Blackbody Radiation, Photoelectric Effect,

Wave-Particle Duality

Physics 102: Lecture 22

Demo

Hour Exam 3

• Monday, April 14• Covers

– lectures through Lecture 20 (last Monday’s lecture)

– homework through HW 10– discussions through Disc 10

• Review, Sunday April 13, 3 PM, 141 LLP

These objects are just resolved

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Two objects are just resolved when the maximum of one is at the minimum of the other.

Resolving Power

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To see two objects distinctly, need objects > min

min

objects

Improve resolution by increasing objects or decreasing min

objects is angle between objects and aperture:

sinmin ≈ min = 1.22 /D

min is minimum angular separation that aperture can resolve: D

dy

sinmin min 1.22D

Resolving Power

How does the maximum resolving power of your eye change when the brightness of the room is decreased.

1) Increases 2) Constant 3) Decreases

When the light is low, your pupil dilates (D can increase by factor of 10!) But actual limitation is due to density of rods and cones, so you don’t notice an effect!

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Recap.• Interference: Coherent waves

– Full wavelength difference = Constructive– ½ wavelength difference = Destructive

• Multiple Slits– Constructive d sin() = m m=1,2,3…)– Destructive d sin() = (m + 1/2) 2 slit only– More slits = brighter max, darker mins

• Huygens’ Principle: Each point on wave front acts as coherent source and can interfere.

• Single Slit:– Destructive: w sin() = m m=1,2,3…)– Resolution: Max from 1 at Min from 2

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oppo

site

!

Everything comes unglued

The predictions of “classical physics” (Newton’s laws and Maxwell’s equations) are sometimes completely, utterly WRONG.

– classical physics says that an atom’s electrons should fall into the nucleus and STAY THERE. No chemistry, no biology can happen.

– classical physics says that toaster coils radiate an infinite amount of energy: radio waves, visible light, X-rays, gamma rays,…

The source of the problem

It’s not possible, even “in theory” to know everything about a physical system.

– knowing the approximate position of a particle corrupts our ability to know its precise velocity (“Heisenberg uncertainty principle”)

Particles exhibit wave-like properties.– interference effects!

The scale of the problemLet’s say we know an object’s position to an accuracy x.

How much does this mess up our ability to know its speed?

Here’s the connection between x and v (p = mv):

That’s the “Heisenberg uncertainty principle.” h 6.610-34 J·s

4hvm x

Atomic scale effectsSmall x means large v since

4hvm x

Example: an electron (m = 9.110-31 kg) in an atom is confined to a region of size x ~ 510-11 m.

How fast will the electron tend to be moving?

Plug in, using h = 6.610-34 to find v > 1.1106 m/sec

Quantum Mechanics!• At very small sizes the world is VERY different!

– Energy is discrete, not continuous.– Everything is probability; nothing is for certain.– Particles often seem to be in two places at same time.– Looking at something changes how it behaves.

• If you aren’t confused by the end of this lecture, you weren’t paying attention!

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Hot objects glow (toaster coils, light bulbs, the sun).

As the temperature increases the color shifts from Red to Blue.

The classical physics prediction was completely wrong! (It said that an infinite amount of energy should be radiated by an object at finite temperature.)

Blackbody Radiation

Blackbody Radiation Spectrum

Visible Light: ~0.4m to 0.7m

Higher temperature: peak intensity at shorter

Blackbody Radiation:First evidence for Q.M.

Max Planck found he could explain these curves if he assumed that electromagnetic energy was radiated in discrete chunks, rather than continuously.

The “quanta” of electromagnetic energy is called the photon.

Energy carried by a single photon is

E = hf = hc/

Planck’s constant: h = 6.626 X 10-34 Joule sec

Preflights 22.1, 22.3A series of light bulbs are colored red, yellow, and blue.Which bulb emits photons with the most energy?

The least energy?

Which is hotter?

(1) stove burner glowing red

(2) stove burner glowing orange

Blue! Lowest wavelength is highest energy.

E = hf = hc/Red! Highest wavelength is lowest energy.

Hotter stove emits higher-energy photons

(lower wavelength = orange)

80% correct!

ACT: PhotonA red and green laser are each rated at 2.5mW.

Which one produces more photons/second?

1) Red 2) Green 3) Same

Red light has less energy/photon so if they both have the same total energy, red has to have more photons!

# photons Energy/secondsecond Energy/photon

Power

Energy/photon

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Powerhf

Nobel Trivia

For which work did Einstein receive the Nobel Prize?

1) Special Relativity E=mc2

2) General Relativity Gravity bends Light3) Photoelectric Effect Photons4) Einstein didn’t receive a Nobel prize.

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Photoelectric Effect

• Light shining on a metal can “knock” electrons out of atoms.

• Light must provide energy to overcome Coulomb attraction of electron to nucleus

• Light Intensity gives power/area (i.e. Watts/m2)– Recall: Power = Energy/time (i.e. Joules/sec.)

Demo

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Photoelectric Effect: Light Intensity

• What happens to the rate electrons are emitted when increase the brightness?

• What happens to max kinetic energy when increase brightness?

Photoelectric Effect: Light Frequency

• What happens to rate electrons are emitted when increase the frequency of the light?

• What happens to max kinetic energy when increase the frequency of the light?

Photoelectric Effect Summary

• Each metal has “Work Function” (W0) which is the minimum energy needed to free electron from atom.

• Light comes in packets called Photons– E = h f h=6.626 X 10-34 Joule sec

• Maximum kinetic energy of released electrons – K.E. = hf – W0

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Is Light a Wave or a Particle?• Wave

– Electric and Magnetic fields act like waves– Superposition, Interference and Diffraction

• Particle– Photons– Collision with electrons in photo-electric effect

BOTH Particle AND Wave

Are Electrons Particles or Waves?

• Particles, definitely particles.• You can “see them”.• You can “bounce” things off them.• You can put them on an electroscope.

• How would know if electron was a wave?

Look for interference!

Young’s Double Slit w/ electron

• JAVA

Screen a distance L from slits

Source of monoenergetic electrons

d

2 slits-separated by d

L

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Electrons are Waves?

• Electrons produce interference pattern just like light waves.– Need electrons to go through both

slits.– What if we send 1 electron at a time?– Does a single electron go through

both slits?

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ACT: Electrons are Particles

• If we shine a bright light, we can ‘see’ which hole the electron goes through.

(1) Both Slits (2) Only 1 Slit

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But now the interference is gone!

Electrons are Particles and Waves!• Depending on the experiment electron

can behave like– wave (interference) – particle (localized mass and charge)

• If we don’t look, electron goes through both slits. If we do look it chooses 1.

I’m not kidding it’s true! 46

Schroedinger’s Cat• Place cat in box with some poison. If we

don’t look at the cat it will be both dead and alive!

Poison

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HereKitty, Kitty!

More Nobel Prizes!

• 1906 J.J. Thompson – Showing cathode rays are particles (electrons).

• 1937 G.P. Thompson (JJ’s son)– Showed electrons are really waves.

• Both were right!

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Quantum Summary

• Particles act as waves and waves act as particles

• Physics is NOT deterministic

• Observations affect the experiment– (coming soon!)

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See you Wednesday!