According to Wien's displacement law:

$A$ body at $1500 \ K$ emits maximum energy at a wavelength $20,000 \ \mathring{A}$. If the Sun emits maximum energy at a wavelength $5500 \ \mathring{A}$,then the temperature of the Sun is ....... $K$.

Two bodies $A$ and $B$ of equal surface area have thermal emissivities of $0.01$ and $0.81$ respectively. The two bodies are radiating energy at the same rate. Maximum energy is radiated from the two bodies $A$ and $B$ at wavelengths $\lambda_A$ and $\lambda_B$ respectively. The difference in these two wavelengths is $1 \mu m$. If the temperature of body $A$ is $5802 \ K$, then the value of $\lambda_B$ is:

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?

The maximum wavelength of radiation emitted by a star is $289.8 \ nm$. The intensity of radiation for the star is (Given: Stefan's constant $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$,Wien's constant $b = 2898 \ \mu m \ K$)

If the wavelengths of maximum intensity of radiation emitted by the Sun and the Moon are $0.5 \times 10^{-6} \, m$ and $10^{-4} \, m$ respectively,then the ratio of their temperatures is ............