Lecture 13 - Electromagnetic radiation Pt. 2

Here are some rules governing the emission of electromagnetic radiation:

Unless an object is very cold (0 K) it will emit EM radiation. Everything in a classroom: the people, the furniture, the walls and the floor, even the air, are emitting EM radiation. Often this radiation will be invisible so that we can't see it and weak enough that we can't feel it. Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature.

The second rule allows you to determine the amount of EM radiation (radiant energy) an object will emit. Don't worry about the units, you can think of this as amount, or rate, or intensity (it is actually energy per unit area per unit of time, calories per square centimeter per minute for example). Don't worry about σ either, it is just a constant. The amount depends on temperature to the fourth power. If the temperature of an object doubles the amount of energy emitted will increase by a factor of 2 to the 4th power (that's 2 x 2 x 2 x 2 = 16). A hot object just doesn't emit a little more energy than a cold object it emits a lot more energy than a cold object. This is illustrated in the following figure:

The third rule tells you something about the kind of radiation emitted by an object. We will see that objects usually emit radiation at many different wavelengths. There is one wavelength however at which the object emits more energy than at any other wavelength. This is called lambda max (lambda is the greek character used to represent wavelength) and is called the wavelength of maximum emission. The third rule allows you to calculate "lambda max." This is illustrated below:

The following graphs also help to illustrate Stefan-Boltzmann's law and Wien's law.

Notice first that both the warm and the cold objects emit radiation over a range of wavelengths (the curves above are like quiz scores, not everyone gets the same score, there is a distribution of grades)

Lambda max has shifted toward shorter wavelengths for the warmer object (red). This is Wien's law in action. The warmer object is emitting a lot of short wavelength radiation that the colder object (blue) doesn't emit.

The area under the warm object curve is much bigger than the area under the cold object curve. The area under the curve is a measure of the total radiant energy emitted by the object. This illustrates the fact that the warmer object emits a lot more radiant energy than the colder object.

In the classroom version of this course, a 200 W tungsten bulb connected to a dimmer switch is used to demonstrate these rules We look at the EM radiation emitted by the bulb filament.

The three graphs below show the EM radiation emitted (both wavelength and intensity) for the 3 switch settings in the figure above.

We start with the bulb turned off (switch Setting 0). The filament will be at room temperature which we will assume is around 300 K (remember that is a reasonable and easy to remember value for the average temperature of the earth's surface). The bulb will be emitting radiation, it's shown on the top graph above. The radiation is very weak so we can't feel it. It is also long wavelength, far IR, radiation that we can't see. The wavelength of peak emission is 10 micrometers.

Next we turn the dimmer switch to switch Setting 1 where the bulb's filament just begins to glow (the temperature of the filament is now about 900 K). The bulb wasn't very bright at all and had an orange color. This is curve 1, the middle figure. Note the far left end of the emission curve has moved left of the 0.7 micrometer mark and into the visible portion of the spectrum. That is glow from the filament that we are able to see, just the small fraction of the radiation emitted by the bulb that is visible light (but just long wavelength red and orange light). Most of the radiation emitted by the bulb is to the right of the 0.7 micrometer mark and is invisible IR radiation (it is strong enough now that you could feel it if you put your hand next to the bulb).

Finally we turn on the bulb completely (it was a 200 Watt bulb so it got pretty bright). The filament temperature is now about 3000 K. The bulb is emitting a lot more visible light, all the colors, though not all in equal amounts. The mixture of the colors produces a "warm white" light. It is warm because it is a mixture that contains a lot more red, orange, and yellow than blue, green, and violet light. It is interesting that most of the radiation emitted by the bulb is still in the IR portion of the spectrum (lambda max is 1 micrometer). This is invisible light. A tungsten bulb like this is not especially efficient source of visible light; more than half the light emitted by the bulb is at IR wavelengths and is invisible.

Diffraction gratings are handed out during this demonstration. The students can use the diffraction gratings to separate the white light produced by the bulb into its separate colors. When you look at the bright white bulb filament through one of the diffraction gratings the colors are smeared out to the right and left as shown below.

The sun emits electromagnetic radiation. That shouldn't come as a surprise since you can see it and feel it. The earth also emits electromagnetic radiation. It is much weaker and invisible. The kind and amount of EM radiation emitted by the earth and sun depend on their respective temperatures.

The curve on the left is for the sun. We first used Wien's law and a temperature of 6000 K to calculate lambda max and got 0.5 micrometers. This is green light; the sun emits more green light than any other kind of light. The sun doesn't appear green because it is also emitting lesser amounts of violet, blue, yellow, orange, and red - together this mix of colors appears white. 44% of the radiation emitted by the sun is visible light, 49% is IR light (37% near IR + 12% far IR), and 7% is ultraviolet light. More than half of the light emitted by the sun is invisible.

100% of the light emitted by the earth (temperature = 300 K) is invisible IR light. The wavelength of peak emission for the earth is 10 micrometers.

Because the sun (surface of the sun) is 20 times hotter than the earth a square foot of the sun's surface emits energy at a rate that is 160,000 times higher than a square foot on the earth. Note the vertical scale on the earth curve is different than on the sun graph. If both the earth and sun were plotted with the same vertical scale, the earth curve would be too small to be seen.

This is an appropriate point for a demonstration in the classroom version of the course, a demonstration that might save students some students some money (students that live off campus and pay electric utility bills).

Ordinary tungsten bulbs (incandescent bulbs) produce a lot of wasted energy. They emit a lot of infrared light that is wasted because it doesn't light up a room (it will heat up a room but there are better ways of doing that). The light that they do produce is a warm white color (tungsten bulbs emit lots of orange, red, and yellow light and not as much blues, greens and violets). Energy efficient compact fluorescent lamps (CFLs) are being touted as an ecological alternative to tungsten bulbs because they use substantially less electricity, don't emit a lot of wasted infrared light, and also last longer. CFLs come with different color temperature ratings.

The bulb with the hottest temperature rating (5500 K ) in the figure above is meant to mimic or simulate sunlight. The temperature of the sun is 6000 K and lambda max is 0.5 micrometers. The spectrum of the 5500 K bulb is similar.

The tungsten bulb (3000 K) and the CFLs with temperature ratings of 3500 K and 2700 K produce a warmer white.

Three CFLs with the temperature ratings above are set up in class so that you could see the difference between warm and cool white light. Personally I find the 2700 K bulb "too warm," it makes a room seem gloomy and depressing. The 5500 K bulb is "too cool" and creates a stark sterile atmosphere like you might see in a hospital corridor. I prefer the 3500 K bulb in the middle.

This figure below is from an article on compact fluorescent lamps in Wikipedia. You can see a clear difference between the cool white bulb on the left in the figure below and the warm white light produced by a tungsten bulb (2nd from the left) and 2 CFCs with low temperature ratings (3rd and 4th from the left).

There is one downside to these energy efficient CFLs. The bulbs shouldn't just be discarded in your ordinary household trash because they contain mercury. They should be disposed of properly at a hazardous materials collection site or perhaps at the store where they were purchased.