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

The black discs $x, y$ and $z$ have radii $1 \ m, 2 \ m$ and $3 \ m$ respectively. The wavelengths corresponding to maximum intensity are $200 \ nm, 300 \ nm$ and $400 \ nm$ respectively. The relation between emissive power $E_{x}, E_{y}$ and $E_{z}$ is

$A$ black body is at a temperature of $2880\;K$. The energy of radiation emitted by this object with wavelength between $499\;nm$ and $500\;nm$ is ${U_1}$,between $999\;nm$ and $1000\;nm$ is ${U_2}$ and between $1499\;nm$ and $1500\;nm$ is ${U_3}$. The Wien's constant $b = 2.88 \times {10^6}\;nm\,K$. Then

Two stars $A$ and $B$ radiate maximum energy at wavelengths $3.9 \times 10^{-7} \text{ m}$ and $5.2 \times 10^{-7} \text{ m}$ respectively. The ratio of the temperature of star $A$ to that of star $B$ will be

An extremely hot star would appear to be

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 $b = 2898 \ \mu m \ K$)