Final answer:
The peak wavelength of light from a star would become longer if the temperature of the star decreased by a factor of two, adhering to Wien's displacement law which states that as temperature decreases, peak wavelength increases.
Step-by-step explanation:
If the temperature of a star decreased by a factor of two, the peak wavelength of its light would change according to Wien's displacement law, which relates the temperature of a blackbody to the peak wavelength of the electromagnetic radiation it emits. According to this law, as temperature decreases, the wavelength associated with the peak of the emitted spectrum increases. Thus, the peak wavelength of light from the star would become longer.
In relation to the given options, the correct answer is that the wavelength of the most intense radiation will increase (option b). This law can be mathematically expressed as λmax = b/T, where λmax is the peak wavelength, b is Wien's displacement constant, and T is the temperature of the blackbody. Consequently, if the temperature falls, the peak wavelength gets longer. This is observed in practice when stars cooler than the Sun emit light that peaks in the infrared rather than visible range.