Answer :
(a) [tex]1.61\cdot 10^5 K[/tex]
The problem can be solved by using the Wien's displacement law, which states that the peak wavelength of a blackbody spectrum is inversely proportional to the absolute temperature of the blackbody:
[tex]\lambda=\frac{b}{T}[/tex]
where in this case we have
[tex]\lambda=18 nm=18\cdot 10^{-9}m[/tex] is the peak wavelength
[tex]b=2.898\cdot 10^{-3} m\cdot K[/tex] is the Wien's displacement constant
Solving the formula for T, we find the temperature of the body:
[tex]T=\frac{b}{\lambda}=\frac{2.898\cdot 10^{-3} m \cdot K}{18\cdot 10^{-9} m}=1.61\cdot 10^5 K[/tex]
(b) [tex]1.45\cdot 10^{-6} m[/tex]
As before, the problem can be solved by using Wien's displacement law:
[tex]\lambda=\frac{b}{T}[/tex]
where in this case we have
[tex]T=2000 K[/tex] is the peak wavelength
[tex]b=2.898\cdot 10^{-3} m\cdot K[/tex] is the Wien's displacement constant
Solving the formula for [tex]\lambda[/tex], we find the peak wavelength:
[tex]\lambda=\frac{b}{T}=\frac{2.898\cdot 10^{-3} m \cdot K}{2000 K}=1.45\cdot 10^{-6} m[/tex]