If the wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5 \times 10^{-6} \ m$ and $10^{-4} \ m$ respectively,the ratio of their temperatures is:

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

$A$ black disc has a radius $R$ and the wavelength corresponding to the maximum intensity is $\lambda$. The emissive power $(E)$ for the different radii and maximum wavelengths is directly proportional to:

If wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5 \times 10^{-6} \ m$ and $10^{-4} \ m$ respectively,the ratio of their temperatures is

The wavelength of maximum emitted energy $(\lambda_m)$ of a body at $700 \ K$ is $4.08 \ \mu m$. If the temperature of the body is raised to $1400 \ K$,then the value of $\lambda_m$ will be (in $\mu m$)

Two stars $A$ and $B$ radiate maximum energy at the wavelengths of $360 \ nm$ and $480 \ nm$ respectively. Then the ratio of the surface temperatures of $A$ and $B$ is