21.April.98 class:

• Facilitators: Rich, Charlie, Cayli, Sasha
• two students' BRIEF summaries of the section
• questions on each section
• discuss each section... new applications/ connections?

Ch.4, THE ORIGIN AND NATURE OF LIGHT

Blackbody Radiation

4-1 Peak color shifts to shorter wavelengths as an object is heated. Stefan-Boltzmann law: Intensity = s T⁴ (Watts/m²) where s=sigma = 5.67 x10^-8 (J/m².K⁴.s). Wien's law: TL=constant. Ex: If temp doubles, intensity increases by 16, wavelength drops by half, and energy doubles (E~kT). Blackbody shape derived by Planck; peak shifts bluer = hotter.

4-2 The color of electromagnetic radiation reveals an object's temperature. Sun peaks at blue-green but looks yellow because

• longer wavelengths scatter more, making sky appear blue
• eye is most sensitive to yellow-green (and green scatters out more than yellow)

4-3 Discovering Spectra Each chemical element produces its own unique set of spectral lines.

1860 blue line in mineral water -> cesium

1861 red line in minerals -> rubidium

1868 new line in soar corona (during eclipse) -> helium. Also decay product in radioactivity (alpha)

"Because each chemical element produces its own unique pattern of spectral lines, scientists can determine the chemical composition of a remote astronomical object by identifying the spectral lines in its spectrum.

4-4 The brightness of spectral lines depends on conditions in the spectrum's source. Kirchhoff's laws (you'll discover these for yourself in workshop on Thursday):

• hot dense gas or solid: blackbody spectrum
• hot rare gas: emission lines
• cool rare gas in front of emitter: absorption liens

Atoms and Spectra

4-5 An atom consists of a small, dense nucleus surrounded by electrons. Bohr model for H: proton = nucleus, electron orbits with quantized angular momentum. Like the Sistine chapel with BB in the middle of the dome.

4-6 Spectral lines occur when an electron jumps from one energy level to another. Hydrogen transitions to n=2 are visible Balmer lines.

4-7 A spectral line is shifted by the relative motion between the source and the observer. Doppler effect: blue = toward, red = away. Hubble law : redder galaxies are further away and moving faster away: universe is expanding.

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Discussion Question: 18 (p.96)

Suppose you look up at the night sky and observe some of the brightest stars with your naked eye. Is there any way of telling which stars are hot and which are cool? Explain.

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Deriving Wien's Law

Recall from Ch.3 last week that shorter-wavelength (L) light has more energy: E=hc/L, where Planck's constant h=6.63 x 10^-34 kg.m²/s and c=3 x 10⁸ m/s.

Wien's law describes how hot bodies radiate energy. In general, E=akT where T=Temperature (in Kelvin) and the Boltzmann constant k=1.38x10^-23 J/K. (Energy has units of Joules = Newton.meter = kg.m²/s², or electron volts: eV=1.602x10^-19 J). The wavelength at which the blackbody radiation spectrum peaks corresponds to a proportionality constant of about a~5.

You can put these two relationships together to find out that hot objects radiate primarily shorter-wavelength light:

hc/L = akT yields LT = hc/ak ~ 3 x 10^-3 m.K, which is Wien's law for the peak wavelength in the spectrum of a blackbody of temperature T.

Example: What wavelength of light emits the most energy from an A-star with a temperature of 10,000 K? What color will the star appear?

L=(hc/ak) / T ~ (3 x 10^-3 m.K) / 10⁴ K = 3 x 10^-7 m ~ 300 nm. From the EM spectrum on p.55, we see that the spectrum peaks in ultraviolet light, so the star will look bluish or white (there's much more energy radiated by blue than by red light in this star).

Derving Bohr's energy levels for H atom: quantized angular momentum L=n*hbar = nh/2*Pi = mvR, F=kgQ/R2 yields R~ (n/e)², and E=U/2 yields E~e⁴/n²

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Maintained by E.J. Zita