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 32, 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 law of blackbody radiation. 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 B21N 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.