$A$ black body emits radiation of maximum intensity of wavelength '$\lambda$' at temperature '$T$' $K$. Its corresponding wavelength at temperature $(2.5T)$ $K$ will be

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).

If $\lambda_{m}$ denotes the wavelength at which the radioactive emission from a black body at a temperature $T \; K$ is maximum,then

The Earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

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