Final answer:
The peak wavelength of a star's light will halve if its temperature doubles, shifting to a shorter wavelength according to Wien's Law.
Step-by-step explanation:
If the temperature of a star increases by a factor of two, the peak wavelength of its light will change according to Wien's Law. Wien's Law states that the peak wavelength is inversely proportional to the temperature of the blackbody, which a star can often be approximated as. Therefore, if the temperature doubles, the peak wavelength will halve, meaning it will shift to a shorter wavelength. This is because the product of the temperature and the peak wavelength is a constant, so increasing the temperature results in a corresponding decrease in the peak wavelength.
Additionally, as the temperature increases, the frequency of the light providing the greatest intensity also increases. Given that the speed of light is constant, an increase in the frequency entails a decrease in the wavelength. This concept is indicated by the leftward shift of the peak wavelength as the temperature increases.