Answer
See explanation.
Work Step by Step
Use Wien’s displacement law, equation 39.21.
$$\lambda_m =\frac{2.90\times10^{-3}m \cdot K}{T}$$
$$\lambda_m =\frac{2.90\times10^{-3}m \cdot K}{3.00K}=9.67\times10^{-4}m$$
Now find the frequency.
$$f=\frac{c}{\lambda_m}=3.10\times10^{11}Hz$$
b. Raising the temperature by 100 lowers the peak wavelength by a factor of 100 to $9.67\times10^{-6}m$ and raises the frequency by a factor of 100 to $f=3.10\times10^{13}Hz$.
c. By the same reasoning the peak wavelength is $9.67\times10^{-7}m$ and the frequency is $f=3.10\times10^{14}Hz$.
