Dual Nature of Light

Is light a wave or a particle?

Wave Properties

• -Diffraction

• -Interference

• -Polarization

Diffraction

Constructive & Destructive Interference

Polarization

Energy

Wave E increases with A2/I2.

Studies of Wave E

• Planck – color (f, ) vs. T.

• As T inc. , f inc, (decr)

Radiation & TemperatureHot Objects Emit Waves

Inte

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Classical physics could not accurately predict f vs. Temperature

Problem:

Max Planck related f to T.

Light (EM) E, is quantized--it can only take on certain whole number values.

E comes in little "chunks" of f x a constant now called Planck's constant, h:

• EM radiation waves

• chunks

• quanta

• photons

Can calculate E in EM waves units quanta or photons based on frequency.

E = hf.

h is Plank’s constant 6.63 x 10-34 Js.E is energy in Joulesf is frequency of radiation

Show that if E = hf,

E = hc.

• For waves, v = f.

• Rearrange f = v/.• Vacuum/air EM v = c (3 x 108m/s).

• f = c/.

• E = hf f = c/.

• E = hc.

Ex 1. Each photon of a certain color light has an energy of 2.5 eV. What is the frequency of and color of the light?

Solution:

E = hf f = E/h

convert eV to Joules.

(2.5 eV)(1.6 x 10-19J/eV) = 6.03 x 1014 Hz 6.626 x 10-34 J s

Green Light

2. The energy of a certain photon is 2.9 eV. What type of wave is it? Be specific.

• 2.9 eV x 1.6 x 10-19 J = 4.64 x 10-19 J.

eV

E = hf

f = 7 x 10 14Hz Violet Light

(4.64 x 10-19 J) = (6.63 x 10-34 Js) f

Finish Ex Sheet

• Hwk : Text Read 830 – 833 Do pg 833 #1-4 and 839 #2, & 856 # 2-4, 9.

Do Now.

• Plank’s Formula Sheet from yesterday.

• Solve problem 2. Show work

Do Now: A photon of light has energy = 2.072 eV. What color is it?

• 2.072 eV (1.6 x 10-19 J/eV).

• 3.3152 x 10-19 J

• E = hf.

• (3.3152 x 10-19 J) = (6.63 x 10-34 Js)f

• f = 5.00 x 1014 Hz.

• Orange

So Energy of EM Radiation comes in chunks, E = hf, maybe it’s not waves.

• All objects above 0 K radiate EM waves as E.

• Hotter = more total E = higher freq. (different color)

• Energy quantized, E = hf (J).

Other evidence:

• Photoelectric effect.

http://phet.colorado.edu/en/simulation/photoelectric

More evidence for E particlesPhotoelectric Effect

When EM waves shine on a metal surface, the E in wave may be absorbed by e- in metal. It may have enough E to kick out surface e-.

Materials that emit e- are photoemissive. The ejected e- are called photoelectrons.

Phet observations

http://phet.colorado.edu/en/simulation/photoelectric

• Use higher Amplitude/Intensity/brightness – • more e- fly off w same speed. • Current increases (A, C/s)• Increased f • e- fly off faster w higher KE.

• Boat would be tossed higher & faster with increased wave amplitude.

• But ejected e- not faster.

Classical Mechanics cannot explain why increasing A or exposure time does not increase photoemission. After all:

Einstein: EM wave E is quantized– photons.

• The collision of a photon with e- causes e- ejection.

• Increasing f, increases E (p) of each photon, so photoelectron has more KE (faster)

• Increasing Intensity (A) increases number of photons hitting more e- so more fly out – higher current!

• Envision EM as little chucks. High f are heavier.

• http://phet.colorado.edu/en/simulation/photoelectric

Photoemission only works with metals with weakly bound e-.

Photo-emissive metals have:

•Threshold Frequency fo.

•Work Function, Wo.

Threshold frequency fo = lowest f that will free an e-.

Light frequencies below the fo eject no e-, no matter how intense or bright the light.

Light frequencies above the fo eject e-, no matter how low the A (how dim).

A metal has a threshold frequency fo in the blue light range.

1. What will happen if very bright red light is shone upon the metal?

a) No e- will be emitted

b) more e- will be emitted

c) The emitted e- will have less energy.

Einstein confirmed EM waves/photons have E =hf.

Very high f give e- more KE. e- flies out faster.

High f vs. Low f.

a) nothing

b) the emitted e- will have more energy (KE)

c) more e- will be emitted with the same energy.

*2. A metal has a threshold frequency fo in the blue light range.

Predict what will happen to e- if UV light is shone upon the metal?

Increasing the I/A/brightness, increases the number of photons

increases rate of e- emission - the current; more e- ejected, but each e- won’t gain any extra E/speed.

A metal has a threshold frequency in the blue light range.

3. What will happen to photo e- if the blue light is made twice as bright?

a) nothing

b) the emitted e- will have more energy (KE)

c) more e- will be emitted with the same energy.

EM waves can be described as quanta or photons. The E carried by photons is:

Ephoton = hf or

Ephoton = hc/.

(for photon traveling at speed of light).

This E can be absorbed by photo-emissive materials.

Energy & Frequency

The min. frequency to free e- is fo.

The min energy needed to free an e- is called work function Wo, or .

Metals have low Wo.

Wo = hfo.

If photon f is higher than fo.

• E photon greater than Wo.

• Any photon E left over after the work function, goes into KE of e-.

4. A certain metal has a work function (Wo) of 1.7 eV. If photons of energy 3.0 eV are absorbed by the metal:

• a) No e- will be emitted at that energy.

• b) More e- will be emitted than would be at the Wo.

• c) Higher KE e- will be emitted than would be at Wo.

Classical (wave) vs. Modern (particle) theory different predictions

• Wave

• Metal needs time to absorb energy (like boiling water on a stove), eventually e- will be ejected.

• Higher amplitude/intensity waves (brighter), will give photo e- more E.

• Photon Theory

• Photons are particles that collide with e- so no time needed for e- to absorb E.

• High f photons have more E, ejected e- come out faster – more KE.

• High amplitude/brighter = more photons of EM so can eject more e- but with same E.

Summary:• EM waves as chunks of energy/photons travel at c.

• Calculate the Energy J E = hf, or

• E = hc/.

• Evidence for photons – from Photoelectric Effect Experiment –

• f not A responsible for KE of ejected e-.

• High f = high E, photon.

• High A = high number of photons.

• Photo-emissive materials have:

• fo = min f to eject e- (Hz)

• Wo= min E to eject e- (J)

Read Txt 834-837

Photoelectric Effect Questions

Graph of Photoelectric Experiment

• KE of photoelectron vs. frequency.

max KE of photo e- vs. f for metal. As f of EM wave increases, KE increases, slope = h. (work function), is minimum energy needed to eject e-.

Work function

2 3 4 5 6 7 8x 1014 Hz

0.40.00.40.81.0

eV

State the work function & threshold frequency of this metal

5. A particular metal has a threshold frequency fo, of 5 x 1014 Hz.

What is its work function Wo in J & eV?

Wo = hfo.

3.3 x 10-19 J

2.07 eV

• Ephoton = hf is the total E available.

• Absorbed photon E splits between Wo & KE photo e-, so total E of absorbed by e- is:

• Epho = Wo + KE.

• The maximum KE of ejected e- is:

• KEelc = Epho – Wo.

• Don’t forget Wo = hfo.

6: Photoelectric Effect:

Light having f = 1 x 1015 hz shines on a sodium surface. The photoelectrons have a maximum KE of 3 x 10-19 J.

Find the threshold frequency for sodium.

Photon Photoelectron.

Etot = Wo + KE.

Etot – KE = Wo.

hf – KE = hfo.

fo = (hfphoton – KEmax)(h)

change eV to Joules:(1.86 eV) (1.6 x 10-19 J/eV) = 2.85 x 10-19 J

fo = (hfphoton – KEmax)/(h)

(6.63 x 10-34 Js)(1 x 1015 hz) - (2.85 x 10-19 J)(6.63 x 10-34 Js)

fo = 5.5 x 1014 Hz.

Below this frequency no electrons will be ejected.

In 1913-1914, R.A. Millikan did a series of extremely careful experiments involving the photoelectric effect. He found that all of his results agreed exactly with Einstein's predictions about photons, not with the wave theory.

Einstein actually won the Nobel Prize for his work on the photoelectric effect, not for his more famous theory of relativity.

Some experimental results, like this one, seem to prove that light consists of particles; others insist, that it's waves.

We can only conclude that light is somehow both a wave and a particle--or that it's something else we can't quite visualize, which appears to us as one or the other depending on how we look at it.

Reg Hwk Intro Photoelectric Effect Prac Packet

• Hwk Text 834 – 837

• Finish photo elec packet

• Do Regents Packet

Light Fantastic BBC part 3 58 min

• http://www.youtube.com/watch?v=VuGjo9oNqao

Review of photoelec w german accent 4.11

• http://www.youtube.com/watch?v=GpcWc5KLVRo

• Photoelectric Effect Explained 6 min

• http://www.youtube.com/watch?v=0qKrOF-gJZ4

Particle Properties of Waves extend to conservation of energy and momentum.

Photons may give up all or part of their energy in collisions, but the sum of the momentums and energy before must equal the sum after.

Compton Effect

If light behaves like a particle, then a collision btw photon & e- should be similar to billiard balls colliding. Photons must have momentum (p), & energy.

In collision of photons with particles (like e-), conservation of energy & conservation of momentum apply.

If the photon gives only part of its energy & momentum to an e-, its momentum decreases after the collision by the same amount as absorbed by the electron.

Therefore, the frequency or energy of the photon decreases. The wavelength increases.

pbefore = pafter.

E photon before = KEelc after. + E photon after

hfi = KEelc after + hff photon after

pphoton = hf/c = h/. The wavelength of the photon increases after collision.

Matter has wave-like properties.

1924 Louis DeBroglie suggested that since waves had particle properties, matter might have wave properties.

It turns out that matter does have wave properties which are inversely related to the momentum of the particle.

For matter:

=h/p or

= h/mv.

Since the mass of most objects is so large, the wavelengths would be very small & not measurable.

Electrons, however, do show diffraction & other wave characteristics.