The wavelength of maximum emission from a body at a temperature of $200 \, K$ is $14 \, \mu m$. If the temperature of the body is increased to $1000 \, K$,find the new wavelength of maximum emission.

Black bodies $A$ and $B$ radiate maximum energy with wavelength difference $4 \mu m$. The absolute temperature of body $A$ is $3$ times that of $B$. The wavelength at which body $B$ radiates maximum energy is (in $\mu m$)

Observations of light from three different stars $A, B$,and $C$ show that the intensity of the red color is maximum for star $A$,the intensity of the blue color is maximum for star $B$,and the intensity of the yellow color is maximum for star $C$. Which of the following conclusions can be drawn from these observations?

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

The surface temperature of the sun, which has maximum energy emission at $500 \, nm$, is $6000 \, K$. The temperature of a star, which has maximum energy emission at $400 \, nm$, will be ........ $K$.

Star $S_1$ emits maximum radiation of wavelength $420 \, nm$ and the star $S_2$ emits maximum radiation of wavelength $560 \, nm$. What is the ratio of the temperature of $S_1$ and $S_2$?