If the average temperature of the sun increased, the wavelength of peak solar emission would:

The correct answer is: A. Shift to a shorter wavelength.

The peak wavelength of solar emission is determined by the temperature of the sun. The hotter the sun, the shorter the peak wavelength. This is because the hotter the sun, the more energetic the photons that are emitted. More energetic photons have shorter wavelengths.

Option B is incorrect because the peak wavelength of solar emission would shift to a shorter wavelength, not a longer wavelength.

Option C is incorrect because the peak wavelength of solar emission would shift, not remain the same.

Option D is incorrect because it is possible to tell from the given information that the peak wavelength of solar emission would shift to a shorter wavelength.