The Sun's surface has a temperature of 5800 K. What will be the peak wavelength of the spectrum of a star that emits twice the Sun's flux of energy? A)2.1 × 10^-7 m B)4.0 × 10^-7 m C)5.0 × 10^-7 m D)1.0 × 10^-6 m

Question

Quizplus · Accepted Answer

According to Wien's Law, the peak wavelength of radiation from a black body is inversely proportional to its temperature. So, for a star that emits twice the Sun's flux of energy, its temperature would be higher than the Sun's by a factor of fourth root of 2 (since the flux is proportional to the fourth power of temperature). Thus, the temperature of the star would be approximately 7360 K. Using Wien's Law, we can calculate the peak wavelength to be:
peak wavelength = 2898 / 7360 = 3.94 × 10^-7 m
which is closest to option B: 4.0 × 10^-7 m.

The Sun's Surface Has a Temperature of 5800 K