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

For a perfectly black body,a graph is plotted between the frequency of radiation with maximum intensity $(v_m)$ and the absolute temperature $T$. Which of the following graphs is correct?

The absolute temperatures of two black bodies are $2000 \ K$ and $3000 \ K$ respectively. The ratio of wavelengths corresponding to maximum emission of radiation by them will be

The wavelength of the radiation emitted by a black body is $6 \ mm$ and Wien's constant is $3 \times 10^{-3} \ mK$. Then the temperature of the black body is (in $K$)

The temperature of a black body is $2880 \, K$. $U_1$ is the energy of radiation between $499 \, nm$ and $500 \, nm$,$U_2$ is the energy of radiation between $999 \, nm$ and $1000 \, nm$,and $U_3$ is the energy of radiation between $1499 \, nm$ and $1500 \, nm$. Given Wien's constant $b = 2.88 \times 10^6 \, nm \cdot K$,which of the following is correct?