Solutions to Exercises

1) Wien’s law is

To get a temperature from this equation we have to solve for T

Using a peak wavelength for Betelgeuse of 855 nm we have

Thus the temperature of Betelgeuse is 3391 degrees Kelvin.

2) In the Applet, the closest temperature to 3391 K you can input is about 3364 K. The peak of the curve does indeed occur at about 900 nm which is in the infrared part of the spectrum (meaning wavelengths longer than the red light). Note the color of the star has a dusky reddish/brown appearance. Your computer will display colors based on its own color tables so appearances will vary depending on your machine. Try going outside tonight and looking at red stars and see what range of colors your eye detects.

3) Using Wien’s law we have

Thus the star has a peak wavelength of only 287 nanometers. The appearance of this star is distinctly blue as the peak occurs just at the edge of the blue part of the visible spectrum.

4) Using Wien’s law with T = 4000 K we have

Thus the star has a peak wavelength of only 725 nanometers.

To find the relative power output of our big and little stars we use the luminosity relation

The easy way to do this part of the problem is to write down the equation for each star and then divide one equation by the other. You will end up with an expression for the luminosity of the big star relative to the small one.

Dividing these two equations and canceling out all the constants and the temperature (since it is the same for both stars) gives

So the big star is 10,000 times brighter than the small star.