Chapter 7 Atoms and Spectra

Introduction Modern astrophysics links physics experiments and theory to astronomical observations We can learn about objects using the rich information derived from their spectra to uncover the secrets of their internal structures and histories

7-1 Atoms Consist of a compact atomic nucleus (protons and neutrons) and a cloud of electrons surrounding it Figure 7-2 Magnifying a hydrogen atom by 10^12 makes the nucleus the size of a grape seed and the diameter of the electron cloud more than 2.6 times larger than the length of a U.S. football field.

Atomic Nucleus Size: If the H atom was magnified by 1012: Atom ~2.5 times the length of a football field Nucleus would be the size of a grape seed Density: One teaspoon of atomic nucleus matter: Would weigh ~2 billion tons

Different Kinds of Atoms The number of protons in the nucleus determines which element it is: For example, carbon has 6 protons while nitrogen has 7 The number of neutrons in the nucleus is less restricted, resulting in isotopes: Carbon-12 has 6 protons + 6 neutrons = lighter Carbon-13 has 6 protons + 7 neutrons = heavier The number of electrons in the electron cloud can vary because electrons can be gained or removed, resulting in ions. Periodic Table

Electron Orbits Electron orbits in the electron cloud are restricted to very specific radii and energies, different for each element Figure 7-3 An electron in an atom may occupy only certain permitted orbits. Because each element has a different number of protons and therefore a different electrical charge in the nucleus attracting the electrons, each element has a different, unique pattern of permitted orbits.

How Do We Know? 7-1 Quantum mechanics Set of rules that describe how atoms and subatomic particles behave Quantum mechanical uncertainty: You cannot know simultaneously the exact location and the exact motion of a particle Because of the huge numbers of atoms in interactions, this averages out Quantum mechanics model: e- = clouds of negative charge surrounding the nucleus

7-2 Interactions of Light and Matter An electron can be kicked into a higher orbit when it absorbs a photon with exactly the right energy Figure 7-4 A hydrogen atom can absorb only those photons that have the right energy to move the atom’s electron to one of the higher-energy orbits. Here three photons with different wavelengths are shown along with the changes they each would produce in the electron’s orbit if they were absorbed.

An Absorption Spectrum Each feature is due to the presence of particular element and an electron transitioning from a lower to higher energy Figure 7-4 A hydrogen atom can absorb only those photons that have the right energy to move the atom’s electron to one of the higher-energy orbits. Here three photons with different wavelengths are shown along with the changes they each would produce in the electron’s orbit if they were absorbed.

Interactions of Light and Matter (cont'd.) The photon is absorbed, and the electron is in an excited state All other photons pass by the atom unabsorbed Figure 7-5 An atom can absorb a photon only if the photon has the correct amount of energy. The excited atom is unstable and within a fraction of a second returns to a lower energy level, radiating new photons in random directions relative to the original photon’s direction.

Color and Temperature Stars appear in different colors These colors tell us about the star’s temperature Figure 7-6 Graphs of blackbody radiation intensity versus wavelength for three objects at temperatures of 7000 K, 6000 K, and 5000 K, respectively ( top to bottom ). Comparison of the graphs demonstrates that a hot object radiates more total energy per unit area than a cooler object (Stefan- Boltzmann law) and that the wavelength of maximum intensity is shorter for hotter objects than for cooler objects (Wien’s law). The hotter object here would look blue to your eyes, whereas the cooler object would look red.

Blackbody Radiation The light from a star is usually concentrated in a rather narrow range of wavelengths The spectrum of a star’s light is approximately a thermal spectrum called a black body spectrum A perfect black body emitter would not reflect any radiation, thus the name “black body”

Two Laws of Blackbody Radiation The Stefan-Boltzmann law: The hotter an object is, the more energy it emits where E = Energy Flux = Energy given off in the form of radiation, per unit time and per unit surface area [J/s/m2] s = Stefan-Boltzmann constant E = s*T4

Two Laws of Blackbody Radiation (cont'd.) Wien’s Law: The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases lmax ≈ 3,000,000 nm / T where T is the temperature in Kelvin

7-3 Understanding Spectra Photons are emitted/absorbed when an electron makes a transition from one energy level to another Wavelength depends upon the energy difference between the two levels Each spectral line represents an electron transition between two energy levels Each element has a unique set of spectral lines that can be used to identify its presence

Kirchhoff’s Laws of Radiation (1) A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum To understand how to analyze a spectrum, begin with a simple incandescent lightbulb. The hot filament emits blackbody radiation, which forms a continuous spectrum.

Kirchhoff’s Laws of Radiation (2) A low-density gas excited to emit light will do so at specific wavelengths and thus produce an emission spectrum An emission spectrum is produced by photons emitted by an excited gas. You could see emission lines by turning your telescope aside so that photons from the bright bulb do not enter the telescope and the excited gas has a dark background. The photons you would see would be those emitted by the excited atoms near the bulb, and the observed spectrum is mostly dark with a few bright emission lines. Such spectra are also called bright-line spectra.

Kirchhoff’s Laws of Radiation (3) If light comprising a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum An absorption spectrum results when radiation passes through a cool gas. In this case you can imagine that the lightbulb is surrounded by a cool cloud of gas. Atoms in the gas absorb photons of certain wavelengths that are then missing from the observed spectrum, and you see dark absorption lines at those wavelengths. Such absorption spectra are also called dark-line spectra.

The Doppler Effect Sound waves always travel at the speed of sound – just like light always travels at the speed of light, independent of the speed of the source of sound or light: Dl/l0 = vr/c Figure 7-8 The Doppler effect. (a) The sound waves (black circles) emitted from a siren on an approaching truck will be received more often, and thus be heard with a higher pitch, than the sound waves from a stationary truck. The siren will have a lower pitch if it is going away from the observer. (b) A moving source of light emits waves that move outward (black circles). An observer toward whom the light source is moving observes a shorter wavelength (a blueshift ); an observer for whom the light source is moving away observes a longer wavelength (a redshift).

The Doppler Effect (cont’d.) Figure 7-8 c) Absorption lines in the spectrum of the bright star Arcturus are blueshifted in winter, when Earth’s orbital motion carries it toward the star, and redshifted in summer when Earth moves away from the star.

The Doppler Effect (cont’d.) The Doppler effect allows us to measure the component of the source’s velocity along our line of sight The relation between the line of sight speed and the wavelength shift is Δλ/λ = v/c Figure 7-9 (a) Police radar can measure only the radial part of your velocity (V^r) as you drive down the highway, not your true velocity along the pavement ( V ). That is why police using radar should never park far from the highway. This police car is actually poorly placed to make a good measurement. (b) From Earth, astronomers can use the Doppler effect to measure the radial velocity (V^r) of a star, but that is less than its true total velocity, V, through space.

The Doppler Effect (cont'd.) Take l0 of the Ha (Balmer alpha) line: l0 = 656 nm Assume, we observe a star’s spectrum with the Ha line at l = 658 nm. Then, Dl = 2 nm We find Dl/l0 = 0.003 = 3*10-3 Thus, vr/c = 0.003 or vr = 0.003*300,000 km/s = 900 km/s The line is red shifted, so the star is receding from us with a radial velocity of 900 km/s

Discussion Questions Why do different atoms have different lines in their spectra? Hint: See Figure 7-3. What affect might tighter orbits have? What about more orbits? Why does the amount of blackbody radiation emitted depend on the temperature of the object? Hint: What happens to the vibration of molecules (aka frequency) as you raise the temperature of an object?

Discussion Questions (cont’d.) If all the lights are turned off in a room and there is no ambient light in the room, do you or your neighbor standing nearby emit any light? If so, can you see that light with your eyes? If not, why not? Hint: Human body temperature is 310K (absolute zero = 0K)

Problem If a star has a surface temperature of 20,000 K, at what wavelength will it radiate the most energy? Is this a cool or hot star? Use Wiens Law: Wavelength = 3(10^6) / T nm  Wavelength = 150 nm This wavelength is in the ultraviolet Star is pretty hot. If it has the same radius as the Sun what is its energy output in terms of the Sun? Stefan Boltzman Law: E = σT^4 Energy Ratio = Ehot / Esun = (20000/5744)^4 = 147