Physics 127 - Descriptive Astronomy                                                                                       Homework Key - Assignment #5
Revised - 23-Oct-2009

5-14.  The bright star Bellatrix in the constellation Orion has a surface temperature of 21,500 K.  What is the wavelength of maximum emission in nanometers?  What
              color is this star?

    Using Wien's law for a blackbody:  λ max [m] = 0.0029 / T [K], yields λ max [m] = 0.0029 / λ max [m]  = 0.0029 / 21500 =
1.3410-7 m = 134 nm
.  This wavelength is ultraviolet as is most of the energy radiated by such a hot star.  Radiation in the visible spectral region slopes steeply upward with decreasing wavelength, therefore the eye perceives a color dominated by short wavelengths, the star appears blue.  (If the eye were as sensitive to violet radiation as blue, the star would appear violet.)

5-24.  Your normal body temperature is 98.6F.  What kind of radiation do you predominantly emit?  At what wavelength (in nm) do you emit the most radiation?

    Human bodies emit primarily infrared radiation.  To find the wavelength of peak radiation we must use Wien's Law.  First, however, the temperature of a human body must be converted to the Kelvin scale.  Since T [K] = 273 + T [C] = 273 + 5/9 (T [F] - 32), it follows that Thuman body [K] = 273 + 5/9 (98.6 - 32) = 310 K.  Therefore λ max [m] = 0.0029 / T [K] = 0.0029 / 310 =
9.35
10-6 m = 9350 nm.

5-29.  The star Alpha Lupi (the brightest star in the constellation Lupus, the Wolf) has a surface temperature of 21,600 K.  How much more energy is emitted each
              second from each square meter of Alpha Lupi than from each square meter of the Sun's surface?

    The surface temperature of the sun is about 5800 K.  Using the Stefan-Boltzmann law for a blackbody:  F = σT 4.  Therefore
Fα Lup /FSun = (Tα Lup /TSun)4 = (21600/5800)4 = 192 times as much energy per square meter of surface.  Or, in an absolute rather than a relative sense, α Lup radiates 192 times more energy per unit area than the sun's 6.4
107 W m-2 , or α Lup radiates
1.22
1010 W m-2 more than the sun.

 5-36.  Certain interstellar clouds contain a very cold, very thin gas of hydrogen atoms.  Ultraviolet radiation with any wavelength shorter than 91.2 nm cannot pass
               through this gas; instead, it is absorbed.  Explain why.

    Cold, neutral hydrogen, in its ground state, is capable of absorbing all radiation of wavelength shorter than 91.2 nm (which ionizes the hydrogen), but not most wavelengths longer than that, since most of them do not match the discrete wavelengths of the hydrogen atom's absorption lines.