Final answer:
An object gains a faint blue tint at a temperature that causes it to emit more blue light in the visible spectrum, which is at approximately 10,000 K.
Step-by-step explanation:
Relative to the peak intensity in the Sun’s spectrum, an object gains a faint blue tint at a temperature that results in it emitting light more intensely in the blue part of the visible spectrum. The Sun's surface temperature is approximately 6000 K and its light appears white in space because it emits roughly equal amounts of reddish and bluish wavelengths. A cooler object at 3000 K would appear red, whereas an object at 10,000 K would have a blue tint, as it peaks around 0.3 µm in the visible spectrum and emits more energy in the blue wavelengths than in the red wavelengths.
According to Wien's Law, which relates the temperature of a blackbody to the peak wavelength of its emission, and the given information, a temperature of 10,000 K would be required for an object to start gaining a blue tint. Therefore, the answer to the student's question is d) 10000 K.