Blackbody Spectrum Question (a
Blackbody Spectrum Question
(a) Examination of the spectrum of a star showsthat it is brightest at the frequency 1.5 × 10^14 Hz. What is itstemperature? How does this compare to the Sun’s temperature? Whatcolor will this star appear to be?
(b) How does the surface brightness of thisstar compare with Sun’s surface brightness, according to theStefan-Boltzmann law?
(c) Somewhat surprisingly, the star in questionappears extremely bright, much brighter than the Sun would appearat that distance! Explain how this phenomenon does not contradictyour answer in (b). (Hint: such stars are calledred giants.)
Answer:
a] The wavelength of this signal is:
= 2000 nm
so, the star will appear to be infrared.
Using Wein’s displacement law, the temperature for the star thenwill be:
.
Surface temperature of the Sun is T = 5778 K which is nearly 4times the temperature of this given star.
b]
Using Stefan Boltzmann law, the surface brightness of this starwill be:
=> 
c] The star can only appear brighter than the Sun at thatdistance if the given star is dying. Because the star is dying, theenergy is radiated over a larger area which is why the surfacebrightness is less.
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