Spectroscopy and Atomic Structure Ch 04

Four essential questions:

• What is an atom? • How do atoms interact with light?• What kinds of spectra do you see when you

look at celestial objects?• What can you learn from a star’s spectrum?

Objectives (Ch 04)

Explain the Formation of Spectral Lines

The Energy Levels of the Hydrogen Atom

The Photoelectric Effect

Chemical Composition

Explain how spectral lines apply to molecules

Explain what information Spectral-Lines provide

So far, l tells us ….• Color• Temperature• Energy Flux• Some Doppler

The Enigma, to understand how stars work need to understand how atoms work????

Stellar SpectraThe spectra of stars

are more complicated than pure blackbody

spectra.They contain

characteristic lines, called absorption lines.

With what we have learned about atomic structure, we can now understand how those lines are formed.

Kirchhoff’s Laws of Radiation (1)1. A solid, liquid, or dense gas excited to

emit light will radiate at all wavelengths and thus produce a continuous spectrum.

Kirchhoff’s Laws of Radiation (2)2. A low-density gas excited to emit light

will do so at specific wavelengths and thus produce an emission spectrum.

Light excites electrons in atoms to higher energy

states

Transition back to lower states emits light at specific

frequencies

Kirchhoff’s Laws of Radiation (3)3. If light comprising a continuous spectrum

passes through a cool, low-density gas, the result will be an absorption spectrum.

Light excites electrons in atoms to higher energy

states

transition energies are absorbed from the continuous spectrum.

The Spectra of StarsThe inner, dense layers of

a star produce a continuous (blackbody)

spectrum.

Cooler surface layers absorb light at specific frequencies.

=> Spectra of stars are absorption spectra.

Analyzing Absorption Spectra• Each element produces a specific set of

absorption (and emission) lines.

By far the most abundant elements in the Universe

• Comparing the relative strengths of these sets of lines, we can study the composition of gases.

Spectral LinesEmission spectrum can be used to identify elements:

Spectral Lines

An absorption spectrum can also be used to identify elements. These are the emission and absorption spectra of sodium:

Spectral Lines … Bottom Line

Kirchhoff’s laws:1. Luminous solid, liquid, or dense gas produces continuous spectrum2. Low-density hot gas produces emission spectrum3. Continuous spectrum incident on cool, thin gas produces absorption spectrum

Formation of Spectral LinesExistence of spectral lines required new model of atom, so that only certain amounts of energy could be emitted or absorbed.Bohr model had certain allowed orbits for electron:

Quantized Energy

• Continuous energy is like a ramp.

• Quantized energy is like a stair case.

• Each stair increases the energy by the value of Planck’s constant

• h = 6.63x10-34 J-s• E = hf• C = lf• 1eV = 1.602 x 10-19 J• En = 13.6 eV (1 – [1/n2])

The Dual Nature of LightLight is a wave

– Reflection– Refraction– Interference– Polarization

Light is a particle– Photoelectric effect– reflection

E = hfLight is both a wave and particle!!

http://jersey.uoregon.edu/vlab/elements/Elements.html;

Become familiar with the absorption and emission of various elemental spectra. Pay particular attention to H, He, and the noble gases. 1. Set the applet to “absorption.” What do you notice about the spectral lines? What is happening at the atomic level with respect to electron transitions?     2. Set the applet to “emission.” What do you notice about the spectral lines? What is happening at the atomic level with respect to electron transitions?   

The Bohr model is a primitive model of the hydrogen atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics, and thus may be considered to be an obsolete scientific theory.

However, because of its simplicity, and its correct results for selected systems, the Bohr model is still commonly taught to introduce students to quantum mechanics, before moving on to the more accurate but more complex valence shell atom. The quantum theory of the period between Planck's discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory. In the model above, various electron transitions are shown, where n = energy level. The ground state is given by, n = 1. Transitions starting or ending at the ground state are known as the “Lyman” series, discovered in 1914 by Theodore Lyman. The first is Lyman-a (n = 2 to n = 1), then Lyman-b (n = 3 to n = 1), and so on. When n = ∞, ionization occurs

Formation of Spectral Lines

Energy levels of the hydrogen atom, showing two series of emission lines:

Formation of Spectral Lines … bottom line

Absorption can boost an electron to the second (or higher) excited state

Two ways to decay:1. to ground state2. cascade one orbital at a time

Formation of Spectral Lines(a) Direct decay (b) cascade

Formation of Spectral Lines

Absorption spectrum: created when atoms absorb photons of right energy for excitation

Multielectron atoms: much more complicated spectra, many more possible statesIonization changes energy levels

Formation of Spectral Lines

Emission lines can be used to identify atoms:

Molecules

Molecules can vibrate and rotate, besides having energy levels

a) Electron transitions produce visible and ultraviolet lines

b) Vibrational transitions produce infrared lines

c) Rotational transitions produce radio-wave lines

Molecules

Molecular spectra are much more complex than atomic spectra, even for hydrogen:

(a) Molecular hydrogen (b) Atomic hydrogenH2 H

Spectral-Line AnalysisInformation that can be obtained from spectral lines:• Chemical composition• Temperature• Radial velocity:

Spectral-Line AnalysisLine broadening can be due to Doppler shift • from thermal motion• from rotation

http://phys.educ.ksu.edu/vqm/free/zeemanspec.html

Zeeman Effect … It’s magnetic

The Doppler Effect

The Doppler Effect

Take l0 of the Ha (Balmer alpha) line:

Assume, we observe a star’s spectrum with the Ha line at l = 658 nm. What is the shift and radial velocity?

Spectral-Line Analysis

Summary

• Spectroscope splits light beam into component frequencies

• Continuous spectrum is emitted by solid, liquid, and dense gas

• Hot gas has characteristic emission spectrum

• Continuous spectrum incident on cool, thin gas gives characteristic absorption spectrum

Summary, cont.

• Spectra can be explained using atomic models, with electrons occupying specific orbitals

• Emission and absorption lines result from transitions between orbitals

• Molecules can also emit and absorb radiation when making transitions between vibrational or rotational states

The Amazing Power of Starlight

Just by analyzing the light received from a star, astronomers can retrieve information about a star’s

1. Total energy output2. Surface temperature/color3. Radius4. Chemical composition5. Velocity relative to Earth6. Rotation period