(a) What is the wavelength of the waves? That is, what do you think is the distance separating the crest of one wave from the crest of the next wave? I'd guess something between 2 and 10 meters - let's take 5 meters.

(b) What is the frequency of the waves? (Hint: use the formula: wave frequency = 1/wave period. If a wave comes once a minute, wave period is 1 minute; if a wave comes once an hour, wave period is 1 hour.) I would guess that ocean surf comes in at about 1 wave per second - perhaps a little less.

(c) Figure out how fast the waves must be traveling. (Calculate v.) Speed = wavelength x frequency = 5 meters x 1 per second = 5 meters per second.

(2) The speed of light is 3.00 x 10⁸ m/sec = 3 x 10⁵ km/sec. What is the speed of light in miles/hour? 3 x 10⁵ km/sec x 60 x 60 = 1 x 10⁹ km/hr ~ 6 x 10⁸ mph

(3) The figure above shows the visible part of the electromagnetic spectrum--the rainbow of colors that is produced when white light is spread out according to wavelength.

(a) Which has a longer wavelength, blue or red light? Red

(b) Note the units--nanometers (nm)--i.e. 10^-9 meter. Green light has a wavelength of 500 nm. How many wavelengths of green light are there in a meter? 1 meter / (500 x 10^-9 meter) = 2 x 10⁶= 2,000,000

(4) This next figure (above) shows the electromagnetic spectrum from gamma rays to radio. Note that the range of wavelengths covers ten factors of 10, from 10^-14 meter to 10⁴ meters (or 10 km).

(a) Infrared radiation is the energy you feel from a fire. The wavlength of infrared light is about 1 "micro-meter" = 1 micron. How many infrared wavelengths are there in a meter? 1 meter / (1 x 10^-6 meter) = 1 x 10⁶ = 1,000,000

(b) Microwave radiation is easily absorbed by water and allows us to heat up food quickly. How many microwave wavelengths, each 1mm long, are there in a meter? 1 meter / (1 x 10^-3 meter) = 1,000

(5)(a) Convert the typical Earth temperature to Fahrenheit and Centigrade degrees. 300K = 27C ~ 80F

Is the 273° difference between Centigrade and Kelvin significant when we are talking about

(b) temperatures of planets? Yes - since planets are around 300 Kelvin or 0 Centigrade (or Celsius).
(c) temperatures of stars? No, since the temperature of stars is thousands to 10s of thousands of degrees - we rarely can measure temperatures of stars with enough accuracy that the 273 is worth worrying about.

(6) The figure below shows the spectrum of sunlight (the thermal emission from the Sun), as well as that from other kinds of astronomical objects. Comparing this to the last example above, find at what wavelength is the maximum intensity of sunlight? Give both the color and value of the wavelength. The wavelength of maximum intensity of sunlight is in the visible part of the spectrum - around the yellow - at 480 nm.

(7) Look again at the figure in the last Exercise. To see light from stars like the Sun (and any object that has a temperature of about 6000 K--such as the filament of a light bulb) we can use our eyes or a camera. To observe objects that emit thermal emission at wavelengths that are not visible to the eye, we require special detectors. To detect thermal emission from (a) hot stars and (b) cool stars or planets, we need detectors that are sensitive to what regions of the electromagnetic spectrum? (a) from the figure it looks like we would need detectors sensitive at shorter wavelengths than for the sun - so in the ultraviolet region - to see hot stars. (b) For cool stars we need a detector sensitive to longer wavelengths - red to infrared.

(8) Here is an example of how to use this equation: A hot star looks bluish, with a wavelength of maximum emission of 290 nm. Let us calculate the star's temperature -

(a) Re-arrange the equation with Temperature on the left side.

T_Kelvin = 2,900,000 / _max

(b) Now, evaluate the temperature of this bluish star. T= 2.9 x 10⁶ / 290 = 1 x 10⁴ = 10,000 Kelvin

(9) What happens to the wavelength of maximum thermal emission when an object is cooled down towards absolute zero? The wavelength of maximum emission becomes VERY long - longer than radio - with VERY low energy per photon.

(10) Look again the example plots, above. How does the Intensity of thermal radiation vary as the temperature increases? Does it increase or decrease? Does the intensity change a large or small amount when the temperature increases (look at the numbers on the intensity scales on the left of the graphs)? The intensity INCREASES as the temperature increases (makes sense!). The intensity increases rapidly as the temperature is increased.

(11) The surface of Jupiter's moon Ganymede is at a temperature of about 120 Kelvin. The surface of Pluto is at at temperature of about 40 Kelvin. So Ganymede's temperature is 3 times Pluto's. How many times more thermal energy is emitted from Ganymede's surface than Pluto's? Ganymede is 3 times hotter than Pluto so that the surface of Ganymede emits 3⁴ = 3x3x3x3 = 9x9 = 81 times more energy per unit area than Pluto's surface.

(12a) Mars is 1.5 times further from the Sun than the Earth. How many times dimmer will the Sun appear to someone at Mars's distance? Since the flux of sunlight decreases as the square of the distance, Mars will receive 1.5² = 2.25 times less sunlight per unit than Earth - the Sun will appear 2.25 times dimmer from Mars.

(b) Jupiter is 5.2 times the distance of the Earth from the Sun. How much dimmer will the Sun appear to a Jovian being? From Jupiter the Sun will appear to be 5.2² = 27 times weaker than from Earth.

(c) What about to someone at Pluto (about 40 times farther away than Earth from the Sun)? From Pluto the Sun will be 40² = 1600 times fainter than from Earth.

(13) Distinguish between the following:

(a) Atoms vs. molecules - Atoms are single - molecules contain multiple atoms.

(b) Atom vs. nucleus The nucleus is at the center of the atom (and contains only protons and neutrons) - surrounded by electrons.

(c) Electron vs. element - Electrons surround the nucleus of an atom - or can float around on their own. An element is the same as an atom - or a collection of atoms of the same kind - such as copper or hydrogen or oxygen.

(d) Proton vs. photon - Protons are subatomic particles - positively charged, and having mass. Photons are light particles - they do not have any mass.

(14)Do all atoms look alike? Do all atoms of hydrogen or of iron look alike? Not all atoms look alike - all atoms of hydrogen or of iron look alike - but different from atoms of nitrogen or carbon, etc.

(15) Thermal spectra Sketch the spectrum from a regular light bulb where the light is emitted by running electricity through a small wire and heating the wire to temperatures of about 5700 Kelvin. Label the Wavelength axis with appropriate units. What is the wavelength of maximum emission _max? The spectrum will be a single "hump", like the Thermal Emission Spectrum above - with a peak at a wavelength of about 500 nm - just like the Sun.

(16a) Which photons have greater energy, x-ray photons or visible photons? (Hint: look at at the figure of the electromagnetic spectrum above) X-ray photons.

(b) Which photons have greater energy, infrared photons or radio photons? Infrared photons have shorter wavelengths and more energy than radio photons.

(17) Emission spectra

(a) How can an atom become excited? They can be excited by being hit by either electrons or photons.

(b) Look at the emission spectrum of atomic hydrogen. Which of these emission lines correspond to photons of highest energy? The ones farthest in the blue region of the spectrum.

(c) Which of these lines is produced when an electron makes the biggest drop in energy? The blue emission lines correspond to photons of the highest energy - produced when an atom's electrons drop the greatest energy.

(18) Absorption spectra

(a) Absorption lines occur when an atom "absorbs" a photon. Where does the photon's energy go? The energy is given to an electron within the atom.

(b) Compare the wavelengths of the absorption lines in the absorption spectrum of hydrogen to the wavelengths of the emission lines of hydrogen in the emission spectrum. The absorption and emission lines are at the same wavelengths.

(19) Below are two cases where you might expect to see spectral signatures of hydrogen. Which would produce an emission spectrum and which would produce an absorption spectrum (look in your book for example pictures)? Figure 7.13 in the book shows that emission from a hot gas produces emission lines (the upper diagram in the hand-drawn figure below). The light passing through the atmosphere of a star will show absorption lines - where the atmospheric gases absorb the light coming from the star.

(20) At the surface of the Sun the temperature is about 5700 Kelvin. On its way to us at Earth, the sunlight passes through the Sun's atmosphere which is mostly hydrogen. Sketch the spectrum from the Sun--how does the Sun's spectrum differ from the spectrum of a light bulb? Shape? Location of _max? Line absorption features? The spectrum from the Sun will look exactly like that of a light bulb - in shape, location of _max - but there will also be absorption lines due to absorption of sunlight by the Sun's atmosphere.

(21) Sodium is a relatively common element in the universe and the spectral signature of sodium is a useful diagnostic of the properties of stars and planets. Why do you think astronomers talk about sodium street lights being a major source of "light pollution?" Because it is sometimes difficult to separate the emission from sodium street lights from the emissions from sodium atoms in stars or planet. The street light sodium light is a source of interference for astronomy.

(22a) What does the location of _max tell us about the star? It tells us the star's temperature - using Wein's law.

(b) What do the absorption lines tell us about the star's atmosphere? They tell us about the composition of the star's atmosphere.

(23a) In what regions of the electromagnetic spectrum are these two components? The reflected sunlight is visible light. The thermal emission from the planet is in the infrared part of the spectrum.

(23b) Furthermore, each component can have absorption lines or broad absorption bands. What do these absorption features tell us about the planet? They tell us about the composition of the planet's surface or atmosphere.

(23c) Thinking first about the thermal radiation emitted by the planet, if the planet's atmosphere contains molecules (rather than single atoms), what kind of absorption features would you expect to see in the thermal component of a planet's spectrum? (Hint: Look at the figure of emission spectra above). Figure 7.14 gives a clue too - molecules tend to produce multiple absorption features (because molecules are more complicated than single atoms).

(23d) Next, think about the sunlight hitting the planet. The sun is a star with an absorbing atmosphere of hydrogen with small quantities of metal atoms (like calcium, magnesium, iron). What kind of absorption features would you expect to see in the incident sunlight hitting the planet? The sunlight hitting the planet will have absorption features at the wavelengths corresponding to the composition of the Sun - hydrogen and metals.

(23e) Finally, think about the reflected sunlight component. There will be additional absorption features in the spectrum of the reflected sunlight. What kind of features do you expect if the planet

(i) has a solid, icy surface (highly reflective - white) with little atmosphere (say like Europa)? Solids produce very broad absorption features rather than narrow "notches".

(ii) has a thick atmosphere of molecular gases? Molecular gases in the atmosphere will produce multiple absorptions - in bands. See Figure 7.14.

(b) Ozone and carbon monoxide are minor constituents of our atmosphere but notice the deep absorption features they carve out of the spectrum. This is how we monitor carbon dioxide and other anthropogenic (=human made) gases (i.e. pollutants). These molecules are absorbing the infrared radiation that is trying to escape the planet--what is going to happen to the atmosphere as a result of this absorption? Is the atmosphere going to get warmer or cooler? If an atmosphere is absorbing energy, then it will get hotter.

(25) This O₃ absorption feature is at what part of the spectrum? Why is this absorption feature extremely important for humans? Absorption by ozone in the ultraviolet part of the spectrum is important for protecting humans from the health hazard of exposure to UV - a major cause of skin cancer.