Monday Feb 21 , 2011

Exam Keys for Exam 1 There were 2 versions of the first exam. They can be differentiated by the first 2 words on the exam- one version says "Print Name" the other says "print name".

If you wish, you can check the scantron machine by comparing the proper key with your answer sheet, a copy of which will be returned to you. If you suspect any problem with the scoring, bring your exam to me and we will look at the original answer sheet (which I keep). The scantron machine VERY RARELY goofs up, but it does happen, particularly if you make incomplete erasures or stray marks on the sheet.

Yakka Foob Mog. Sorry if my multiple- guess exams stifle your creativity!

Helium atom A representation of a helium atom. The inset shows the nucleus, consisting of 2 protons and 2 neutrons. The shaded region is the region over which the electrons orbit the nucleus. An Angstrom is a unit of distance, equal to 1 ten-billionth of a meter. A "fm" is a Fermi, a distance unit 100,000 times smaller than an Angstrom. Atoms are roughly an Angstrom or so in size, while atomic nuclei are roughly 1 Fermi in size.

Bohr model of atom The workings of atoms are described by a branch of physics called quantum mechanics. These 2 words strike fear into the hearts of even the nerdiest physics majors, so I won't tell you much about quantum mechanics. But we do need one of the key results of quantum mechanics: ELECTRONS IN ATOMS CAN ONLY EXIST IN CERTAIN DISCRETE ALLOWABLE ENERGY LEVELS. Think of a stepladder- you can stand on a step, but not between the steps. This "energy stepladder" in atoms is often depicted as a set of circular orbits of the electron around the nucleus. This is fine for thinking about the workings of an atom, but the actual motions of the electron are far more complicated.

To change steps, the atom must either gain energy from some external source (for electron to move "up") or lose energy (if electron goes down in energy). Electrons can gain or lose energy in two ways: collisions or radiation. In this diagram, an electron moves from the 3rd energy step to the second. As the 2nd step has less energy, the electron must get rid of energy in the move. (Energy is conserved, so you can't just say the energy "goes away"- it has to go somewhere or get turned into some other form.) In this instance, the energy is given off as a bit of EMR (a photon) represented by the red wavy line.

Periodic Table of the Elephants The type of atom is set by the number of protons in the nucleus. All 1 proton atoms are Hydrogen, all 2 proton atoms are Helium, all 6 proton atoms are Carbon, etc. There are 92 naturally occurring elements, and a dozen or so heavier ones that have been made artificially. The elements are usually arranged into a Periodic Table of the Elements, which is a way of grouping the elements to show their chemical and other physical properties.

This is a takeoff on the usual table, but the element abbrviations are correctly arranged. The pictures of elephants have something to do with the element. E.G. for Carbon (C, element 6) the elephant is having a cookout, using a charcoal grill (charcoal is made of carbon). I guess this is the kind of thing chemists do for laughs. (And you thought astronomers were weird!)

Three types of spectra. The three basic types of spectra can be illustrated with this system of a hot glowing solid body (think an incandescent light bulb) and a thin cooler cloud of gas. The triangular object marked "prism" represents a spectrograph, a device for spreading out the light from a source to see how much light there is at each wavelength.

If we look directly at the hot solid (top spectrum) we see a continuous spectrum- there are no sharp "bumps and wiggles" in the amount of light versus wavelength.

If we were to look at the hot solid by looking THROUGH the cooler gas cloud, the cooler gas would absorb or scatter some light at very specific wavelengths, rather than just dimming the light at all wavelengths. This happens because the atoms aborb light at those particular wavelengths. These wavelengths correspond to the amount of energy needed to excite one of the electrons in an atom to a higher energy level. This is called an absorption line (or dark line) spectrum. Further explanation is provided in Fig 6-5 of book.

If we look at just the cooler gas cloud (off to the side, so that we are not looking at the hot solid through the gas cloud), then we would see a spectrum that is mostly dark, but that has light concentrated at certain specific wavelengths. This is called an emission line (or bright line) spectrum.

Each atom (and molecule) has its own unique set of lines. Thus the spectral lines act as "fingerprints" for the elements. By seeing which lines are in the spectrum of an object out in space, we can learn something about the elemental composition of the body, without ever going there. Pretty amazing! But true!

Hydrogen emission spectrum

Iron emission spectrum Here are emission spctrum for two elements: hydrogen and iron. Hydrogen is the simplest elelemnt, as it has only 1 electron. Thus, it has a fairly simple spectrum. Iron has 26 electrons, and so it has a much richer spectrum, as there are more electrons to jump around.

The important point is that you could easily tell the elements apart just by looking at their spectra.

"Neon" sign "Neon" signs work due to the existence of permitted electron orbits in atoms and nicely illustrate the effects of collisional electron excitation and radiative deexcitation. (Huh?)

OK, so here is what is going on: the neon light is a clear glass tube filled with atoms of a gas of a particular element or mixture of elements. (Neon is only one of the elements used.) An electric current (moving electrons) is made to move though the gas. As the electrons collide with the gas atoms, some of the electrons in the atoms are moved to a higher enery level (excited by collisions= collisional excitation). Once the electrons are excited, some of them lose energy by emitting a photon (radiative de-excitation). A photon is just a small "chunk" of EMR which has a definite energy, and a definite wavelength, or color for visible light photons. Because the electrons can have only certain permitted energy levels, the photons can have only certain energies or colors. Our eyes see the different patterns of wavelengths from different elements as different colors.

The different colors of "neon" lights are due to use of different elements or combination of elements. The different colors are NOT due to different temperatures for this type of light.

Doppler shift. When a source of a wave (sound or electromagnetic radiation) is moving towards you, the waves are "bunched up" and the wave you detect has a shorter wavelength (higher frequency) than the emitted wave. If the source is moving away from you, the waves are "stretched out" and the wavelength is longer (frequency lower).

The bottom shows two spectra of the star Arcturus, taken at two different times. The absorption lines (the dark vertical lines) in the spectrum of Arcturus are slightly shifted between the two specta. This means the lines have different wavelengths, which is due to the motion of Arcturus in a binary star system, and the consequent Doppler shift of the light from Arcturus.

Temperature scales "Temperature" can be defined in several ways, but the most common is that temperature is a measure of how fast atoms and molecules are moving around. As the temperature goes down, the particles move slower. At some temperature, all motion would cease. This temperature is called absolute zero. Because absolute zero is a logical zeropoint, or starting place, for temperature, it would make sense to call absolute zero a temperature of, well, zero and start from there. That is what scientists do. The temperature scale starting at absolute zero is called the Kelvin scale.

The scales you are used to, Farenheit and Celsius, use different starting points, so they have negative temperatures. There are no negative temperatures in Kelvin.

Continuous spectrum of Sun. This is a graph of the spectrum of the overall energy distribution of sunlight around the visible wavelengths. A more detailed spectrum would show absorption lines, but these are a relatively minor effect on the overall spectrum (but are very important in studying the chemical makeup and other physical properties of stars!) The Sun has a surface temperature of about 5800 K (degrees kelvin) and peaks in the yellowish-green part of the spectrum.

Spectra of stars of different temperature. This graph shows the overall spectral energy distrubution of 3 blackbodies with temperatures of 4500, 6000 and 7500 degrees Kelvin. Also shown are the visible colors corresponding to wavelengths between about 400 and 700 nm, to which our eyes are sensitive. The cooler body has a wavelength of peak emission (lambda- max) at about 650 nm. Although it does emit some light of other colors, the body would look reddish to our eyes, as this is the color of peak emission. The 6000 K (Kelvin degree) blackbody would appear yellowish - the Sun has a surface temperature near this temperature. The hotter body peaks at 400nm, and so would appear bluish to our eye.

Spectrum of the filament in an ordinary incandescaent light bulb.. An ordinary (incandescent) light bulb produces light when a metal filament (made of the metal tungsten) is heated to about 2300 degrees Kelvin by passing an electric current though the filamant. The filament gives off blackbody radiation, with the maximum emission at a wavelength (lamda- max) of about 1250 nm. As seen in the graph, only a small fraction of the light's EMR is in the visible region of the spectrum, from about 400 to 700 nm, where our eyes are sensitive. Thus, most of the electrical energy is wasted, as it produces infrared radiation which can not be detected by the human eye. The infrared radiation is absorbed by the bulbs surroundings and turned into heat, which may be fine in the winter, but in the summer this wasted energy is doubly bad- you have to pay more for your airconditioning bill to get rid of the useless heat generated by the filament. If we could run the filament at a higher temperature, then the bulb would make a higher fraction of useful light, but then the filament would melt.

Because of the extreme wastefulness of the incandescent lamp, some countries are outlawing them. This is really *19th* century technology, that is, from the 1800s. Newer types of bulbs, such as fluorescent and LED, are much more efficient. They may cost more, but the new lamps last much longer and use MUCH less electricity to make same amount of useful EMR, so the new lamps cost less in the long run.

Continuous spectra of blackbodies of various temperatures Every solid or dense gaseous body radiates a continuous spectrum called a blackbody spectrum. The word "blackbody" is quite confusing- the Sun radiates a blackbody spectrum (with some minor absorption -or dark- line), but it sure isn't black! The wavelength of the peak of the emission depends on the surface temperature of the body. The hotter the body, the shorter the wavelength of the peak emission. The Sun, with a surface temperature of about 5700 Kelvin, radiates mostly visible light (visible EMR). A hotter star (an example of a 50000 Kelvin star is shown) would radiate mostly ultraviolet EMR. You and I, with a body temperature of 98.6 Farenheit (or 310 Kelvin) radiate or emit infrared EMR- yes, you and I *DO* glow in the dark- but only in infrared EMR, not visible EMR. Of course, our eyes are not sensitive to infrared EMR, which is why you can't see yourself glowing if you are in a dark room (one with no sources of visible EMR). In your normal everyday life, you see people and objects near room temperature only by visible light that is REFLECTED by the body- not EMITTED by the body. The visible light is usually from a hot body (Sun or lightbulb filament, but there are also "cool" things that emit visible light- such as LEDS - but these do not emit blackbody radiation, but a form of emission line spectrum).