Astronomy 110 | PRINT Name __________________________ |

Fall 2005 Section 006 | |

Homework
6 : Measuring Temperature |
(Due Thursday, Oct 20, 2005) |

The spectrum of sunlight, the "rainbow", is related to the ideal "black
body" spectrum, three of which are shown below. For a "black body" (an ideal
emitter), once you know the temperature, the amount of light emitted from each
square centimeter of its surface is known exactly. The three plots below are
the intensity of light as a function of wavelength in Angstroms for three black
bodies at different temperatures. The range of visible wavelenths of light is
also shown. Answer the questions on the back.

- Mark on the diagram which is the blue end and which is the red end of the
visible wavelengths.
**The visible region of the spectrum is marked by the dashed vertical lines in the figure. We can determine which dashed line is on the blue side and which is on the red side by looking at the wavelength scale at the bottom. In the diagram wavelength is increasing to the right, so that means blue will be on the left and red on the right, since blue light has shorter wavelengths than red light.** - Measure the wavelength where each of the spectra, A, B and C, is at a
maximum and enter it in the table below. Obviously you won't be able to
measure very accurately, particularly with curve C, but do the best you can.
It would be best to use a metric ruler with fine divisions. Also, try to make
a realistic estimate of how well you can actually measure these wavelengths,
and have that reflect in the numbers you enter in the table. For example,
could you
*really*measure a wavelength of 11,001 Angstroms, or can you only say that it is*nearly*11,000 Angstroms (as far as you can measure it). If not, enter 11,000 Angstroms, not 11,001 Angstroms.

A B C Peak Wavelength in Angstroms **2000****5000****10000**Temperature in Kelvin **15000****6000****3000** - Now you are in a position to measure the temperatures of bodies A, B and
C, which you do by using
**Wien's Law**which says that the wavelength of peak intensity (that you just measured),*w*(in Angstroms) is related to the temperature,*T*(in Kelvin) by

.*w = 3 x 10*^{7}/ TCalculate the temperatures of bodies A, B, and C and enter them in the table above.

**We can rewrite the equation as:***T = 3 x 10*^{7}/ w**and plug in the values that we measured off of the figure (which are listed in the table above). Note: this equation works for temperature in Kelvin and wavelength in Angstroms only, the constant 3 x 10**^{7}is different for different units.

- Which curve is closest to representing the light from the Sun?
**B****There are a couple of ways to know this. Curve B peaks inside the visible spectrum, and the Sun is brightest in the visible part of the spectrum (in fact this is why our eyes are sensitive to this part in the first place). Another way to know that it is curve B is by knowing that the temperature of the Sun is about 5800 Kelvin, which is close to what we calculated for curve B.** - Consider the visible light portion of curves A and C. Which of these
curves represents a hot body that is giving off light that looks
**blue**to your eye?**A****Reason :****To determine what color we see, we look at the curves in the visible part of the spectrum and ignore the rest. From problem 1, we know that the left vertical dashed line marks the blue wavelengths, and the right one marks the red wavelengths. Curve A is higher on the blue side than the red, so that means the hot body whose light curve is represented by curve A will look blue to us. Note: using this same logic we can tell that the hot body for curve C will look red, and the one for curve B will look yellowish because it is brightest somewhere between blue and red.**