Astronomy The Nature of Light> Measuring the speed of light> Light is an electromagnetic wave> The relationship between Light and

temperature an object> The relationship of energy and

temperature from an object> Wave particle duality> Each element has a 'fingerprint'> Quantum rules of atoms> How atoms emit light> How motion of an object changes light

(Doppler shift)

A. Dayle Hancock

adhancock@wm.eduSmall 239

Office hours: MTWR 10-11am

Page 1http:// physics.wm.edu/~hancock/171/

2

The Speed of Light

Using lanterns and an assistant on a distant hill, Galileo could not tell if light traveled instantaneously or with a finite speed.

RØmer in 1676 showed that light had a finite speed. By carefully studying the eclipses of a moon (Io) of Jupiter he showed the timing of the eclipses varied by the distance between Earth and Jupiter.

3

The Speed of Light

In 1850, Fizeau & Foucault measured the speed of light. They used a rapidly rotating mirror and observed the angle of deflection. With the path lengths

and the rotation speed the speed of light can be calculated.

The speed of light in vacuum is:

c = 2.998 x 108 m/s ≈ 3.0 x 108 m/s

Nothing can travel faster than the speed of light.

Later, Thomas Young (1773-1829) and others showed that light behaves like a wave

Newton thought light consisted of particles('corpuscles')

Interferencepatterns: lightand dark bands

Historical views

Page 4

The waves travel, but the matter does not travel Energy is transported by the waves

Some General Properties of Waves

Page 5

AMPLITUDE height of the disturbanceWAVELENGTH (λ) distance from peak to peakSPEED (v) speed at which any peak travels (For light v = c!)FREQUENCY (ν) number of full waves passing a point in one second.

Anatomy of a wave

Page 6

7

Speed, Frequency and Wavelength

The speed, frequency and wavelength of a light wave are related by:

v = c = λ ν

For an FM radio broadcast the frequency is 100 MHz (1.0 x 108 Hz). As we will see radio waves are atype of 'low frequency light waves'. The wavelength is then:

λ = c/ν = (3.0 x 108 m/s) / (1.0 x 108 s-1) = 3.0 m

8

Light is an Electromagnetic WaveElectric and magnetic fields are associated with electric and magnetic forces.

In the 1860's, James Maxwell showed that light is an electromagnetic wave. Heinrich Hertz later showed the validity of Maxwell's equations by generating and detecting radio waves.

The wavelength determines the type of electromagnetic wave.

9

Electromagnetic Spectrum

The wavelength (λ ) determines the type of electromagnetic wave.

The wavelength of radio waves is very long. AM radio wave are about 300 m. Gamma rays can be as short as 10-15 m. Visible light has a wavelength of 400 – 700 nm. The wavelength of visible light determines the color.

10

The Wavelength and Frequency of Light

The wavelength of orange light is about 600 nm (6.0 x 10-7 m). Using the relationship between speed, frequency and wavelength:

c = λ ν

We have:

ν = c/λ = (3.0 x 108 m/s) / (6 x 10-7 m)

ν = 5 x 1014 Hz !

Light from the Sun has many wavelengths mixed together and appears

The wavelengths can be split apart using a prism or diffraction grating

Page 11

WHITE

12

Heat and Temperature

Heat is the energy contained in an object because of the (random) motion of the atoms (or molecules). Temperature is a measure of the average kinetic energy of the atoms or molecules.All the atoms or molecules do not move with the same speed. The atoms or molecules have a broad distribution of speeds in random directions.

13

Temperature Scales

In science, we normally use the Kelvin scale for temperature. 0 K is absolute zero where (almost) all the motion of the atoms or molecules stop. One Kelvin degree is the same temperature change as one Celsius degree. Ice freezes as 0o C, 32o F or 273 K. Water boils at 100o, 212o F and 373 K

14

Heat and Radiation

An object with a temperature > 0 K radiates electromagnetic radiation. The higher the temperature, the more total radiation is emitted. The higher the temperature, the shorter peak in the wavelength.

15

Heat and Radiation

Some objects (at the same temperature) emit radiation better than others. A perfect emitter is called a 'blackbody'. The object does not have to be black to be a blackbody

The Sun is a blackbody emitter of radiation at 5800 K.

16

Wein's Law

The wavelength of the peak intensity of a blackbody curve is given by Wein's Law

λmax

= 0.0029 K m / T

Where T is in kelvin and the wavelength is in meters.

17

Intensity vs TemperatureStefan-Boltzmann Law

• Higher temperature (T)>More energy output>Area under curve in the plot

• F is the energy flux of the object• Power = Energy/time• F = power/area

• σ is the Stefan-Boltzmann constant

F = σ T4

σ = 5.67 x 10-8 W/m2K4

“σ ” is a lower case sigma

18

Energy Flux from the Sun

The energy flux (or luminosity) from the Sun at the the EarthIs 1.37 kW/m2

19

A Surprise about Light 'Waves'

In 1905 along with the famous paperson special relativity, Albert Einstein published a paper on the 'photoelectric effect'. To account for the this effect he proposed that light come in small packets that had many of the properties of a particle! We call these wave packet particles 'photons'. These light particles still have a wavelength and frequency. The travel at 3 x 108 m/s (speed limit for the universe).

a PHOTONis a particle of lighta “quantum” of light

Energy carried by a photon

Planck's constant – extremely tinyh = 6.626 x 10-34 J-s

‘a wavepacket'

Energy from light is quantized in chunks of hc/ λ

Light is also a particle

Page 20

λhc

E =

Spectra – An Important Tool in Astronomy

22

The Light from different Elements

Heat up an a chemical substance and 'split' the wavelengths with a prism and a series of spectral lines will appear. This bright emission lines identify the chemical elements. Helium was discovered on the Sun from its spectral lines before it was found on Earth.

23

Each Element has a 'Fingerprint'

A. Continuous Spectrum Made from opaque thermal objects

obey Wien & Stefan-Boltzmann laws apply Kirchoff's law 1

B. Emission spectrumFingerprint of an element emitted directly from a gas (here- hydrogen gas) Kirchoff's law 2

C. Absorption spectrum Continuous spectrum absorbed by a gas

(here hydrogen gas) Kirchoff's law 3

Types of spectra

Page 24

Examples of SpectraEmission line spectra of several elements (their 'fingerprints')

Emission line spectrum of the Orion nebula (UV)

Page 25

26

The Suns Spectrum We can learn a tremendous amount about the chemical composition in the solar atmosphereby the characteristic spectral patterns

27

Blue Sky and Red Sunsets

The molecules of O2 and N

2

that make up the atmosphere are > 1 nm. Visible light has a wavelength of 400-700 nm. When a wave scatters from a much small object, the shorter wavelengths scatter more.This is know as Rayleigh scattering. Thus blue light scatters better than red light in the atmosphere. This blue scattered light makes the sky blue. So much light can be scatter at sunset that the sunset can appear red.

28

Atoms and Light

All of the known matter is made of atoms. In the Rutherford model, atoms consist of a very small nucleus with 'orbiting' electrons. The nucleus contains protons ( + charge) and neutrons ( no charge). The protons electrostatic repulsion is overcome by the 'strong force' or nuclearforce. The number of

protons (atomic number) determine the number of electrons to make the atom neutral. The number of electrons determine the chemistry of the element. The number of neutrons and protons determine the atomic weight.

29

Periodic Table of the Elements

Chemical properties of elements are similar in each column

30

Bohr's Model of Hydrogen

Niels Bohr in 1913 proposed a model of the atoms where the electrons 'orbit' only at certain radii labeled n=1, n=2, n=3 etc. Each orbit corresponds to the electron having a certain energy. The electron can only 'orbit' at certain radii. The model was

'ad hoc' and violated ideas from classical physics. It only worked well with the simplest atom (hydrogen). It did explain atomic spectra of simple atoms and was the first step to quantum mechanics.

31

Bohr's Model of Hydrogen

When a photon of light with the correct wavelength (and energy) is absorbed by a hydrogen atom, it can cause an electron at the correct radius (an energy) to 'hop' to a higher energy level (and large radius)

32

When an electron is in an energetic excited state (large radius), it can fall or 'hop' down to a lower energy and smaller radius. In the process, the atom emits a photon of light.

Bohr's Model of Hydrogen

33

Spectra of Hydrogen

The visible spectrum of hydrogen is know as the Balmer series. By trail and error, Balmer worked out the wavelengths wavelengths as:

1λ

=R (14−

1

n2 )

Where R is the Rydberg constant (R = 1.097 x 107 m-1) and n is an integer (1, 2, 3, etc)

34

Bohr formula – Balmer, Lyman & Paschen

1λ

=R (1

N 2−1

n2 )

Bohr's model gives the correct formula for the Lyman spectrum (ultraviolet with N =1), Balmer spectrum (visible with N=2 and Paschen spectrum (infrared with N=3)

'ev' is an energy unit 1 ev = 1.602 x 10-19 joules

Page 35

The Doppler effect: Moving source of waves

• For sound> Approaching is shorter wavelength> Shorter wavelength is higher pitch

> Receding is longer wavelength> Longer wavelength is lower pitch

• For light> Approaching is shorter wavelength> Shorter wavelength is bluer

> Receding is longer wavelength> Longer wavelength is redder

Perceived Doppler shift

36

Doppler shift• For a moving wave source

VR is the relative velocity

• How fast it is coming or going from youV is the velocity of the wave

• Speed of sound or speed of light (c)λo is the original (lab or stationary) wavelength

λ is the observed wavelength

Δλ is the change in wavelength (observed – original)

For Light (c=v)

Page 37

VR

V

0

0

VR

c

0

VR

c

0

• A green laser has a wavelength of about 510nm• If we see a green laser from the Andromeda galaxy it would have a

wavelength of 509.5 nm• How fast are we moving relative to Andromeda?

Δλ = λ – λ0 = 509.5 nm – 510nm = –0.5nm

vR = Δλ/λ × c = –0.5nm/510nm × 3×108 m/s

= –2.94×105 m/s

= –294 km/s

Useful units: 109 nm = 1 m & 106 μm = 1 m

a nanometer is the size of a molecule

What does the “–” sign mean ?Page 38

Example: Doppler shift used to measure velocity

l

Doppler shift and a rotating body

39

• Temperature records amount of random motion in the molecules

> Some towards you> Some away from you

• Different Doppler shifts for different emitting photons

> Makes lines broader• Hot clouds usually are

too hot for molecules> Only atoms is a clue also

The effect of temperature on spectral lines:Broader = hotter

Page 40

Hot cloud in space

Cold cloud in space