To solve this problem we will apply the Wien displacement law (in honor of Wilhelm Wien) which is a law of physics that states that there is an inverse relationship between the wavelength at which the emission peak of a body occurs Black and its temperature. Mathematically, the law is:
[tex]\lambda_{max} = \frac{0.29 cm\cdot K}{T}[/tex]
Here,
T = Temperature
We know at the same time that the range of red to infrared wavelength is
[tex]\lambda = 700nm -10^6nm (1mm)[/tex]
Calculating each quasi infinite point of this range would be somewhat complex, so it is easier to replace temperatures and see if the temperature falls on the range. We can realize that the first option is the correct one, because:
[tex]\lambda_{max} = \frac{0.29}{3500K}[/tex]
[tex]\lambda_{max} = 8.28*10^{-5}cm[/tex]
[tex]\lambda_{max} = 829nm[/tex]
Therefore the temperature is A. 3500K
