Question

According to Wien's Law, if the surface temperature is increased by a factor of 2, what will happen to its peak wavelength?

Answer 1

Maybe you ought to read this first:
https://socratic.org/questions/hot-objects-with-temperatures-of-10-million-kelvin-give-off-most-of-their-radiat

Then, we find that Wien's displacement law for blackbody radiation is:

`lambda_(max) = (2.8977729 xx 10^(-3) "m"cdot"K")/T`

Hence, plug in `2T` to obtain the peak wavelength at twice the temperature...

`lambda_(max)' = (2.8977729 xx 10^(-3) "m"cdot"K")/(2T)`

`= color(blue)(1/2) lambda_(max)`

Clearly, the peak wavelength has halved, as the peak wavelength is inversely proportional to the surface temperature.