1

Blackbody radiationBasic laws of radiation

Wien’s law max = 2897/T mmStefan-Boltzmann law: E = T4

Lecture 6

Solar and Earth Radiation

6,000 K 300 K

Earth is heated by visible radiation from the sun and cools by radiating infrared energy back to space

Solar Spectrum

The sun emits radiation at all wavelengths

Most of its energy is in the UV-VIS-IRportions of the spectrum

~50% of the energy is in the visible region ~40% in the near-IR ~10% in the UV

Radiation

Energy is transferred by electromagnetic waves

This includes all radiant energy:

X-rays Radio waves Light (sunlight) Microwaves

Properties of Waves

All electromagnetic waves travel at the same speedThe speed of light: 300,000 km/s

trough

crest

Properties of Waves

Wavelength

(length/cycle)

Wavelength (): the length of one complete cycle

trough

crest

Properties of Waves

Wavelength

(length/cycle)

Amplitude: 1/2 height between trough and crest

Amplitude

trough

crest

Properties of Waves

Wavelength

(length/cycle)

Frequency (): the number of cycles/second

Amplitude

trough

crest

Speed = wavelength x frequency

c =

(length/second) = (length/cycle) x (cycle/second)

Light speed is constantC= 300,000 km/s

Long wavelength (l), low frequency (n) short wavelength (l), high frequency (n)

Who is faster? Same

Whose frequency is higher? And why?

Energy of a wave

Energy is proportional to frequency,

and inversely proportional to wavelength

E = h

= h (c/ )

where h = Planck’s constant

In other words, waves with shorter wavelengths

(or higher frequency) have higher energy

Electromagnetic Spectrum

(m)

10001001010.10.01

denotes wavelength

m is micrometer unit of wavelength

110

103

10-310-210-1

10-6

10-9

1 meter (m)

1 kilometer (km)

1 cm (centimeter)1 mm (millimeter)

1 m (micrometer)

1 nm (nanometer)

103 meters = 1 kilometer

100 cm = 1 m103 mm = 1 m

106 m = 1 m

109 nm = 1 m

Re 0.65d m

0.51green m

0.42violet m

Different color light has different wavelength

Electromagnetic Spectrum

(m)

visiblelight

0.4 to 0.7 m

10001001010.10.01

ultraviolet infrared microwavesx-rays

LowEnergy

HighEnergy

( = “micro” = 10−6)

Radiant EnergyAll objects that have

temperature greater than 0K emit

radiation

sun and earth’s surface behave approximately as blackbodies

Basic laws of blackbody radiation

BlackbodyAny object that is a perfect emitter

and also a perfect absorber of radiation

Q: How much radiation is being emitted by an object, and at what wavelengths?

Q: At what wavelength does the earth emits most of its radiation? (Tearth=288K)

Q: At what wavelength does the sun emits most of its radiation? (Tsun=6000K)

Wien’s Law

Blackbody radiation curve

most objects emit radiation at many wavelengthshowever, there is one wavelength where an object emits

the largest amount of radiation energyThis wavelength is found with Wien’s Law

max

2897 m

(K)T

max

Q: At what wavelength does your body emits most of its radiation? (Tyou=310K)

Wavelength (m)

Incre

asin

g e

nerg

y

Wien’s law max = 2897/T mmThe Nobel Prize in Physics 1911

Rayleigh-Jeans Law

Bla

ckbody

Radia

tion

Wavelength (m)

Incre

asin

g e

nerg

y

Planck’s law

3

3

8 1( , )

1h

kT

hu T

ce

The Nobel Prize in Physics 1918

hPhotonenergy

Planck found that he could use a formula to fit the blackbody radiation curve

The beginning of quantum mechanics

Wavelength (m)

Incre

asin

g e

nerg

y hotter bodiesemit more andat higher energy(shorter wavelength)

E1=sT14

Total radiation energyStefan-Boltzmann law: E = T4

Boltzmann1844-1906 (Austria)

E2=sT24

Q: If T1=2T2, how many times E1 is E2?

His very famous formula (about entropy) is inscribed on Boltzmann's tombstone in Vienna.

Blackbody Radiation

Blackbody radiation—radiation emitted by a body that

emits (or absorbs) equally well at all wavelengths

Visible Light (VIS)

0.4 to 0.7 m

Our eyes are sensitive to this region of the spectrum

Violet-Indigo-Blue-Green-Yellow-Orange-Red

Infrared Radiation (IR)

We can’t see IR, but we can feel it as radiant heat

Lower energy than visible light

Ultraviolet Radiation (UV)

Higher energy than visible light

Can burn human skin and damage cells