Answer:
Wavelength, [tex]\lambda=9.72\times 10^{-6}\ m[/tex]
Frequency, [tex]f=3.08\times 10^{13}\ Hz[/tex]
Explanation:
We need to find the intensity of the radiation is a maximum for a black body at 298 K. It can be calculated using Wein's displacement law. It is given by :
[tex]\lambda T=2.898\times 10^{-3}\ m-K[/tex]
[tex]\lambda=\dfrac{2.898\times 10^{-3}}{T}[/tex]
Here, T = 298 K
[tex]\lambda=\dfrac{2.898\times 10^{-3}}{298}[/tex]
[tex]\lambda=9.72\times 10^{-6}\ m[/tex]
If f is the frequency of black body radiation. It is given by :
[tex]f=\dfrac{c}{\lambda}[/tex]
[tex]f=\dfrac{3\times 10^8}{9.72\times 10^{-6}}[/tex]
[tex]f=3.08\times 10^{13}\ Hz[/tex]
Hence, this is the required solution.