Light 31

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Making Light

• How do we make light?

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Making Light

• How do we make light?

– Heat and Light: Incandescent Lighting

(3-5% efficient)

– Atoms and Light: Fluorescent Lighting

(20-40% efficient)

We’ll consider Heat and Light first. Later in this part

we will consider Atoms and Light.

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Blackbody Radiation:

• What is a blackbody?

A BLACK object absorbs all the light incident

on it.

A WHITE object reflects all the light incident

on it, usually in a diffuse way rather than in

a specular (mirror-like) way.

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• The light from a blackbody then is light that

comes solely from the object itself rather

than being reflected from some other source.

• A good way of making a blackbody is to

force reflected light to make lots of reflections: inside a bottle with a small

opening.

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• If very hot objects glow (such as the filaments of

light bulbs and electric burners), do all warm

objects glow?

• Do we glow? (Are we warm? Are you HOT?)

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• What are the parameters associated with

the making of light from warm objects?

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• What are the parameters associated with the

making of light from warm objects?

– Temperature of the object.

– Surface area of the object.

– Color of the object ? (If black objects absorb

better than white objects, will black objectsemit better than white objects?)

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• Consider the following way of making your

stove hot and your freezer cold:

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Put a white object in an insulated and

evacuated box with a black object. The

black object will absorb the radiation fromthe white object and become hot, while the

white object will reflect the radiation from

the black object and become cool.Put the white object in the freezer, and the

black object in the stove.

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• Does this violate Conservation of Energy?

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• Does this violate Conservation of Energy?

NO

• Does this violate the Second Law of

Thermodynamics (entropy tends to

increase) ?

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• Does this violate Conservation of Energy? NO

• Does this violate the Second Law of

Thermodynamics (entropy tends to

increase) ? YES

• This means that a good absorber is also a

good emitter, and a poor absorber is a poor emitter. Use the symbol to indicate the

blackness (=1) or the whiteness (=0) of an

object.

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• What are the parameters associated with

the making of light from warm objects?

– Temperature of the object, T.

– Surface area of the object, A.

– Color of the object,

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• Is the for us close to 0 or 1?

(i.e., are we white or black?)

We emit light in the IR, not the visible.

So what is our for the IR?

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So what is our for the IR?

Have you ever been near a fire on a cold

night?

Have you noticed that your front can get hot

at the same time your back can get cold?

Can your hand block this heat from the fire?

Is this due to convection or radiation?

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Blackbody radiation:

• For humans in the IR, we are all fairly good

absorbers (black). An estimated value for

for us then is about .97 .

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Experimental Results• At 310 Kelvin, only get IR

Intensity per

wavelength

(log scale)

wavelengthUV IR blue yellow red

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Experimental Results• At much higher temperatures, get visible

• look at blue/red ratio to get temperature

Intensit

y

per wavelength

(log scale)


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Experimental ResultsItotal = Ptotal/A = T4 , or Ptotal = AT4

where = 5.67 x 10-8 W/m2 *K 4

peak = b/T where b = 2.9 x 10-3 m*K

Intensit

y

per wavelength

(log scale)


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Example• Given that you eat 2000 Calories/day,

your power output is around 100 Watts.

• Given that your body surface temperature is

about 90o F , and

• Given that your surface area is about

1.5 m2,

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Example• Given Ptotal = 100 Watts

• Given that T body = 90o F

• Given that A = 1.5 m2

WHAT IS THE POWER EMITTED VIA

RADIATION?

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Example• Pemitted = AT4

– = .97

– = 5.67 x 10-8 W/m2 *K 4

– T = 273 + (90-32)*5/9 (in K) = 305 K

– A = 1.5 m2

Pemitted = 714 Watts

(compared to 100 Watts generated!)

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Example• need to consider power absorbed at room T

• Pabsorbed = AT4

– = .97 – = 5.67 x 10-8 W/m2 *K 4

– T = 273 + (90-72)*5/9 (in K) = 295 K

– A = 1.5 m

2

Pabsorbed = 625 Watts

(compared to 714 Watts emitted!)

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ExampleTotal power lost by radiation =

714 W - 625 W = 89 Watts

(Power generated is 100 Watts.)

Power also lost by convection (with air)

and by evaporation.

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Example• At colder temperatures, our emitted power

stays about the same while our absorbed

power gets much lower. This means thatwe will get cold unless

– we generate more power, or

– our skin gets colder, or – we reflect the IR back into our bodies.

• Use metal foil for insulation!

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Wave Theory• Certain waves resonate in an object (due to

standing wave), such that n(/2) = L.

From this it follows that there are more smallwavelengths that fit than long wavelengths.

• From thermodynamics, we have theequipartition of energy: Each mode onaverage has an energy proportional to theTemperature of the object.

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Wave Theoryn(/2) = L

Example: for L = 1 meter, we have the

following wavelengths that “fit”: 1 = 2 m; 2 = 1 m; 3 = .67 m; 4 = .50 m;

5

= .40 m; 6

= .33 m; 7

= .29 m; 8

= .25 m; etc.

For the range of ’s, we have permitted

1 - 1.99 m; 1

.50 - .99 m (half the range size), 2

.25 - .49 m (half again the range size), 4

etc.

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Wave TheoryThe standing wave theory and the

equipartition of energy theory together

predict that the intensity of light shouldincrease with decreasing wavelength:

This work very well at long wavelengths, but

fails at short wavelengths. This failure atshort wavelengths is called the ultraviolet

catastrophe.

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Wave Theory

wave theory: UV catastrophe

Intensity per

wavelength

wavelength

experiment

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Planck’s idea • Need to turn the curve down when gets

small (or frequency gets large).

• Keep standing wave idea and number of modes.

• Look at equipartition theory and how the

energy per mode got to be kT (where k isBoltzmann’s constant: k = 1.38 x 10-23 J/K.

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Planck’s idea Eavg = Ei /1 = P(E)*E / P(E)

where P(E) is the probability of having energy, E.

From probability theory (see page 5 of Study Guidefor Part 3), we have the Boltzmann probability

distribution function: P(E) = Ae-E/kT .

If we assume that energy is continuous, then thesummation can become an integral:

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BOLTZMANN DISTRIBUTION

Probability of one atom having n units of

energy is based on equal likelihood of any

possible state. Following is a listing of all possible states for two cases.

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CASE I: four atoms having three units of energy:

ABCD ABCD ABCD ABCD ABCD ABCD

(3000) 4 (2100) 12 (1110) 4

3000 2100 1200 1020 1002 1110

0300 2010 0210 0120 0102 1101

0030 2001 0201 0021 0012 1011

0003 0111

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Case I: Prob of atom A having n of 3 units:

P(3) = 1/20 = .05

P(2) = 3/20 = .15

P(1) = 6/20 = .30

P(0) =10/20 = .50

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CASE II: four atoms having five units of energy:

Prob of atom A having:

P(5) = 1/56 = .018P(4) = 3/56 = .054

P(3) = 6/56 = .107

P(2) =10/56 = .179P(1) =15/56 = .268

P(0) =21/56 = .375

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Plot of P(E) vs E

P(E) vs E

0

0.2

0.4

0.6

0 1 2 3 4 5 6

E

P ( E ) Series1

Series2

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Plot of E*P(E) vs E

P(E) and E*P(E)

0

0.2

0.4

0.6

0.8

1

0

0 .

5 1

1 .

5 2

2 .

5 3

E

E * P ( E Series1

Series2

P(E)

E*P(E)

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Planck’s idea Eavg = LIM

E->0 [P(E) / P(E)] =

=

= Area under the curve / 1 = kT .

E P E dE P E dE * ( ) / ( )00

E Ae dE Ae dE E kT E kT * // /

0 0

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Planck’s idea Planck recalled that the SUM only became the

INTEGRAL if you let E go to zero.

Planck’s idea was NOT to let E go to zero.

If you require P(E) to be evaluated at the end

of each E, then the SUM will decrease as

E increases!

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Planck’s idea As E gets bigger, Eavg gets smaller:

E*P(E) = A*E*e-E/kT . Area under red curve

is more than area under blue

is more than area under green.E*P(E)

E

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Planck’s idea • It’s easy to see on the leading edge that as

E gets bigger, the total Energy under the

curve and hence the average energy getssmaller. This is in fact confirmed by an

actual summation.

• The mathematical details of the actualsummation are considered in PHYS 447

(Modern Physics).

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Planck’s idea • To get the curve to fall at small wavelengths

(big frequencies) Planck tried the simplest

relation:E = (constant) * f

since we need to decrease the averageenergy per mode more as the wavelengthsget smaller - and the frequency gets bigger.

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Planck’s idea • Planck found that he could match the curve

and DERIVE both empirical relations:

– P = AT4

where = 5.67 x 10-8

m2

*K 4

– max = b/T where b = 2.9 x 10-3 m*K

with the simplest relation:

E = (constant) * f

if the constant = 6.63 x 10-34 J*sec = h.

The constant, h, is called Planck’s constant.

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How to Make Light

• The wave theory combined with the

equipartition of energy theory failed to

explain blackbody radiation.• Planck kept the wave idea of standing

waves but introduced E = hf, the idea of

light coming in discrete packets (or photons) rather than continuously as the

wave theory predicted.

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How to Make Light

• From this theory we now have a way of

relating the photon idea to color and type:

E = hf . – Note that high frequency (small wavelength)

light has high photon energy, and that low

frequency (large wavelength) light has low

photon energy.

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How to Make Light

• E = hf

– High frequency light tends to be more

dangerous than low frequency light (UV versusIR, x-ray versus radio). The photon theory

gives a good account of why the frequency of

the light makes a difference in the danger.

Individual photons cannot break bonds if their energy is too low while big photons can!

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Photons and Colors

• Electron volts are useful size units of energy

1 eV = 1.6 x 10-19 Coul * 1V = 1.6 x 10-19 J.

• radio photon: hf = 6.63 x 10-34 J*s * 1 x 106 /s =

6.63 x 10-28 J = 4 x 10-15 eV

• red photon: f = c/ 3 x 108 m/s / 7 x 10-7 m =

4.3 x 1014 Hz, red photon energy = 1.78 eV

• blue: = 400 nm; photon energy = 3.11 eV .

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Making and Absorbing Light

• The photon theory with E = hf was useful

in explaining the blackbody radiation.

• Is it useful in explaining other experiments?

• We’ll consider next the photoelectric effect.

Light 31

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