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 ............

Two bodies $A$ and $B$ have emissivities $0.01$ and $0.81$ respectively. The outer surface areas of both bodies are the same. Both bodies emit total radiant power at the same rate. The wavelength $\lambda_B$ corresponding to the maximum spectral radiance of $B$ is $1.0 \mu m$. If the temperature of $A$ is $5802 \ K$,calculate the wavelength $\lambda_A$ in $\mu m$. (Note: The original question asked for $\lambda_B$ but provided $\lambda_B$ as $1.0 \mu m$ and asked for $\lambda_A$ based on the context of the solution provided).

The black body spectrum of an object $O_1$ is such that its radiant intensity (i.e.,intensity per unit wavelength interval) is maximum at a wavelength of $200\,nm$. Another object $O_2$ has the maximum radiant intensity at $600\,nm$. The ratio of power emitted per unit area by source $O_1$ to that of source $O_2$ is

$A$ body at $3000 \,K$ emits maximum energy at a wavelength of $9660 Å$. If the sun emits maximum energy at a wavelength of $4950 Å$, what would be the temperature of the sun (in $\,K$)?

If $\lambda$ denotes the wavelength at which the radiative emission from a black body at a temperature $T$ is maximum, then

Wien's displacement law expresses the relation between: