Download Blackbody in Infrared

General Astronomy
Spectra
Spectra
Early in this course, it was noted that we only
detect light from the stars. They are too
far away to do much more than that. As
such, we can see:
• Brightness
• Position
• Color
Color
Recall that we can separate the star's
visible light into its component colors
by use of a prism
Color
We can also use a Diffraction Grating
to disperse light into its component
colors. A grating is thousands of
'slits'
The Continuous Spectrum
Kirschoff's First Law:
A hot solid, liquid or dense gas produces a
continuous spectrum
The Continuous Spectrum
Solid
The Continuous Spectrum
GAS
Compact Fluorescent Bulb
Note the gaps in the spectrum
The Continuous Spectrum and Temperature
• Blackbody Radiation
– A blackbody (a perfect absorber and
emitter of radiation) relates its color to
its temperature
The Continuous Spectrum and Temperature
Wein's Law relates the wavelength of
greatest intensity to the temperature
λmax = 2.88x107 / T
Where wavelength is in Angstroms
and temperature is in Kelvin
For example, the surface temperature of the Sun is
about 5980K. So,
2.88x107 / 5980 = 4816 angstroms,
(a yellowish color)
The Continuous Spectrum and Temperature
Stefan-Boltzmann Law relates the total
amount of energy radiated to the
temperature of the body:
E = σ T4
For example, the Sun’s surface temperature is about
6000K; Your skin temperature is about 300K.
The Sun’s surface is about 20 times hotter than your
skin. But what’s the difference in energy radiated?
Esun / Eskin = σ Tsun4 / σ Tskin4 = (Tsun / Tskin)4
= (20)4 = 160,000
Blackbody in Infrared
Much of a person's energy is radiated away in the form of infrared
energy. Some materials are transparent to infrared light, while opaque
to visible light (note the plastic bag). Other materials are transparent
to visible light, while opaque or reflective to the infrared (note the
man's glasses).
The Emission Spectrum
Kirschoff's Second Law:
A hot, rarified gas produces an emission,
or bright line, spectrum
The Absorption Spectrum
Kirschoff's Third Law:
A cool, rarified gas produces an absorption,
or dark line, spectrum
Kirschoff's Laws
ComparingThe Bright and Dark Lines
Notice that, for a given element, the bright and
dark lines in the spectrum show up in exactly
the same positions (actually this depends on
the temperature of the gas – but we'll discuss
this later)
Bohr Theory
What’s wrong with the Rutherford
model of the atom?
•
Let’s put together some facts:
• By Newton’s 1st Law, an
electron circling a nucleus
must be accelerating
• An accelerating charge radiates
• Charges that radiate, lose energy
Loss of energy + conservation of angular
momentum mean that the electron must spiral
into the nucleus. The charges annihilate each
other and destroy the atom
Doesn’t seem to happen, Does it?
Bohr Theory
• Niels Bohr came up with a radical idea
– If the electron stays within certain
allowed orbits, it will not radiate.
– These allowed orbits are called ‘energy
levels’
– An electron may move between energy
levels by absorbing or emitting the exact
difference in energy between the levels
While Bohr Theory is not “correct” it provides an easy
model – which is adequate to explain the spectra we
will observe.
Bohr Theory: The H atom
The first few energy levels
n=3
n=2
1st Excited State, n = 1
Ground State, n = 0
Hydrogen Spectral Series
13.6
13.0
3
12.7
Brackett
12.0
2
Paschen
1
10.2
Balmer
0
Lyman
The Balmer Series of lines are in Visible Light
External Influences
The Zeeman Effect
External Influences
The Stark Effect
Like a magnetic field, an Electric field can also cause
a spectral line to split into components.
The difference is this type of splitting is not
symmetrical (like the magnetic type).
This is known as the Stark Effect
A Spectral Line
Let's magnify a single spectral line.
Normally we would be looking at absorption lines, but it
is easier to see an emission line on the slides.
Funny, you would think that an exact amount of energy
would produce a very thin line.
What is causing the 'spread' in the shape of the line?
The Heisenberg Uncertainty Principle
Early last century, Werner Heisenberg stated a guiding
principle, known as the Uncertainty Principle.
It can be stated in two possible, but equivalent, ways:
1. The better you can fix the location of an object, the
worse you can fix its momentum and vice versa.
2. The better you can fix the energy of an object, the
worse you can fix its time duration and vice versa.
Natural Line Widths
The photons emitted by an atom are related to the amount
of energy given up by a electron moving between the
levels.
Since the time that an electron stays in a level varies by a
tiny amount, then – via Heisenberg – the small difference
in time causes a small difference in energy and therefore
a small spread in wavelength
Doppler Broadening
This extra spreading of a spectral line is caused by the
Doppler Effect – sources of light moving toward us
('blueing' the light) and away from us ('reddening' the
light. This generally occurs through three mechanisms:
1. Turbulence
Motions of masses of gas churning in the star
2. Pulsing
The surface of the star expanding and contracting
3. Rotation
Rapid rotation of the star
Pressure Broadening
Sometimes called Collisional Broadening, as the
atoms are squeezed together by gas pressure
in the star, they are more likely to collide.
Collisions may cause the photon to be created
with (again the Uncertainty Principle) slightly
different energies.
Also, as the atoms become closer together
their electric fields start to cause the Stark
Effect causing a slight splitting of the line
which also looks like broadening when
unresolved.