Transcript DTU_9e_ch04 - University of San Diego Home Pages

Neil F. Comins • William J. Kaufmann III
Discovering the Universe
Ninth Edition
CHAPTER 4
Atomic Physics and Spectra
WHAT DO YOU THINK?
1.
2.
3.
Which is hotter, a “red-hot” or a “blue-hot”
object?
What color does the Sun emit most brightly?
How can we determine the age of space debris
found on Earth?
In this chapter you will discover…





the origins of electromagnetic radiation
the structure of atoms
that stars with different surface temperatures emit
different intensities of electromagnetic radiation
that astronomers can determine the chemical
compositions of stars and interstellar clouds by studying
the wavelengths of electromagnetic radiation that they
absorb or emit
how to tell whether an object in space is moving toward
or away from Earth
WHEN FIRST
HEATED, THE
POKER GLOWS
DIMLY RED
AS THE
TEMPERATURE
RISES, IT BECOMES
BRIGHTER ORANGE
AT HIGHER
TEMPERATURES, IT
BECOMES BRIGHTER
AND YELLOW
These stars have roughly the same temperatures as the bars above.
Blackbody (Thermal)
Radiation
1. Every object does it
2. Broad distribution over
wavelength, with one peak
3. Hotter – peak shifts to
shorter wavelength
4. Hotter – energy goes up
… a lot more than shown
Rules 3 and 4 are governed
by equations. . .
Blackbody (Thermal)
Radiation
1. Every object does it
2. Broad distribution over
wavelength, with one peak
3. Hotter – peak shifts to
shorter wavelength
4. Hotter – energy goes up
… a lot more than shown
The 3000 K object looks red
The 6000 K object looks white
The 12,000 K object looks blue
Blackbody (Thermal)
Radiation
1. Every object does it
2. Broad distribution over
wavelength, with one peak
3. Hotter – peak shifts to
shorter wavelength
4. Hotter – energy goes up
… a lot more than shown
Rule 3 is Wien’s Law:
λMAX (nm) = 2.9 x 106 / T (K)
Rule 4 is Stephan’s Law:
P = σT4
P = power radiated per
square meter of area
σ = Stephan’s constant
Stellar surfaces emit light that is close to an ideal blackbody. We
can estimate the surface temperature of a star by examining the
intensity of emitted light across a wide range of wavelengths.
THERMAL RADIATION QUESTION
The curves A, B, C, and D represent the
observed spectra of 4 stars.
Which star is the hottest?
THERMAL RADIATION QUESTION
The curves A, B, C, and D represent the
observed spectra of 4 stars.
Which star is the coolest?
THERMAL RADIATION QUESTION
The curves A, B, C, and D represent the
observed spectra of 4 stars.
Between Stars B and C, which is hotter?
A – Both Equal
B – Star B hotter
C – Star C hotter
D – insufficient
information
Stellar surfaces emit light that is close to an ideal blackbody. We
can estimate the surface temperature of a star by examining the
intensity of emitted light across a wide range of wavelengths.
Mystery of Thermal Radiation
In the early 1900s the theory of thermal
radiation worked at long wavelengths, but
held that an infinite amount of energy was
radiated as short wavelengths.
 “Ultraviolet catastrophe” – for the theory,
which was clearly seriously wrong.
 Max Planck proposed that radiation was
emitted in lumps (photons) . This theory
predicted the observed curve exactly.
 Planck’s constant “h” of quantum
mechanics was born.

The combination of lines from the solar spectrum allows us to
determine which chemicals are present and in what abundance.
Gustav Kirchoff and
Robert Bunsen
Pioneers in spectroscopy circa 1860
Kirchoff’s Laws of Spectra
A high-pressure gas (or a solid or
liquid) emits all colors of rainbow.
This is a continuous spectrum.
A low-pressure gas emits bright lines
at specific wavelengths if excited.
This is an emission line spectrum.
When a source of a continuous
spectrum is viewed behind a cool
gas, dark lines are seen on the
rainbow. This is an
absorption line spectrum.
This schematic diagram summarizes how different types of spectra are
produced. The prisms are added for conceptual clarity, A hot, glowing object
emits a continuous spectrum. If this source of light is viewed through a cool
gas, dark absorption lines appear in the resulting spectrum. When the same
gas is viewed against a cold, dark background, its spectrum consists of just
bright emission lines.
When a chemical is heated in the Bunsen burner flame, the
light produced is made of only specific wavelengths.
Each chemical element has its unique series of wavelengths,
which is like a fingerprint.
Absorption and Emission Spectra
Iron in the Sun’s Atmosphere
The upper (absorption) spectrum is a portion of the Sun’s spectrum
from 425 to 430 nm. Numerous dark spectral lines are visible. The
lower (emission) spectrum is a corresponding portion of the spectrum
of vaporized iron. Several emission lines can be seen against the black
background. The fact that the iron lines coincide with some of the solar
absorption lines proves that there is some iron in the Sun’s
atmosphere. It also raises the question as to how the lines arise in
absorption (upper) and emission (lower)
A grating spectrograph separates light from a telescope
into different colors by passing it through a diffraction
grating, which has many tiny parallel grooves.
Diffraction Gratings in Familiar Objects
This peacock feather contains
numerous natural diffraction gratings.
The role of the parallel lines etched
in a human-made diffraction grating
is played by parallel rods of the
protein melanin in the feathers.
CCDs and DVDs store information
on closely spaced bumps located on
a set of nearly parallel tracks. Light
striking these tracks systematically
reflects different colors in different
directions—it behaves like a
diffraction grating.
This image and graph show a/an:
A. Absorption Line Spectrum
C. Continuous Spectrum
B. Emission Line Spectrum
D. None of the above
This image and graph show a/an:
A. Absorption Line Spectrum
C. Continuous Spectrum
B. Emission Line Spectrum
D. None of the above
WHY these fingerprints?
Physics at the atomic level:
 Existence of electron (JJ Thompson 1897)
 Atomic structure (Ernest Rutherford 1910)
 Quantum mechanics (Niels Bohr 1913)
 Quantum mechanics (Werner Heisenberg,
Erwin Schrödinger, ca. 1927)
Rutherford Scattering Experiment (1910)
Most helium nuclei (also called alpha particles) entering a thin foil scatter
slightly as they pass through the medium, but some scatter backward,
indicating that they have encountered very dense, compact objects. Such
experiments were the first evidence that most matter is concentrated in what
are now called atomic nuclei. Electrons must orbit these nuclei.
But … Electrons can’t orbit!
Orbit means they accelerate (recall def)
 Which means they radiate away energy
 And they spiral into the nucleus in a
microsecond …
 So, no chemical element can exist …
 And neither can we … Hmm
 Niels Bohr proposed a rule that …

Certain special allowed orbits don’t radiate
Simple mathematical rule with Planck’s constant “h”for these orbits.
Later Quantum Mechanics (late 1920s) replaced the idea of an allowed orbit
with an electron cloud. This works for all atoms, not just hydrogen.
Energy Level Diagram for Hydrogen
An eV is an electron
volt, a unit of energy.
Energy of photon
determines
wavelength; next
slide)
When an electron moves from a lower energy to a higher energy level, a photon
is absorbed. When an electron moves from a higher energy level to a lower
energy level, a photon is emitted. The energy of the photon, and thus its
wavelength, is the energy difference between the two energy levels.
Photon energy and wavelength
λ=hc/E
λ = wavelength (Greek “lambda”)
h = Planck’s constant (.. Thermal radiation)
c = speed of light
E = energy of photon
λ = 1240 / E … h and c are constants
λ in nm (1 nm = 10-9 m),
E in eV (electron volts, a unit of energy).
Balmer Lines in the Spectrum of a Star
This portion of the spectrum of the star Vega shows eight
Balmer lines, from Hα at 656.3 nm through Hθ at 388.9 nm.
Emission Spectra from Interstellar Gas Clouds
Left: Stars in this interstellar gas cloud (NGC 2363 in the constellation
Camelopardus, the Giraffe) emit absorption spectra. Electrons in the cloud’s
hydrogen gas absorb and reemit the red light from these stars. NGC 2363 is
located some 10 million ly away. (b) Part of the Rosette Nebula (NGC 2237),
an interstellar gas cloud in the constellation Monoceros (the Unicorn). The
green glow is generated by doubly ionized oxygen atoms (O III; oxygen atoms
missing two electrons) in the cloud that emit 501-nm photons. The Rosette is
3000 ly away.
Light comes in “lumps” called:
A. Protons
B. Photons
C. Phonons
D. Pleurons
What relation exists between
photon energy and wavelength:
A. Longer wavelength means higher photon
energy
B. Longer wavelength means lower photon
energy
C. Wavelength has nothing to do with
photon energy because wave and
particle natures are independent aspects
D. All photons have the same wavelength
Some more physics . . .
Doppler effect
 Radioactive decay
 Effect of dust
 Proper motion

Recall that the wavelength of light, and therefore the
wavelength of the photons that light contains, is shifted when
the source is traveling toward or away from the observer, the
Doppler Effect.
The Transformation of Uranium into Lead
This figure shows the rate that 1 kg of uranium decays into
lead, as described in the text. The half life of Uranium is 4.5
billion years. The sample contains 0.125 kg of uranium after
13.5 billion years (3 half lives).
Dust dims and reddens
Red light suffers less
attenuation, compared to blue.
Sunsets are red, and sometimes
the Sun isn’t blinding at sunset.
Related fact: the sky is blue.
Proper Motion
The proper motion of a star is its motion perpendicular to
our line of sight across the celestial sphere. This is so small
that it can only be measured for the closest stars.
The radial velocity of a
star is its motion along
our line of sight either
toward or away from us.
Using the spectrum, we
can measure this for
nearly every object in
space!
Proper Motion of Barnard’s Star
These are two superimposed images of Barnard’s star, taken
a year apart in 2000 and 2001, showing the proper motion of
the star during that time. In addition to having the largest
known proper motion (10.3˝ per year), Barnard’s star is one of
the closest stars to Earth.
Summary of Key Ideas
By studying the wavelengths of electromagnetic
radiation emitted and absorbed by an
astronomical object, astronomers can learn
about the object’s:
● temperature
● chemical composition
● rotation rate,
● companion objects
● movement through space.
Blackbody Radiation



A blackbody is a hypothetical object that perfectly
absorbs electromagnetic radiation at all wavelengths.
The relative intensities of radiation that it emits at
different wavelengths depend only on its temperature.
Stars closely approximate blackbodies.
Wien’s law states that the peak wavelength of radiation
emitted by a blackbody is inversely proportional to its
temperature—the higher its temperature, the shorter the
peak wavelength. The intensities of radiation emitted at
various wavelengths by a blackbody at a given
temperature are shown as a blackbody curve.
The Stefan-Boltzmann law shows that a hotter blackbody
emits more radiation at every wavelength than does a
cooler blackbody. Total Power = Area x σ T4
Discovering Spectra



Spectroscopy—the study of electromagnetic spectra—
provides important information about the chemical
composition of remote astronomical objects.
Kirchhoff’s three laws of spectral analysis describe the
conditions under which absorption lines, emission lines,
and a continuous spectrum can be observed.
Spectral lines serve as distinctive “fingerprints” that
identify the chemical elements and compounds
comprising a light source.
Atoms and Spectra




An atom consists of a small, dense nucleus (composed of
protons and neutrons) surrounded by electrons. Atoms of
different elements have different numbers of protons, while
different isotopes have different numbers of neutrons.
Quantum mechanics describes the behavior of particles and
shows that electrons can only be in certain allowed orbits
around the nucleus.
The nuclei of some atoms are stable, while others (radioactive
ones) spontaneously split into pieces.
The spectral lines of a particular element correspond to the
various electron transitions between allowed orbits of that
element with different energy levels of those atoms. When an
electron shifts from one energy level to another, a photon of
the appropriate energy (and hence a specific wavelength) is
absorbed or emitted by the atom.
Atoms and Spectra





The spectrum of hydrogen at visible wavelengths consists of
part of the Balmer series, which arises from electron
transitions between the second energy level of the hydrogen
atom and higher levels.
Every different element, isotope, and molecule has a different
set of spectral lines.
When a neutral atom loses or gains one or more electrons, it
is said to be charged. The atom loses an electron when the
electron absorbs a sufficiently energetic photon, which rips it
away from the nucleus.
The motion of an object toward or away from an observer
causes the observer to see all of the colors from the object
blueshifted or redshifted, respectively. This effect is generally
called a Doppler shift.
The equation that describes the Doppler effect states that the
size of a wavelength shift is proportional to the radial velocity
between the light source and the observer.
Key Terms
absorption line
absorption line spectrum
atom
atomic number
blackbody
blackbody curve
blueshift
continuous spectrum
(continuum)
diffraction grating
Doppler shift
electromagnetic force
electron
element
emission line
emission line spectrum
energy flux
excited state
ground state
ion
ionization
isotope
Kirchhoff’s laws
luminosity
molecule
neutron
nucleus (of an atom)
periodic table
Planck’s law
proper motion
proton
quantum mechanics
radial velocity
radioactive
redshift
spectral analysis
spectrograph
spectroscope
Stefan-Boltzmann law
strong nuclear force
transition (of an
electron)
transverse velocity
weak nuclear force
Wien’s law
WHAT DID YOU THINK?


Which is hotter, a “red-hot” or a “blue-hot” object?
Of all objects that glow visibly from heat generated or
energy stored inside them, those that glow red are the
coolest.
WHAT DID YOU THINK?


What color does the Sun emit most brightly?
The Sun emits all wavelengths of electromagnetic
radiation. The colors it emits most intensely are in the
blue-green part of the spectrum. Because the human
eye is less sensitive to blue-green than to yellow, and
Earth’s atmosphere scatters blue-green wavelengths
more readily than longer wavelengths, we normally see
the Sun as yellow.
WHAT DID YOU THINK?


How can we determine the age of space debris found on
Earth?
We measure how much the long-lived radioactive
elements, such as 238U, have decayed in the object.
Carbon dating is only reliable for organic materials that
formed within the past 100,000 years. It cannot be used
for determining the age of rocks and minerals on Earth
or from space. These substances were formed more
than 4.5 billion years ago. Radioactive carbon in them
has long since decayed to stable isotopes.