1. Physics of Astronomy week 1 Thus. 6 April 2006
Astronomy: Universe Ch.5: Light
If there’s time: Plank mass
Astrophysics: CO 5: Spectra
Seminar: WebX workshop etc. for new students
Looking ahead

2. Universe Chapter 5: The Nature of Light

3. Guiding Questions
How fast does light travel? How can this speed be measured?
Why do we think light is a wave? What kind of wave is it?
How is the light from an ordinary light bulb different from the light emitted by a neon sign?
How can astronomers measure the temperatures of the Sun and stars?
What is a photon? How does an understanding of photons help explain why ultraviolet light causes sunburns?
How can astronomers tell what distant celestial objects are made of?
What are atoms made of?
How does the structure of atoms explain what kind of light those atoms can emit or absorb?
How can we tell if a star is approaching us or receding from us?

4. Light travels fast.
Galileo unsuccessfully attempted to measure the speed of light by asking an assistant on a distant hilltop to open a lantern the moment Galileo opened his lantern.

5. Light travels through empty space at a speed of 300,000 km/s, called c
In 1676, Danish astronomer Olaus Rømer noted that the exact time of eclipses of Jupiter’s moons varied based on how near or far Jupiter was to Earth.
This occurs because it takes different times for light to travel the different distances between Earth and Jupiter.

6. Improving measurements of c
In 1850, Frenchmen Fizeau and Foucalt showed that light takes a short, but measurable, time to travel by bouncing it off a rotating mirror. The light returns to its source at a slightly different position because the mirror has moved during the time light was traveling a known distance.

7. Light is electromagnetic radiation
Light is electromagnetic radiation. It has a wavelength l and a frequency n.
White light is composed of all colors which can be separated into a rainbow, or a spectrum, by passing the light through a prism.
Visible light has a wavelength ranging from 400 nm (blue) to 700 nm (red).

8. Although Isaac Newton suggested that light was made of tiny particles 130 years earlier, Thomas Young demonstrated in 1801 that light has wave-like properties. He passed a beam of light through two narrow slits which resulted in a pattern of bright and dark bands on a stream.
This is the pattern one would expect if light had wave-like properties.

9. Imagine water passing through two narrow openings as shown below
Imagine water passing through two narrow openings as shown below. As the water moves out, the resulting waves alternatively cancel and reinforce each other, much like what was observed in Young’s double slit experiment.
This is the pattern one would expect if light had wave-like properties.

10. Light is a form of electromagnetic radiation,
It turns out that light has characteristics of both particles and waves. Light behaves according to the same equations that govern electric and magnetic fields that move at the speed c, as predicted by Maxwell and verified by Hertz.
Light is a form of electromagnetic radiation,
Electromagnetic radiation consists of oscillating electric and magnetic fields. The distance between two successive wave crests is the wavelength, l.

11. Where c is the speed of light, 3 x 108 m/s
Stars produce electromagnetic radiation in a wide variety of wavelengths in addition to visible light.
Astronomers sometimes describe EM radiation in terms of frequency, n, instead of wavelength, l. The relationship is:
Speed = distance/time
c = l n
Where c is the speed of light, 3 x 108 m/s

12. A dense object emits electromagnetic radiation according to its temperature.
WIEN’S LAW: The peak wavelength emitted is inversely proportional to the temperature.
In other words, the higher the temperature, the shorter the wavelength (bluer) of the light emitted.

14. BLACKBODY CURVES: Each of these curves shows the intensity of light emitted at every wavelength for idealized glowing objects (called “blackbodies”) at three different temperatures.
Note that for the hottest blackbody, the maximum intensity is at the shorter wavelengths and the total amount of energy emitted is greatest.

15. Astronomers most often use the Kelvin or Celsius temperature scales.
In the Kelvin scale, the 0 K point is the temperature at which there would be no atomic motion. This unattainable point is called absolute zero.
In the Celsius scale, absolute zero is –273º C and on the Fahrenheit scale, this point is -460ºF.

16. The Sun is nearly a blackbody.

17. ENERGY FLUX = sT4 = intensity =Power/Area
Wien’s law and the Stefan-Boltzmann let us discover the temperature and intrinsic brightness of stars from their colors.
Wien’s law relates wavelength of maximum emission for a particular temperature:
lmax = 3 x 10-3 Tkelvins
Stefan-Boltzmann law relates a star’s energy output, called ENERGY FLUX, to its temperature
ENERGY FLUX = sT4 = intensity =Power/Area
ENERGY FLUX is measured in joules per second per square meter of a surface, and the constant s = 5.67 x 10-8 W m-2 K-4

18. Energy of a photon in terms of wavelength:
E = h c / l where h = X J s
or h = X eV
h = Planck’s constant
Energy of a photon in terms of frequency:
E = h n where n is the frequency of light
High energy light has short wavelength and high frequency.

19. Each chemical element produces its own unique set of spectral lines.

22. The brightness of spectral lines depend on conditions in the spectrum’s source.

23. Continuum = rainbow of light
Law 1 A hot opaque body, such as a perfect blackbody, or a hot, dense gas produces a continuous spectrum -- a complete rainbow of colors with without any specific spectral lines. (This is a black body spectrum.)

24. Emission lines due to electron relaxation
Law 2 A hot, transparent gas produces an emission line spectrum - a series of bright spectral lines against a dark background.

25. Absorption lines due to electron excitation
Law 3 A cool, transparent gas in front of a source of a continuous spectrum produces an absorption line spectrum - a series of dark spectral lines among the colors of the continuous spectrum.

26. Kirchhoff’s Laws

27. Here is the Sun’s spectrum, viewed with a prism or diffraction grating.

28. But, where does light actually come from?
Light comes from the movement of electrons in atoms.

29. Rutherford’s experiment revealed the nature of atoms
Alpha particles from a radioactive source are channeled through a very thin sheet of gold foil. Most pass through, showing that atoms are mostly empty space, but a few bounce back, showing the tiny nucleus is very massive.

30. An atom consists of a small, dense nucleus surrounded by electrons

31. Nucleus = protons + neutrons
The nucleus is bound by the strong force.
All atoms with the same number of protons have the same name (called an element).
Atoms with varying numbers of neutrons are called isotopes.
Atoms with a varying numbers of electrons are called ions.

33. Spectral lines are produced when an electron jumps from one energy level to another within an atom.

35. Bohr’s formula for hydrogen lines
DE = hc/l
= E0 [ 1/nlo2 – 1/nhi2 ]
nlo = number of lower orbit
nhi = number of higher orbit
R = Rydberg constant
= wavelength of emitted or absorbed photon

36. The wavelength of a spectral line is affected by the relative motion between the source and the observer.

37. lo = wavelength if source is not moving
Doppler Shifts
Red Shift: The observer and source are separating, so light waves arrive less frequently.
Blue Shift: The observer and source are approaching, so light waves arrive more frequently.
Dl/lo = v/c
Dl = wavelength shift
lo = wavelength if source is not moving
v = speed of source
c = speed of light

38. What can we learn by analyzing starlight?
A star’s temperature
by peak wavelength
A star’s chemical composition
by spectral analysis
A star’s radial velocity
from Doppler shifts

39. Guiding Questions
How fast does light travel? How can this speed be measured?
Why do we think light is a wave? What kind of wave is it?
How is the light from an ordinary light bulb different from the light emitted by a neon sign?
How can astronomers measure the temperatures of the Sun and stars?
What is a photon? How does an understanding of photons help explain why ultraviolet light causes sunburns?
How can astronomers tell what distant celestial objects are made of?
What are atoms made of?
How does the structure of atoms explain what kind of light those atoms can emit or absorb?
How can we tell if a star is approaching us or receding from us?

40. Practice problems Pick a few to work on together
No homework assignment for Universe Ch.5
Do the Universe Online self-test for Ch.5

41. BREAK
Then we’ll derive Planck mass from some of these fundamental concepts, if we have time…

42. Calculating the Planck length and mass:
You used energy conservation to find the GRAVITATIONAL size of a black hole, the Schwartzschild radius R.
Next, use the energy of light to calculate the QUANTUM MECH. size of a black hole, De Broglie wavelength l.
Then, equate the QM size with the Gravitational size to find the PLANCK MASS Mp of the smallest sensible black hole.
Finally, substitute M into R to find PLANCK LENGTH Lp
and then calculate both Mp and Lp.

43. Gravitational size of black hole (BH):
R = event horizon
The Schwarzschild radius, inside which not even light (v=c) can escape, describes the GRAVITATIONAL SIZE of BH.

44. 2. Quantum mechanical size of black hole
The deBroglie wavelength, l, describes the smallest region of space in which a particle (or a black hole) of mass m can be localized, according to quantum mechanics.

45. 3. Find the Planck mass, Mp
If a black hole had a mass less than the Planck mass Mp,
its quantum-mechanical size could be outside its event horizon. This wouldn’t make sense, so M is the smallest possible black hole.

46. 4. Find the Planck length, Lp
These both yield the Planck length, Lp. Any black hole smaller than this could have its singularity outside its event horizon. That wouldn’t make sense, so L is the smallest possible black hole we can describe with both QM and GR, our current theory of gravity.

47. 5. Calculate the Planck length and mass
These are smallest scales we can describe with both QM and GR.

48. Break
Then we’ll continue with Astrophysics…

49. Astrophysics: CO Ch.5 Light and the interaction of matter:
Spectral lines, Kirchhoff’s laws, Dopper shift
Photon energy, Compton scattering
Bohr model
Quantum mechanics, deBroglie, Heisenberg
Zeeman effect, Pauli exclusion principle

50. Astro. Ch.5: Interaction of light & matter
History of Light quantization:
Stefan-Boltzmann blackbody had UV catastrophe
Planck quantized light, and solved blackbody problem
Einstein used Planck’s quanta to explain photoelectric effect
Compton effect demonstrated quantization of light
hc/l = Kmax + F

51. Astro. Ch.5: Interaction of light & matter
History of atomic models:
Thomson discovered electron, invented plum-pudding model
Rutherford observed nuclear scattering, invented orbital atom
Bohr used deBroglie’s matter waves, quantized angular momentum, for better H atom model. En = E/n2
Bohr model explained observed H spectra, derived phenomenological Rydberg constant
Quantum numbers n, l, ml (Zeeman effect)
Solution to Schrodinger equation showed that En = E/l(l+1)
Pauli proposed spin (ms=1/2), and Dirac derived it

52. Improved Bohr model
Solution to Schrodinger equation showed that En = E/l(l+1),
Where l = orbital angular momentum quantum number (l<n).
Almost the same energy for l=n-1, and for high n.

53. Quantum Mechanics Light as waves with wavelength l: classical
Light as particles with discrete energy (Planck) E = hc/l = pc
Electrons as particles with momentum p=mv: classical
Electrons as waves with p=h/l: de Broglie wavelength l = ___
Heisenberg:

54. Magnetic fields can spin charged particles
Cyclotron frequency: An electron moving with speed v perpendicular to an external magnetic field feels a Lorentz force (no change in energy here): F=ma
(solve for w=v/r)
Compare to Zeeman effect
Start HW (see hints): #4, 9, 14, 17

55. Magnetic fields can interact with intrinsic spin
Zeeman effect: A particle with intrinsic spin m has more or less energy depending on its orientation with an external magnetic field
Start HW (see hints): #4, 9, 14, 17