Which one of the following is the $\nu_{m}-T$ graph for a perfectly black body? Here, $\nu_{m}$ is the frequency of radiation with maximum intensity and $T$ is the absolute temperature.

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \, nm$. The radiation intensity for the star is: (Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$,Wien's constant $b = 2898 \, \mu m \cdot K$)

The temperature of a furnace is $200\,^{\circ}C$. In its spectrum,the maximum intensity is obtained at about $400\,\mathring{A}$. If the maximum intensity is at $200\,\mathring{A}$,calculate the temperature of the furnace in $^{\circ}C$. ......... $^{\circ}C$

$A$ black body is at a temperature of $5780 \text{ K}$. The energy of radiation emitted by the body at wavelength $300 \text{ nm}$ is $U_1$, at wavelength $500 \text{ nm}$ is $U_2$, and at wavelength $900 \text{ nm}$ is $U_3$. Wien's constant $b = 2.89 \times 10^6 \text{ nm K}$. This shows that:

The relation between the colour and the temperature of a star is given by

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