How Matter Emits Light: 1. the Blackbody Radiation

Announcements n  Quiz # 3 will take place on Thursday, October

20th; more infos in the link `quizzes’ of the website: ¨ Please, remember to bring a pencil.

n  Solutions for Exam # 1 are available from the website, under `Exam’

n  Looking ahead: ¨ Homework # 3 is due on Thursday, Oct. 20th ¨ Homework # 4 starts on Thursday, Oct 20th . It is due

on Thursday, Oct. 27th

Assigned Reading

n  Complete Unit 22; n  Unit 23

Dimming with distance n As you move away from a light source (a

light bulb, a street light, etc.) it becomes dimmer. Why?

The energy emitted by the source is constant, but get spread over a larger surface at larger distance

Dimming with Distance

n As distance R increases, the area over which the total light output L is distributed increases as 4πR2

n  Thus:

Brightness = ______ 4πR2

L

How Matter and Light Interact

Matter interacts with light in four different ways: n  Absorption – the energy in the photon is

absorbed by the matter and turned into thermal energy

n  E.g., Your hand feels warm in front of a fire.

n  Reflection – no energy is transferred and the photon “bounces” off in a new (and predictable) direction

n  E.g., Your bathroom mirror

n  Transmission – no energy is transferred and the photon passes through the matter unchanged.

n  Emission – matter gives off light. Can be done in two different ways, as we will see.

Absorption Photon deposits energy into material. Thermal energy is increased and the material gets warmer.

Transmission Photon passes through material without depositing energy. Everything remains unchanged.

Reflection Photon reflects off of material. No energy is lost but outgoing photon has a new direction.

These processes depend on both the material and the wavelength of the photon

Survey Question Our eyes work via the process of:

1) absorption 2) reflection 3) transmission 4) emission 5) none of the above

Survey Question Leaves are green because:

1) they only emit frequencies corresponding to green 2) they only reflect frequencies corresponding to green 3) they only transmit frequencies corresponding to green 4) they only absorb frequencies corresponding to green

The Difference Between Black and White n  “White” light – contains all the frequencies

of the visible part of the spectrum.

n  White paint – reflects all frequencies of the visible part of the spectrum equally.

n  Black paint – absorbs all frequencies of the visible part of the spectrum equally.

Discussion Question Why does NASA paint spacecraft white?

Abso

rptio

n

Frequency

Infrared Visible

Absorption Spectrum of White Paint

40%

0%

Absorption Spectrum of Black Paint

80%

Emission: How do objects make light in the first place?

n There are two principal mechanisms for producing electromagnetic radiation ¨ Blackbody radiation ¨ Spectral line emission of atoms and

molecules

Both of these mechanisms result from accelerating/decelerating electrons! I.e., you accelerate or decelerate an electric charge to create EM radiation

Light from Objects

n  We perceive this `acceleration’ or `deceleration’ of electrons as `light from objects’

n  Imagine to heat up a piece of metal in a furnace: ¨  It will first turn red (temperature raising) ¨  then orange ¨  then yellow ¨  then whitish-blue (highest temperature)

The higher the temperature, the bluer the object will appear

[you are linking temperature to color!]

What happens? n  The higher the temperature, the faster the atoms/

molecules in the object are (T ~ v2), thus more energetic collisions

n  More energetic collisions cause more sudden accelerations/decelerations of the electrons in the matter, thus light with shorter wavelength (higher energy)

What does it mean? n Higher Temperature = faster atoms n Faster atoms = more frequent and

energetic collisions n more frequent and energetic collisions =

more sudden electron accelerations/decel n more sudden electron accelerations/decel

= higher photon energy n Higher photon energy = bluer light

(E=hc/λ)

The color of light emitted is connected to the Temperature

How to Measure Temperature n  Using the Kelvin Temperature scale:

¨  At T=0 K (the lowest possible temperature) all atoms/molecules are still (virtually zero energy)

¨  Directly linked to an object’s thermal energy (T=0 K means zero thermal energy)

¨  Room temperature is ~300 K ¨  Freezing water point 273.15 K, boiling point is 373.15 K

n  Celsius scale: ¨  Freezing water point = 0 C ¨  Boiling water point = 100 C

n  Fahrenheit scale: ¨  Freezing water point = 32 F ¨  Boiling water point = 212 F

Do not confuse Heat and Temperature! n  Temperature refers to the

degree of motion of the particles in a material, i.e. the speed with which the particles move (T~kinetic energy~v2).

n  Heat refers to the amount of energy stored in a body as motion among its particles and depends on density as well as temperature.

Survey Question:

n  You heat an oven to 450 F, and you also, separately, boil some water in a pot (boiling point is 212 F). What happens if you stick your hand first in the oven and then in the boiling water [don’t do that!]? Why?

I get burned in both I only get burned in the oven, because of the higher

temperature I only get burned in the water, because of the higher

heat

Survey Question:

n  You heat an oven to 450 F, and you also, separately, boil some water in a pot (boiling point is 212 F). What happens if you stick your hand first in the oven and then in the boiling water [don’t do that!]? Why?

I get burned in both I only get burned in the oven, because of the higher

temperature I only get burned in the water, because of the higher

heat

What is a Blackbody?

n  An object that can absorb all the radiation falling on it (light at all wavelengths), so it appears black when cold

n  When it gets heated up, it can also emit radiation at all wavelengths (think of the heated piece of metal).

n  A stove burner (conducting material), a furnace, planets (radiating solids), and stars (dense gas) are excellent examples of close-to-blackbodies

n  Materials that are insulating, non-burning, or liquid are usually not good blackbodies

Blackbody Radiation n  Take a blackbody (e.g., a piece of metal) and heat it up. n  After it becomes hot, keep the temperature constant (this is called thermal equilibrium) n  Then plot, on a graph, the intensity of the radiation (light) emitted as a function of wavelength: this is called a spectrum n  The shape of the spectrum and the maximum intensity of a

Blackbody will only depend on the Temperature n  Think of Temperature as motion of the atoms/molecules in the

blackbody; if T=constant, the motion does not change, and the acceleration/deceleration of the electrons also does not change. The `color’ of the B.B. will not change.

Black Body radiation is the e.m. emission of matter at thermal equilibrium (constant T)

One Temperature=one spectrum

Blackbodies are excellent thermometers

Wien’s Law

n Hotter objects emit photons with a higher average energy = shorter wavelength.

¨ The peak of the blackbody emission spectrum is

given by

!

"max =2.9 #106

T(Kelvin)nm

Stefan-Boltzmann Law:

n Hotter objects emit more total radiation per unit surface area.

n The luminosity of a hot body rises rapidly with Temperature: L=A σT4

Survey Question The graph below shows the blackbody spectra of three different

otherwise identical stars. Which of the stars is at the highest temperature?

1) Star A 2) Star B 3) Star C

A

B

C

Relative Intensity

Wavelength

Survey Question: You are gradually heating two rocks (one larger than the

other) in an oven to an extremely high temperature. As they heat up, the rocks emits nearly perfect theoretical blackbody radiation – meaning that

1) the larger rock is bluer and brighter. 2) the larger rock is redder and brighter. 3) the larger rock is bluer but the same brightness. 4) the larger rock is the same color but brighter. 5) the larger rock is the same color and brightness.

Emitted power = σ A T4

Survey Question: You are gradually heating two rocks (one larger than the

other) in an oven to an extremely high temperature. As they heat up, the rocks emits nearly perfect theoretical blackbody radiation – meaning that

1) the larger rock is bluer and brighter. 2) the larger rock is redder and brighter. 3) the larger rock is bluer but the same brightness. 4) the larger rock is the same color but brighter. 5) the larger rock is the same color and brightness.

Emitted power = σ A T4

Survey Question The graph below shows the blackbody spectra of two totally

different stars. What can you conclude from the plot about the two stars? 1) Star A is hotter but smaller than Star B 2) Star A is hotter and larger than Star B 3) Star A is cooler and larger than Star B 4) Star A is cooler and smaller than Star B

A B

Relative Intensity

Wavelength

Summary

n Blackbody Radiation (a.k.a. Thermal Radiation) ¨ Many objects with a temperature greater than

absolute zero (0 K) emit blackbody radiation. ¨ Hotter objects emit more total radiation per

unit surface area. ¨ Hotter objects emit photons with a higher

average energy.

Survey Question

n You emit radiation:

¨  True ¨  False

Survey Question

n You emit radiation:

¨  True ¨  False

Your skin feels warm, you emit infrared radiation