CHAPTER 7 | ATOMS AND STARLIGHT 129
X-ray or gamma-ray photon. Your wavelength of maximum
intensity lies in the infrared part of the spectrum.Two Radiation Laws
Th e two features of blackbody radiation that you have just con-
sidered can be given precise mathematical form, and they have
proven so dependable that they are known as laws. One law is
related to energy and one to color.
As you saw in the previous section, a hot object emits more
blackbody radiation than a cool object. Th at is, it emits more
energy. Recall from Chapter 5 that energy is expressed in units
called joules (J); 1 joule is about the energy of an apple falling
from a table to the fl oor. Th e total radiation given off by 1 square
meter of the surface of the object in joules per second equals a
constant number, represented by times the temperature raised
to the fourth power.* Th is relationship is called the Stefan–
Boltzmann law:
E T^4 (J/s/m^2 )How does this help you understand stars? Suppose a star the
same size as the sun had a surface temperature that was twice as
hot as the sun’s surface. Th en each square meter of that star
would radiate not twice as much energy, but 2^4 , or 16, times as
much energy. From this law you can see that a small diff erence
in temperature can produce a very large diff erence in the amount
of energy a star’s surface emits.
Th e second radiation law is related to the color of stars. In
the previous section, you saw that hot stars look blue and cool
stars look red. Wien’s law written for conventional intensity units
tells you that the wavelength at which a star radiates the most
energy, its wavelength of maximum intensity (max), depends
only on the star’s temperature:
max 2.90 106 /TTh at is, the wavelength of maximum radiation in nanometers
equals 2.9 million divided by the temperature on the Kelvin
scale.
Th is law is a powerful tool in astronomy, because it relates
the temperature of a star to its wavelength of maximum intensity.
For example, you might fi nd a star emitting light with a maxi-
mum intensity at a wavelength of 1000 nm—in the near-infrared.
Th en the surface temperature of the star must be 2900 K. Later
you will meet stars much hotter than the sun; such stars radiate
most of their energy at very short wavelengths. Th e hottest stars,
for instance, radiate most of their energy in the ultraviolet.■ Figure 7-6
Graphs of blackbody radiation intensity versus wavelength from three objects
at different temperatures demonstrate that a hot body radiates more total
energy and that the wavelength of maximum intensity is shorter for hotter
objects. The hotter object here would look blue to your eyes, while the
cooler object would look red.
0 200 400 600 800 10000 200 400 600 800 1000Object at 6000 K
6000 KObject at
7000 KObject at
5000 KWavelength (nanometers)Wavelength (nanometers)IntensityIntensityIntensity7000 KλmaxλmaxλmaxUltraviolet Visual Infrared
More blue light than red
gives this star a bluer color.Only 1000 degrees cooler
makes a big difference in color.More red light than blue
gives this star a redder color.
5000 Kred. Now you can understand why two of your Favorite Stars,
Betelgeuse and Rigel, have such diff erent colors. Betelgeuse is
cool and looks red, but Rigel is hot and looks blue.
Cool objects don’t glow at visible wavelengths but still pro-
duce blackbody radiation. For example, the human body has a
temperature of 310 K and emits blackbody radiation mostly in
the infrared part of the spectrum. Infrared security cameras can
detect burglars by the radiation they emit, and mosquitoes can
track you down in total darkness by homing in on your infrared
radiation. Although you emit lots of infrared radiation, you
rarely emit higher-energy photons; and you almost never emit an
*For the sake of completeness, you can note that the constant equals 5.67
10 ^8 J/(s m^2 K^4 ) (units of joules per second per square meter per degree Kelvin
to the fourth power).