## 20120713

### Presentation: Kirchhoff's laws

Personally, not a great fan of The Big Bang Theory (Warner Bros. Television, 2007), but the show has its moments.
Patty: "Oh, hi!"
Leonard: "Hi."
Sheldon: "Hello."
Patty: "So, what are you supposed to be?"
Sheldon: "Me?" (Beat.) "I'll give you a hint. Neeeeooooowwwww!"
Okay, I give up. What is Sheldon supposed to be?

We'll be going over Kirchhoff's laws (note two h's and two f's in "Kirchhoff"), applying them to distinguish between three different types of spectra, and also analyzing the motions of stars by looking at their "neeeeooooowwwww."

Consider this beam of sunlight, passing through the corner of a glass door, which splits different wavelengths apart into a rainbow of colors. But if you were to look very closely, there would be an assortment of very tiny dark lines in this rainbow.

And every star and other source of light, when split up into a rainbow, will show different dark or light lines. So in astronomy, we are literally "tasting the rainbow," from which we can find out all sorts of information.

These dark or light lines in the spectrum of a star are like the bar codes on different products. Each bar code is unique, and if you completely understand the bar code system, you can readily tell what product it corresponds to just by looking at it.

First, distinguishing between three different types of spectra.

A continuous spectrum, or a rainbow spectrum is where light is split apart into different wavelengths, and no colors are missing--a complete, unbroken rainbow of colors, or all wavelengths are approximately equal when plotted on a intensity versus wavelength graph.

An emission spectrum, or a bright-line spectrum is where light is split apart into different wavelengths, and only certain colors are present as bright lines, seen as humps or spikes when plotted on an intensity versus wavelength graph.

An absorption spectrum, or a dark-line spectrum is where light is split apart into different wavelengths, and certain colors are missing from an overall rainbow as dark lines, seen as valleys and dips when plotted on an intensity versus wavelength graph.

Second, distinguishing between three different types of sources of light. Kirchhoff's laws are the connections between these three different sources and spectra, which we'll practice in a picto-quiz.

A light bulb filament that is hot enough to glow will give off blackbody radiation (something we'll cover in more detail in a later presentation), which when split apart into different wavelengths will produce a __________ spectrum.

Gas atoms whose electrons are excited to jump up, then jump back down to give off certain photons (as discussed in a previous presentation), which when split apart into different wavelengths will produce a __________ spectrum.

Stars turn out to be the most complicated source. The inner part of the star is hot and dense, much like a light bulb, while the outer layers of the star are cooler and diffuse. It is in these outer layers that atoms have electrons that absorb certain photons (and re-emit them in different directions). The result is that you start with the rainbow of a continuous spectrum, and then certain wavelengths are missing, producing a __________ spectrum.

Let's start the picto-quiz, where you'll look at different sources of light, and identify the type of spectrum it will produce (and describe the characteristics of the spectrum, as well).

Hot, molten metal produces a [continuous/emission/absorption] spectrum, which appears as a [rainbow/series of bright lines/dark lines on a rainbow background].

The sun produces a __________ spectrum, which appears as a __________.

The lights atop the Fremont Theater in San Luis Obispo, CA, produces a __________ spectrum, which appears as a __________.

Your instructor produces a __________ spectrum, which appears as a __________. (The temperature of your instructor is not this hot--probably a miscalibrated infrared monitor is to blame--but note the cool goatee.)

Here's a question for all you fanboys and fangirls out there--who do you think is the "hottest" character from The Lord of the Rings?

Maybe Aragorn (Viggo Mortensen), or Legolas (Orlando Bloom)? Or Frodo (Elijah Wood)? What about Gandalf (Ian McKellen)? Or characters not pictured here, such as Arwen (Liv Tyler) or Eowyn (Miranda Otto)?

But for me, personally, the hottest character from The Lord of the Rings would have to be...the balrog. Now that is hot. But wait--the balrog produces a __________ spectrum, which appears as a __________.

Third, the Doppler effect.

Student: "Alright. We're uh, we're going to come up this road...when I hit the speed that I'm shooting for, I'm going to light on the horn, and you can, uh, hear what the effect is. Here's the frequency of the horn..."
(Presses on horn.)
Student: "Alright?"

(Car passes by student, horn sound is changed by Doppler effect: "neeeeooooowwwww!") (Video link: "Doppler Effect.")

Let's draw a picture to represent the sound waves from a stationary car. Note that the wavelengths are the same in either direction.

However, if the car is moving from left-to-right, the sound waves from the car as it heads towards an observer are "squished," and are perceived as having a higher pitch than a stationary car horn. When the car passes by, and is moving away from an observer, the sound waves are "stretched," and are perceived as having a lower pitch than a stationary car horn. This is the "neeeeooooowwwww!" from the The Big Bang Theory clip earlier in this presentation.

In astronomy we know what an absorption (dark-line) spectrum looks like from a stationary star. However, if a star is moving towards us, or away from us, then the light waves are going to be "scrunched" or "stretched" from their usual wavelength values.

Here, arrows denote the expected absorption line wavelength values for a stationary star. For a star that is moving towards us, the light gets "squished," such that each absorption line has slightly shorter wavelengths than expected, moving towards the left side of the spectrum--this is a "blueshift," but this effect is very subtle, and does not mean the lines all move entirely over to the blue end of the spectrum!

For a star that is moving away from us, the light gets "stretched," such that each absorption line has slightly longer wavelengths than expected, moving towards the right side of the spectrum--this is a "redshift," but this effect is very subtle, and does not mean the lines all move entirely over to the red end of the spectrum!

In the subsequent in-class activity you will be working in groups to analyze emission and absorption spectra, and the Doppler effect. (Continuous spectra from blackbodies will be covered in a later in-class activity.)