Download The Interaction of Light and Matter

Lecture 11
Matter and Light
Astro161 – Fall 2011
Dr. Matthias Dietrich
Homework
The second home-work assignment is
available after class today and it is also
posted on the class web-site, as well as
on Carmen.
It will be due on Monday, Oct. 24th .
The home work has to be returned either in class
or as e-mail:
[email protected]
[email protected]
some announcement
This Friday, October 21st, will be the
second midterm.
On Thursday, Oct. 20th, there will be a
review session in the planetarium on
the 5th floor of Smith Lab at 5pm.
A practice test is posted, again on the class web-site
and also on Carmen.
Smith Lab. 5th floor
Planetarium
Oct. 03
Oct. 04
Oct. 05
Oct. 11
Oct. 12
Oct. 13
Oct. 17
Oct. 18
Mon.
Tue.
Wed.
Tue.
Wed.
Thu.
Mon.
Tue.
done
done
done
done
done
done
@ 6:00 pm
@ 6:00 pm
Roof Nights
Oct. 06 Thu. 8:00 pm done
Oct. 19 Wed. 8:00 pm (Oct. 26)
Lecture 11
Matter and Light
In the late 17th and early 18th century experiments with
prisms and slits – dispersion and diffraction – lead to the
picture that light can be described as a wave phenomenon.
Particle ?
Wave ?
6
Properties of Waves
wavelength
• Light waves are characterized
• by three numbers:
– wavelength, λ (size of the wave)
– frequency, f
(number of waves/second)
– wave speed, c (the same for all wavelengths)
• These are all related by:
c=λf
• longer wavelengthLecture
means
2: Lightsmaller frequency
The Black Body Radiation Curve
Wien’s Law
T = 10000 K
T = 6000 K
0
5000
Stefan - Boltzmann
Hotter blackbodies:
• emit more energy at
all wavelengths
• peak at shorter
wavelengths
10000
Wavelength (Å)
15000
20000
9
The Doppler Effect
• Shift in the observed wavelength when the
source is moving relative to the observer.
• Examples:
– Sound Waves (Siren or Train Horn)
– Light Waves
• Amount of the shift and its sign depends on
• relative speed of the source and observer
• direction (towards or away)
Lecture 2: Light
The Doppler Effect for Light
• Amount of the shift depends upon the emitted
wavelength (λem) and the relative speed v:
• If the motion is away from observer
• Wavelength gets longer = REDSHIFT
• If the motion is towards the observer
• Wavelength gets shorter = BLUESHIFT
Lecture 2: Light
Way to Measure Speeds
• Observe the wavelength (obs) of a source with a
known emitted wavelength (em)
• The difference is directly proportional to
the speed of the source, v:
rest frame
5050Å – 5007Å
·c
v = 0.0086
2575
km/s
5007Å
observed
(For v very small compared
to the velocity c of light)
Doppler Effect in Practice
• Used by astronomers to measure the speeds of
objects towards or away from the Earth.
• Other Uses:
• Traffic Radar Guns:
– Bounce microwaves or laser light of known
wavelength off of cars, measure reflected
wavelength: Doppler shift gives the car’s speed.
• Doppler Weather Radar:
– Bounce microwaves off of clouds, measure speed and
direction of motion. Strength of the reflected signal
gives the amount of rain or snow.
13
Doppler Effect and the Shifts of Wavelength
– shift to the red if the object is moving away
– shift to the blue if the object is moving closer
– a way to measure speeds at a distance
e.g. how fast a star or galaxy moves away
or how fast a car is moving
Analysis of Light
• Energy which is emitted
• Temperature of a body, e.g. a star
• Motion of an object
along the line of sight
Lecture 2: Light
What is Matter ?
First Ideas
• Greek philosophers
e.g. Democritus (~460 – ~370 BC)
‘Matter consists of tiny particles (Greek atomos)
which cannot be further divided and they have
already the properties of the matter they build.’
Ernest Rutherford (1910):
Experiments to get an idea about
the internal structure of atoms.
Most of the mass is concentrated in a compact nucleus
smaller than 10-15 m and containing at least 99.98% of
the mass which is surrounded by negatively charged
electrons.
α-particles
radioactive
material
Rutherford’s Model of an Atom
not in scale!
This only a simple model to provide
a sort of picture of an atom.
But remember, this is only a picture
which tries to visualize an atom.
Just to illustrate the size and emptiness of an atom
imagine:
the size of the Sun is scaled down to the size of the
nucleus of an atom (~10-15 m).
The electrons would move around the nucleus
(~10-10 m) in a distance which would correspond to
~25x the distance of Pluto to the Sun.
Electrons don’t orbit around the nucleus
like planets around the Sun.
Electrons, protons, and neutrons are not little particles
but they have particle and wave properties like light.
WRONG
How do we know all this?
Particle accelerator
for example CERN
near Geneva.
~9 km
Underground there are labs with huge detectors which
record the decay of particles which are created when
for example protons or electrons collide head-on.
Atomic Structure
Whereas the gravitational force is always
attractive, the electromagnetic force can
be attractive or repulsive because charges
come in two types (positive and negative):
– opposite charges attract ✚
– like charges repel
✚
✚
Atomic Structure
• Atomic Structure
– Atoms are formed by the electromagnetic force
q1
-
r
q1q2
F 2
r
Coulomb Law
+
q2
Atomic Structure
• The atomic nucleus (size ~10–15 m)
consists of two types of particles of nearly
equal mass:
– Protons (positive electric charge)
– Neutrons (no electric charge)
+
Atomic Structure
• The atomic nucleus (size ~10 –15 m) consists of
two types of particles of nearly equal mass:
– Protons (positive electric charge)
– Neutrons (no electric charge)
• The atomic nucleus is held together by the
strong nuclear force, the strongest force in
nature, but with a very short range.
The Strong Nuclear Force
Electromagnetic repulsion
F
0
r
Strong nuclear attraction,
a very short-range force
Principal Subatomic Particles
Name
Size
Mass
Charge
Electron
(e–)
Proton
(p+)
Neutron
(n)
Photon
Point?
–1
-
m
9.1 × 10–31 kg
(= 1 me)
1836 me
+1
+
m
1838 me
0
0
0
10
10
–15
–15
--------
Important Atomic Nuclei
• Hydrogen (H)
– 1p, 0n
– Weight = 1
+
Important Atomic Nuclei
• Hydrogen (H)
– 1p, 0n
– Weight = 1
• Deuterium (D)
– 1p, 1n
– “heavy hydrogen”
– Weight = 2
+
+
the isotope of hydrogen
Important Atomic Nuclei
• Helium (He)
– 2p, 2n
– Weight = 4
+
+
Important Atomic Nuclei
• Carbon (C12)
– 6p, 6n (common)
– Weight = 12
Other isotopes have
different numbers of
neutrons
C13 (7n)
C14 (8n)
+
+
+
+
+
+
latest count – 116 elements
Atoms
Massive nucleus held
together by strong
nuclear force.
Electrons “orbit”,
held by electromagnetic force.
cloud of
electrons
nucleus
-
+
+
number of electrons
equals
number of protons
-
Ions
Ions are “charged”
Atoms, i.e.
number of e-  number of p+
Here two protons
and only one electron
+
+
positively charged ion
-
Molecules
Molecules are collections of atoms that
“share” electrons. Molecules are held
together weakly by the electromagnetic
force.
H2
Hydrogen
Helium
Oxygen
Neon
Iron
Atomic Structure
Niels Bohr (1885 – 1962)
postulated:
• Electrons are allowed only in
certain orbits which have
specific energies.
• Electrons can change orbits by gaining or
losing fixed amounts of energy.
• This can be done by absorbing or emitting
a photon of the correct energy.
The Atomic Model by Niels Bohr
Electrons are allowed only on discrete orbits
with specific energies.
Transitions between the orbits require
discrete excitation energies.
Balmer discovered that
for hydrogen the
wavelengths for specific
transitions are given by
Emission/De-excitation
An electron drops to a lower-energy orbit,
emitting a photon.
photon
Before
After
Absorption/Excitation
A photon is absorbed, the electron goes to an
excited state.
photon
Before
After
Absorption/Re-Emission Sequence
Photoionization
A high-energy photon can remove an electron
from an atom.
high
energy
photon
Before
After
Cooling by Collisions
• Since photons can carry away energy,
photon emission can cool a hot gas.
– Temperature is a measure of average speed
of particles in the gas.
Cool Gas
Hot Gas
Slow Average Speeds
Faster Average Speeds
Step 1: Two
high-speed atoms
collide.
Step 1: Two
high-speed atoms
collide.
Step 2: Some of
collision energy is
used to excite
electrons.
Exchange of
kinetic for
internal energy.
Step 1: Two
high-speed atoms
collide.
Step 2: Some of
collision energy is
used to excite
electrons.
Exchange of
kinetic for
internal energy.
Step 3: Atoms
de-excite, losing
energy to photons,
which escape.
Cooling by Collisions
• The net result of the collision is that the
particles are moving slower (so average
speed of gas particles and temperature
decreases) and photons carry away energy.
• Energy is conserved, but converted from
one form (gas kinetic energy) to another
(photons).
Atomic Structure
• Energy levels (allowed orbits) are different
for each ion. Depends on the following:
– Primarily on number of electrons
– Secondarily on number of protons
– To a small extent on the number of neutrons
• Each element has a unique signature
(like a fingerprint)
Model Hydrogen Atom
Infrared
Visible
UV
Atomic Line Spectra
Hydrogen
Helium
Sodium
Mercury
If atoms are densely crowded, energy levels
are perturbed by neighboring charges
Atomic Structure
• If atoms are densely crowded, energy levels
are perturbed by neighboring charges
 random shifts of energy levels
 random shifts of photon energies
 broadening of spectral lines
Low Pressure
Medium Pressure
High Pressure
Solid, Liquid, or Dense Gas
Atomic Structure
• If atoms are densely crowded, energy
levels are perturbed by neighboring
charges
 random shifts of energy levels
 random shifts of photon energies
 broadening of spectral lines
• Solids, liquids, and very dense gases emit
continuous spectra
What can we learn from
analyzing light ?
• Temperature (Kelvin Scale)
– measures internal energy content.
• The size of an object (L = 4πR2 σT4)
• Kirchoff’s Rules of Spectroscopy
Kirchhoff’s Rules
Kirchhoff’s rules are a set of empirical guide
lines that tell us what happens when light and
matter interact.
1 a hot dense object produces a
continuous spectrum
2 a cool diffuse gas in front of a hot source
produces an absorption spectrum
3 a diffuse gas seen against a dark background produces an emission-line spectrum
Continuous Spectrum
Hot
Continuum
Source
Emission-Line Spectrum
Cool, Diffuse
Gas Cloud
Absorption
Spectrum
Absorption-Line Spectrum
• Light from a continuous spectrum through
a vessel containing a cooler gas shows:
– A continuous spectrum from the lamp crossed
by dark “absorption lines” at particular
wavelengths.
– The wavelengths of the absorption lines exactly
correspond to the wavelengths of emission lines
seen when the gas is hot!
– Light is being absorbed by the atoms in the gas.
Emission-Line Spectra
• 19th century: Chemists noticed that each
element, heated into an incandescent gas
in a flame, emitted unique emission lines.
• (Fraunhofer, Bunsen, Kirchoff)
– Mapped out the emission-line spectra of
known atoms and molecules.
– Used this as a tool to identify the
composition of unknown compounds.
– They did not, however, understand how it
worked.
Next
Telescopes