If at temperature $T_1 = 1000 \ K,$ the wavelength is $1.4 \times 10^{-6} \ m,$ then at what temperature in $K$ will the wavelength be $2.8 \times 10^{-6} \ m$?

Experimental investigations show that the intensity of solar radiation is maximum for a wavelength $480 \, nm$ in the visible region. Estimate the surface temperature of the sun. Given Wien's constant $b = 2.88 \times 10^{-3} \, mK$.

The intensity of radiation emitted by the sun has its maximum value at a wavelength of $510\;nm$ and that emitted by the north star has the maximum value at $350\;nm$. If these stars behave like black bodies,then the ratio of the surface temperature of the sun and north star is

Solar radiation emitted by the Sun resembles that of a black body at a temperature of $6000 \, K$. The maximum intensity of radiation is emitted at a wavelength of $4800 \, \mathring{A}$. If the temperature of the Sun decreases from $6000 \, K$ to $3000 \, K$,then at what wavelength (in $\mathring{A}$) will the maximum intensity of radiation be emitted?

$A$ black body at $200 K$ is found to emit maximum energy at a wavelength of $14 \mu m$. When its temperature is raised to $1000 K$,the wavelength at which maximum energy is emitted is:

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