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 $B$ 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:

$A$ particular star (assuming it as a black body) has a surface temperature of about $5 \times 10^4 \ K$. The wavelength in nanometers at which its radiation becomes maximum is $(b = 0.0029 \ mK)$.

Three stars $A, B, C$ have surface temperatures $T_{A}, T_{B}, T_{C}$ respectively. Star $A$ appears bluish,star $B$ appears reddish,and star $C$ appears yellowish. Hence,

Two stars $P$ and $Q$ are observed at night. Star $P$ appears reddish while star $Q$ is white. From this we conclude:

$A$ black body has a maximum wavelength $\lambda_{m}$ at a temperature of $2200 \ K$. Its corresponding wavelength at a temperature of $3300 \ K$ will be: