Transcript blackbody radiation

PSCI 1414 GENERAL
ASTRONOMY
THE NATURE OF LIGHT
PART 2: BLACKBODY RADIATION AND SPECTRAL ANALYSIS
ALEXANDER C. SPAHN
BLACKBODY RADIATION
The figure depicts quantitatively how the radiation
from a dense object depends on its Kelvin
temperature.
Each curve in this figure shows the intensity of light
emitted at each wavelength by a dense object at a
given temperature: 3000 K (the temperature of a
“cool” star), 6000 K (around the temperature of our
Sun), and 12,000 K (the temperature of a “hot” star).
In other words, the curves show the spectrum of
light emitted by such an object.
BLACKBODY RADIATION
The figure shows that the higher the temperature,
the greater the intensity of light at all wavelengths.
One way to understand this response to
temperature is that the emitted light results from
the motion of the material’s atoms and molecules,
which, as we saw, increases with temperature
BLACKBODY RADIATION
The temperature not only indicates the total
intensity of the light, but also the shape of its
spectrum.
The most important feature in the spectrum—the
dominant wavelength—is called the wavelength of
maximum emission, at which the curve has its peak
and the intensity of emitted energy is strongest.
The location of the peak also changes with
temperature: The higher the temperature, the
shorter the wavelength of maximum emission.
BLACKBODY RADIATION
To summarize these observations:
The higher an object’s temperature, the more
intensely the object emits electromagnetic
radiation and the shorter the wavelength at which
it emits most strongly.
We will make frequent use of this general rule to
analyze the temperatures of celestial objects such as
planets and stars.
BLACKBODY RADIATION
The curves in the figure are drawn for an idealized
type of dense object called a blackbody.
A perfect blackbody does not reflect any light at all;
instead, it absorbs all radiation falling on it.
Because it reflects no electromagnetic radiation, the
radiation that it does emit is entirely the result of its
temperature.
BLACKBODY RADIATION
Ordinary objects, like tables, textbooks, and people,
are not perfect blackbodies; they reflect light, which
is why they are visible.
A star such as the Sun, however, behaves very much
like a perfect blackbody, because it absorbs almost
completely any radiation falling on it from outside.
The light emitted by a blackbody is called blackbody
radiation, and the curves are often called blackbody
curves.
TEMPERATURE AND THERMAL ENERGY
This figure shows the blackbody curve for a
temperature of 5800 K as well as the intensity
curve for light from the Sun.
The peak of both curves is at a wavelength of
about 500 nm, near the middle of the visible
spectrum. Note how closely the observed
intensity curve for the Sun matches the
blackbody curve.
This is a strong indication that the temperature
of the Sun’s glowing surface is about 5800 K—a
temperature that we can measure across a
distance of 150 million kilometers!
TEMPERATURE AND THERMAL ENERGY
Blackbody radiation depends only on the
temperature of the object emitting the
radiation, not on the chemical composition of
the object.
The light emitted by molten gold at 2000 K is
very nearly the same as that emitted by
molten lead at 2000 K.
The intensity curve for the Sun (a typical star)
is not precisely that of a blackbody. We will see
that the differences between a star’s spectrum
and that of a blackbody allow us to determine
the chemical composition of the star.
WIEN’S LAW
The previous figures show that the higher the temperature (T) of a blackbody, the shorter its
wavelength of maximum emission (λmax).
In 1893 the German physicist Wilhelm Wien used ideas about both heat and electromagnetism
to make this relationship quantitative. The formula that he derived, which today is
called Wien’s law, is
𝜆max
0.0029 K m
=
𝑇
Wien’s law is very useful for determining the surface temperatures of stars.
CALCULATION CHECK 5-2
Which wavelength of light would our Sun emit most if its temperature
were twice its current temperature of 5800 K?
Wien’s law can be rearranged to calculate the temperature of a star as T =
0.0029 K m ÷ (5800 K × 2) = 2.5x10-7 m = 250 nm, which is ultraviolet.
STEFAN-BOLTZMANN LAW
The other useful formula for the radiation from a blackbody involves the total amount of
energy the blackbody radiates at all wavelengths.
Energy is usually measured in joules (J), named after the nineteenth-century English physicist
James Joule.
The joule is a convenient unit of energy because it is closely related to the familiar watt (W): 1
watt is 1 joule per second, or 1 W = 1 J/s = 1 J s−1.
For example, a 100-watt lightbulb uses energy at a rate of 100 joules per second, or 100 J/s.
STEFAN-BOLTZMANN LAW
The amount of energy emitted by a blackbody depends both on its temperature and on
its surface area.
These characteristics make sense: A large burning log radiates much more heat than a
burning match, even though the temperatures are the same.
To consider the effects of temperature alone, it is convenient to look at the amount of
energy emitted from each square meter of an object’s surface in a second. This quantity
is called the energy flux(F).
STEFAN-BOLTZMANN LAW
Flux means “rate of flow,” and thus F is a measure of how rapidly energy is flowing out of
the object.
It is measured in joules per square meter per second, usually written as J/m2/s or J
m−2 s−1.
Alternatively, because 1 watt equals 1 joule per second, we can express flux in watts per
square meter (W/m2, or W m−2).
STEFAN-BOLTZMANN LAW
Written as an equation, the Stefan-Boltzmann law is
𝐹 = 𝜎𝑇 4
F = energy flux, in joules per square meter of surface per second
σ = a constant = 5.67x10-8 W m-2 K-4
T = temperature, in Kelvins
The value of the Stefan-Boltzmann constant σ (the Greek letter sigma) is known from
laboratory experiments.
CONCEPT CHECK 5-8
Is it ever possible for a cooler object to emit more energy than a warmer
object?
Yes. If the cooler object is much larger than the warmer object, the cooler
object can emit a greater total energy. The energy flux F refers to the energy
emitted per second for each square meter of surface area, so even for a cool
object, the larger the object, the more energy it radiates. This is why some
stars (called red giants) that are much larger than our Sun are actually
brighter than our Sun, even though they are cooler.
PHOTONS
In 1905, the great physicist Albert Einstein developed a radically new model for the
nature of light.
Central to this new picture is that light is made out of particles! Each particle of light is
called a photon, which is a distinct packet of electromagnetic energy.
Photons have a dual nature in that they are both particle-like and wavelike.
PHOTONS
They are particle-like in the sense that they are the small packets of energy that make up light.
As expected with particles, you can count the number of photons in an electromagnetic wave.
But, photons are also wave-like because each one is itself a wave, where each photon has the
same wavelength as the electromagnetic wave of which it is a small part.
As expected with waves, photons exhibit interference patterns when passed through a doubleslit experiment
PHOTONS
The energy of each photon is related to the wavelength of light: the longer the wavelength, the
lower the energy.
Thus, a photon of red light (wavelength λ = 700 nm) has less energy than a photon of violet
light (λ = 400 nm).
Conversely, the shorter a photon’s wavelength, the higher its energy.
PHOTONS
The relationship between the energy E of a single photon and the wavelength λ of the
electromagnetic radiation can be expressed in a simple equation:
ℎ𝑐
𝐸=
𝜆
c = speed of light = 3x108 m/s
h = Planck’s constant = 6.625x10-34 J s
PHOTONS
Because the frequency ν of light is related to the wavelength λ by ν = c/λ, we can rewrite the
equation for the energy of a photon as
𝐸 = ℎ𝜈
The equations E = hc/λ and E = hν are together called Planck’s law.
Both equations express a relationship between a particle-like property of light (the energy E of
a photon) and a wave-like property (the wavelength λ or frequency ν).
SPECTRAL ANALYSIS
In 1814 the German master optician Joseph von
Fraunhofer repeated the classic experiment of
shining a beam of sunlight through a prism.
But this time Fraunhofer subjected the resulting
rainbow-colored spectrum to intense
magnification.
To his surprise, he discovered that the solar
spectrum contains hundreds of fine, dark lines,
now called spectral lines.
SPECTRAL ANALYSIS
spectral line: In a light spectrum, an absorption or
emission feature that is at a particular wavelength.
Dark spectral line arises when light at a specific
wavelength is at least partially absorbed so that
the spectrum appears darker; it is also called
an absorption line.
Fraunhofer counted more than 600 dark lines in
the Sun’s spectrum; today we know of more than
30,000.
SPECTRAL ANALYSIS
Half a century later, chemists discovered that they
could produce spectral lines in the laboratory and
use these spectral lines to analyze what kinds of
atoms different substances are made of.
Chemists had long known that many substances
emit distinctive colors when sprinkled into a flame.
To facilitate study of these colors, around 1857 the
German chemist Robert Bunsen invented a gas
burner (today called a Bunsen burner) that
produces a clean flame with no color of its own.
SPECTRAL ANALYSIS
Bunsen’s colleague, the Prussian-born physicist
Gustav Kirchhoff, suggested that the colored light
produced when substances were added to the flame
might best be studied by passing the resulting light
through a prism.
The two scientists promptly discovered that the
spectrum from the flame consists of a pattern of thin,
bright spectral lines against a dark background.
A bright spectral line arises because at least some
additional light is being emitted at a specific
wavelength; it is also called an emission line.
SPECTRAL ANALYSIS
Kirchhoff and Bunsen then found that each chemical
element produces its own unique pattern of spectral
lines. Thus was born in 1859 the technique
of spectral analysis: the identification of atoms and
molecules by their unique patterns of spectral lines.
You can easily see that each substance produces a
unique pattern of spectral lines; each pattern can be
thought of as a spectral “fingerprint” for
identification.
This is enormously important in astronomy because
it allows us to determine the detailed composition of
distant planets and stars.
THE SOLAR SYSTEM
There is a direct connection between these
two types of spectra. These connections are
summarized in three statements about spectra
that are known as Kirchhoff’s laws.
A hot opaque body, such as a perfect
blackbody, or a hot, dense gas produces a
continuous spectrum—a complete rainbow of
colors without any spectral lines.
Note: a blackbody is an idealized type of dense
object that does not reflect any light at all;
instead, it absorbs all radiation falling on it.
THE SOLAR SYSTEM
A hot, transparent gas produces an emission line spectrum—a series of bright spectral lines against a
dark background.
THE SOLAR SYSTEM
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.
FOR NEXT TIME…
• Read Chapter 16 of the text
• Homework 14: Will be posted later today online, due Monday (no class Friday)