Question

Blackbody Spectrum Question

(a) Examination of the spectrum of a star shows that it is brightest at the frequency 1.5 × 10^14 Hz. What is its temperature? How does this compare to the Sun’s temperature? What color will this star appear to be?

(b) How does the surface brightness of this star compare with Sun’s surface brightness, according to the Stefan-Boltzmann law?

(c) Somewhat surprisingly, the star in question appears extremely bright, much brighter than the Sun would appear at that distance! Explain how this phenomenon does not contradict your answer in (b). (Hint: such stars are called red giants.)

Answer 1

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 then will be:

.

Surface temperature of the Sun is T = 5778 K which is nearly 4 times the temperature of this given star.

b]

Using Stefan Boltzmann law, the surface brightness of this star will be:

=>

c] The star can only appear brighter than the Sun at that distance if the given star is dying. Because the star is dying, the energy is radiated over a larger area which is why the surface brightness is less.