READING Unit 22, Unit 23, Unit 24, Unit 25

Homework 4 Unit 19, problem 5, problem 7 Unit 20, problem 6, problem 9 Unit 21, problem 9 Unit 22, problem 7 Unit 23, problem 8 Unit 24, problem 6 Unit 25, problem 8

Emission If an atom drops from one orbital to the next lower one, it must first emit a photon with the same amount of energy as the orbital energy difference. This is called emission.

Seeing Spectra Seeing the Sun’s spectrum requires a few special tools, but it is not difficult –A narrow slit only lets a little light into the experiment –Either a grating or a prism splits the light into its component colors –If we look closely at the spectrum, we can see lines, corresponding to wavelengths of light that were absorbed.

Emission Spectra Imagine that we have a hot hydrogen gas. –Collisions among the hydrogen atoms cause electrons to jump up to higher orbitals, or energy levels –Collisions can also cause the electrons to jump back to lower levels, and emit a photon of energy hc/ –If the electron falls from orbital 3 to orbital 2, the emitted photon will have a wavelength of 656 nm –If the electron falls from orbital 3 to orbital 2, the emitted photon will have a wavelength of 486 nm We can monitor the gas, and count how many photons of each wavelength we see. If we graph this data, we’ll see an emission spectrum!

Wavelength The colors we see are determined by the wavelength of light. Wavelength is the distance between successive crests (or troughs) in an electromagnetic wave. This is very similar in concept to the distance between the crests in ocean waves! We denote the wavelength of light by the symbol. Wavelengths of visible light are very small! –Red light has a wavelength of 7  meters, or 700 nanometers (nm) –Violet light has a wavelength of 4  meters, or 400 nm –Colors in between red and violet (remember ROY G BIV?) have intermediate wavelengths

Frequency Sometimes it is more convenient to talk about light in terms of frequency, or how fast successive crests pass by a given point You can think of frequency as a measure of how fast you bob up and down as the waves pass. Frequency has units of Hz (Hertz), and is denoted by the symbol Long wavelength light has a low frequency, and short wavelength light has a high frequency Frequency and wavelength are related by: ‘c’ is the speed of light.

White Light Light from the Sun arrives with all wavelengths, and we perceive this mixture of colors as white Newton demonstrated that white light could be split into its component colors with a prism, and then recombined into white light with a lens

Measuring Temperature It is useful to think of temperature in a slightly different way than we are accustomed to –Temperature is a measure of the motion of atoms in an object –Objects with low temperatures have atoms that are not moving much –Objects with high temperatures have atoms that are moving around very rapidly The Kelvin temperature scale was designed to reflect this –0  K is absolute zero –the atoms in an object are not moving at all!

Emission spectrum of hydrogen This spectrum is unique to hydrogen –Like a barcode! If we were looking at a hot cloud of interstellar gas in space, and saw these lines, we would know the cloud was made of hydrogen!

Different atom, different spectrum! Every element has its own spectrum. Note the differences between hydrogen and helium spectra below.

Absorption Spectra What if, instead of hot hydrogen gas, we had a cloud of cool hydrogen gas between us and a star? –Photons of an energy that corresponds to the electronics transitions in hydrogen will be absorbed by electrons in the gas –The light from those photons is effectively removed from the spectrum –The spectrum will have dark lines where the missing light would be –This is an absorption spectrum! –Also like a barcode!

Types of Spectra Kirchoff’s Laws: –If the source emits light that is continuous, and all colors are present, we say that this is a continuous spectrum. –If the molecules in the gas are well- separated and moving rapidly (have a high temperature), the atoms will emit characteristic frequencies of light. This is an emission-line spectrum. –If the molecules of gas are well- separated, but cool, they will absorb light of a characteristic frequency as it passes through. This is an absorption line spectrum.

Spectra of Astronomical Objects

Results of More Collisions Additional collisions mean that more photons are emitted, so the object gets brighter Additional hard collisions means that more photons of higher energy are emitted, so the object appears to shift in color from red, to orange, to yellow, and so on. Of course we have a Law to describe this…

Wien’s Law and the Stefan-Boltzmann Law Wien’s Law: –Hotter bodies emit more strongly at shorter wavelengths SB Law: –The luminosity of a hot body rises rapidly with temperature

Taking the Temperature of Astronomical Objects Wien’s Law lets us estimate the temperatures of stars easily and fairly accurately We just need to measure the wavelength ( max ) at which the star emits the most photons Then,

The Stefan-Boltzmann Law If we know an object’s temperature (T), we can calculate how much energy the object is emitting using the SB law  is the Stefan-Boltzmann constant, and is equal to 5.67  Watts/m 2 /K 4 The Sun puts out 64 million watts per square meter – lots of energy!

Doppler Shift in Light If an object is emitting light and is moving directly toward you, the light you see will be shifted to slightly shorter wavelengths – toward the blue end of the spectrum, or blue-shifted Likewise, if the object is moving away from you, the light will be red-shifted. If we detect a wavelength shift of  away from the expected wavelength, the radial (line-of- sight) velocity of the object is:

As a blackbody object becomes hotter, it also becomes ____________ and _____________ a. more luminous, redder b. more luminous, bluer c. less luminous, redder d. less luminous, bluer

Compare two blackbody objects, one at 200K and one at 400K. How much larger is the flux from the 400K object, compared to the flux from the 200K object? a. Twice as much b. Four times as much c. Eight times as much d. Sixteen times as much

Star A and star B appear equally bright in the sky. Star A is twice as far away from Earth as star B. How do the luminosities of stars A and B compare? a. Star A is 4 times as luminous as star B b. Star A is 2 times as luminous as star B c. Star B is 2 times as luminous as star A d. Star B is 4 times as luminous as star A

a. The luminosity of the Sun b. The distance from the planet from the Sun c. The color of the planet d. The size of the planet Which of the following factors does *not* directly influence the temperature of a planet?