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```Ionization, Resonance excitation,
fluorescence, and lasers
The ground state of an atom is the state where all electrons
are in the lowest available energy level. When an orbital
electron is given energy, it can be excited to a higher energy
level, or removed entirely from the binding to that atom.
When it is removed from the atom, the electron can have
any value of final energy (the continuum).
Ionization is the process of removing an orbital electron
from its ground state energy level En to the continuum.
Resonance excitation is the excitation of an electron to a
particular, higher energy orbital Em (m>n).
An orbital electron can be excited in several ways:
•It can be scattered by a free electron, or by an ion.
•It can absorb a photon of light.
•Another atom can scatter from its atom, delivering an
energy transfer through the interaction of the orbital
electrons.
One thing is always true: So long
as the electron remains bound to
its atom, it must begin and end
any interaction in an allowed
energy level of that atom.
The most common way to analyze problems
of these sorts is by conservation of energy
Resonance excitation by electron scattering: (4.25) In a certain
gas discharge tube containing hydrogen atoms, electrons acquire
a maximum kinetic energy of 13 eV. What are the wavelengths
of all the lines that can be radiated?
Energy transfer is by a free electron scattering from an electron
that is bound in the ground state of a hydrogen atom. The most
energy that can be transferred is the maximum kinetic energy (13
eV) of the free electron. Let’s see which allowed levels are
within 13 eV of the ground state:
En   E1 / n 2 where E1 = -13.6 eV is the ground state energy.
En  E1  13eV
E1
 E1  13eV
2
n
E1
13.6
2
n 

 22.6
E1  13eV 0.6
n  2,3,4
n=2, 3, 4 are within reach. The state energies and
corresponding Lyman series lines are
n
E2 
 13.6
n2
o

hc
2  2000eV A

( En  E1 ) ( En  13.6eV )
2
-3.4 eV
1230 Å
3
-1.5 eV
1038 Å
4
-0.85 eV
985 Å
But we can also observe transitions 32, 4  2, and 4 3:
En  Em
hc

(En  Em )
3 2
1.9 eV
6610 Å
4 2
2.55 eV
4925 Å
4 3
0.65 eV
19323 Å
How do fluorescent lights work?
An electron current passes through Hg vapor. The electrons
excite orbital electrons to the first excited state. The electrons
emit a photon (UV) and return to the ground state. The walls of
the tube are coated with a phosphor, whose atoms are more
closely spaced. The UV photon is absorbed, exciting an electron
to a state n>2. The electron emits a visible photon, and drops to
an intermediate state.
There are 3 processes that can occur to an electron with
two energy states separated by an energy difference E:
•Spontaneous emission by an atom in the upper state,
dropping to the lower state and emitting a photon of energy
h = E;
•Absorption of a photon of energy h = E by an atom in
the lower state, raising it to the upper state;
•Stimulated emission of a photon of energy h = E by an
atom in the upper state, dropping it to the lower state and
emitting an additional photon of energy h = E.
This third process was predicted by Einstein before it had
been observed, in order to make consistency with Plank’s
Consider an ensemble of identical atoms that can only
make transitions between the lowest two levels E1, E2.
The rate of spontaneous emission will be proportional to the
population N2 of atoms in the excited state:
Rspont  AN 2
The rate of absorption will be proportional to the population
N1 of atoms in the lower state and to the density  of
photons with energy h = E:
Ra  B12 N1 
The rate of stimulated emission will be proportional to the
population N2 of atoms in the upper state and to the density
 of photons of energy h = E:
Rstim  B21N 2 
Now suppose that the atoms are in thermodynamic
equilibrium at temperature T. Then N1, N2 are constant.
dN 2
  Rspont  Rstim  Rabs
dt
 -AN2  B21N 2  B12 N1  0
A

N1/ N 2 B12  B21
But now for statistical mechanics: in equilibrium,
 E1 / kT
N1 e
  E2 / kT  e / kT
N2 e
Putting it together:
A
 ( )   / kT
e
B12  B21
But this must yield Plank’s blackbody spectrum!
 3
1
 ( )  2 3  / kT
 c e
1
 3
B12  B21  B
A 2 3 B
 c
A, B are the Einstein coefficients describing the coupling of
light to atoms. Note that Einstein predicted stimulated emission
before it was observed, led by the requirement that the light
intensity that is in equilibrium with atoms at temperature T must
match that of the spectrum of blackbody radiation at that temp.
The laser
Consider the lowest three levels (n = 1, 2, 3) of an atomic
system. The energies are E3 > E2 > E1.
If the system is in thermal equilibrium, the populations of
atoms in each state are
N1  N 0 e  E1 / kT
N 2  N 0 e  E2 / kT
N 3  N 0 e  E3 / kT
N1  N 2  N 3 # atoms
So N1 > N2 > N3 for any temperature T.
Laser Star!
Hubble Space Telescope image of unstable
star Eta Carinae, note the double lobed
structure of the expanding stellar atmosphere.
This bipolar structure is similar to that of
other laser stars.
Ultraviolet spectra of Eta Carinae as observed by
the International Ultraviolet Explorer (IUE). Two
strong emission lines dominate the spectrum at
wavelengths of 2506 and 2508 Å. Their unusual
strength is similar to the strong optical emission
lines commonly found in the spectra of laser stars
such as quasars. Johansson et al. (1993) attribute
them to two transitions in the Fe II ion.
Eta Carinae is one of the best known examples of a bipolar outflow. These
axisymmetric high velocity ejections commonly occur in many types of
astronomical objects such as in young stellar objects (YSO) in x-ray novae like
GRS 1915+105 and GRO J1655-40, in planetary nebulae, in symbiotic stars, and
in many laser stars such as TON 202, 3C345, and Cygnus A.
In 1837 Eta Carinae became one of the brightest stars in the sky. Even today it is
the brightest object in the whole sky at infrared wavelengths of 20 microns. This
indicates a thick circumstellar shell of dust and gas. Its late type spectrum
combined with nova-like emission line characteristics such as P-Cygni and helium
lines make this star 'one of the more unusual emission-line spectra of any celestial
object‘’(according to Hearnshaw, 1986). Stellar plasma expansion velocities of
several hundreds of kilometers per second have been detected.
```
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