

[pic]

Think of the rows of marching soldiers walking off of grass into mud, they move more slowly and pile up on each other.

Snell's law: [pic] which you can write [pic]

θ is the angle from the "normal"

example: for light moving from air to water, coming in at some angle θair,

you can write [pic]

Light behaving like a wave:

Diffraction: the bending of light around corners. Do particles do that?

Interference:

[pic] Maxima [Also good for Diffraction Grating]

Path Difference = λ Produces constructive interference

Path Difference = λ/2 Produces destructive interference

Electricity and magnetism:

Electric force on something that has charge:

F=qE

Electric force on something that has charge and is moving:

F=qvB if v is perpendicular to B, plus a direction given by the right hand rule.

[pic]

For Blackbody Radiation (also called thermal radiation, incandescent radiation, cavity radiation, ...)

[pic]

Total energy radiated: [pic]

The peak intensity: [pic]

quantum oscillator states: [pic]

Only certain frequencies allowed. Like standing waves on a string, only multiples of the fundamental frequency can be there.

[pic]

Definitions: work, energy, potential energy, kinetic energy

Kinetic energy is proportional to [pic]

Momentum is proportional to [pic]

Force

Momentum

Conservation of momentum

Energy

Potential Energy

Kinetic Energy

Conservation of energy!

collisions

elastic - all the energy goes into the bounce and nothing is crushed/smashed/etc. Energy stays in the bouncing system. "Kinetic energy stays the same" The ball bounces back up.

inelastic - things go splat. energy is put into heating up the environment instead of only into the bounce. "Kinetic energy does not stay the same", you lose kinetic energy. The paper wet paper towel does not bounce back up.

Units in the metric system

Length: meter m

Mass: kilogram kg

Time: second s

Frequency: hertz Hz = 1/s

Velocity: [pic]

Acceleration: [pic]

Force: newton N=[pic]

Energy: joule J = Nm = [pic]

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