Final answer:
The statement given is false; hotter stars emit more light at shorter wavelengths, while cooler stars emit more at longer wavelengths.
Step-by-step explanation:
The statement that cooler stars emit more light at shorter wavelengths while hotter stars emit more light at longer wavelengths is false. According to Wien's law and the behavior of blackbody radiation, hotter objects, including stars, actually emit a larger fraction of their energy at shorter wavelengths, which correspond to higher frequencies and energies. As stars increase in temperature, they radiate more at the blue and ultraviolet end of the spectrum, which is evident in their color; hotter stars appear blue or blue-white, whereas cooler stars appear red or red-orange due to the dominance of longer wavelengths in their emission.
For example, a star with a higher temperature will peak at shorter wavelengths and hence will appear to be blue or blue-white. In contrast, a cooler star will peak at longer wavelengths, thus appearing red. The color of the star provides a measure of its intrinsic surface temperature, which does not depend on the distance to the observer but rather on the actual physics of blackbody radiation.