The maximum wavelength of radiations emitted at $900\,K$ is $4\,\mu m$. What will be the maximum wavelength of radiations emitted at $1200\,K$ (in $,\mu m$)?

The temperature of the sun is $5500 \ K$ and it emits maximum intensity radiation in the yellow region $(5.5 \times 10^{-7} \ m)$. The maximum radiation from a furnace occurs at a wavelength of $11 \times 10^{-7} \ m$. The temperature of the furnace is ....... $K$.

$A$ black body at a temperature of $3000 \ K$ cools down. The wavelength corresponding to maximum energy density shifts by $\Delta \lambda = 9 \ \mu m$. What is the new temperature of the black body (in $K$)? (Given $b = 3 \times 10^{-3} \ m \cdot K$)

$A$ black body has a maximum wavelength of $\lambda_m$ at a temperature of $2000 \ K$. What will be the maximum wavelength at a temperature of $3000 \ K$?

What will be the ratio of temperatures of the sun and the moon if the wavelengths corresponding to their maximum emission radiation rates are $140 \mathring{A}$ and $4200 \mathring{A}$ respectively?

What are the values of Wien's constant in $SI$ and $CGS$ units?