Transcript Chapter 5 The Nature of Light

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
Universe Chapter 5: The Nature of Light
Guiding Questions
1. How fast does light travel? How can this speed be
measured?
2. Why do we think light is a wave? What kind of wave is
it?
3. How is the light from an ordinary light bulb different from
the light emitted by a neon sign?
4. How can astronomers measure the temperatures of the
Sun and stars?
5. What is a photon? How does an understanding of
photons help explain why ultraviolet light causes
sunburns?
6. How can astronomers tell what distant celestial objects
are made of?
7. What are atoms made of?
8. How does the structure of atoms explain what kind of
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.
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.
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.
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
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.
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.
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.
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=ln
Where c is the speed of light, 3 x 108 m/s
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.
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.
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.
The Sun is nearly a blackbody.
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
Energy of a photon in terms of
wavelength:
E=hc/l
where h = 6.625 X 10-34 J s
or h = 4.135 X 10-15 eV
h = Planck’s constant
Energy of a photon in terms of frequency:
E=hn
where n is the frequency of light
High energy light has short wavelength and
high frequency.
Each chemical element produces its
own unique set of spectral lines.
The brightness of spectral lines depend
on conditions in the spectrum’s source.
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.)
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.
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.
Kirchhoff’s Laws
Here is the Sun’s spectrum,
viewed with a prism or diffraction grating.
But, where does light actually
come from?
Light comes from the
movement of electrons
in atoms.
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.
An atom
consists of a
small, dense
nucleus
surrounded
by electrons
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.
Spectral lines are produced when an
electron jumps from one energy
level to another within an atom.
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
l= wavelength of emitted or
absorbed photon
The wavelength of a spectral line is
affected by the relative motion between
the source and the observer.
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
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
Guiding Questions
1.
2.
3.
4.
5.
6.
7.
8.
9.
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?
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
BREAK
Then we’ll derive Planck mass from some of
these fundamental concepts, if we have
time…
Calculating the Planck length and mass:
1.
You used energy conservation to find the GRAVITATIONAL
size of a black hole, the Schwartzschild radius R.
2. Next, use the energy of light to calculate the QUANTUM
MECH. size of a black hole, De Broglie wavelength l.
3. Then, equate the QM size with the Gravitational size to find
the PLANCK MASS Mp of the smallest sensible black hole.
4. Finally, substitute M into R to find PLANCK LENGTH Lp
5. and then calculate both Mp and Lp.
1. Gravitational size of black hole (BH):
R = event horizon
Gravitational energy  kinetic energy
GmM 1
2
 mv
r
2
2GM
You solved for r  2
v
The Schwarzschild radius, inside which not even light (v=c)
can escape, describes the GRAVITATIONAL SIZE of BH.
Rgrav
GM
 2
c
2. Quantum mechanical size of black hole
Energy of photon  wavelength of particle
E
hc
l
 pc

p  Mc 
h
l
Solve for wavelength l in terms of mass M :
l  ____________
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.
3. Find the Planck mass, Mp
Schwartzschild radius  deBroglie wavelength
Rl
GM p
h

2
c
M pc
Solve for the Planck mass :
M p 2  ____________
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.
4. Find the Planck length, Lp
hc
Substitute your Planck mass, M p 
, into either R or l :
G
GM p
R  2  ______________
c
h
l
 ______________
M pc
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.
5. Calculate the Planck length and mass
Use these fundamental constants :
h  6 x 1034
3
kg m 2
m
m
, c  3 x 108  ms  , G  7 x 1011
s
s
kg s 2
hc
to evaluate the Planck mass, M p 
 _____________
G
and the Planck length L p 
GM p
c
2
 _________________
These are smallest scales we can describe with both QM and GR.
Break
Then we’ll continue with Astrophysics…
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
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
Dl 
h
1  cos 
me c
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
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.
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:
Dx Dp 
2
DE Dt 
2
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
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