4) Suppose you observe a star that is three times as hot as the sun, but...
4) Suppose you observe a star that is three times as hot as the sun, but also three smaller in radius than the sun.
a) What is the wavelength at which its spectrum peaks? Is that wavelength shorter or longer than that of the sun?
b) How much more (or less) power (ie., luminosity or energy per time) is it emitting in total, compared to the sun?
Homework Answers
The radiation of the sun and the star can be modeled by assuming them as blackbodies.
Given 
and 
(a) The wavelength at which the spectrum of a blackbody peaks is given by
The temperature of the sun is 
, it spectrum's peak is at
The temperature of the star is 
, it spectrum's peak is at
The peak wavelength of the star's spectrum is shorter than that of the sun.
(b) The power emitted by a blackbody per unit surface area is
If R is the radius of a spherical blackbody its total
surface area is 
The total power emitted by the blackbody is
The total power emitted by the sun is
The total power emitted by the star is
The total power emitted by the star is 9 times more than the total power emitted by the sun.
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