Wien's displacement law expresses the relation between:

$A$ black body is at a temperature of $5760 \ K$. The energy of radiation emitted by the body at wavelength $250 \ nm$ is $U_1$,at wavelength $500 \ nm$ is $U_2$ and that at $1000 \ nm$ is $U_3$. Wien's constant,$b = 2.88 \times 10^6 \ nm \ K$. Which of the following is correct?

How is the temperature of stars determined?

$A$ black body emits radiation with maximum intensity at a wavelength of $5000 \mathring{A}$ at a temperature of $1227^\circ C$. If its temperature is increased by $1000^\circ C$, the new wavelength of maximum intensity will be ...... $\mathring{A}$.

$A$ body at $1500 \ K$ emits maximum energy at a wavelength $20,000 \ \mathring{A}$. If the Sun emits maximum energy at a wavelength $5500 \ \mathring{A}$,then the temperature of the Sun is ....... $K$.

$A$ black body has a maximum wavelength $\lambda_{m}$ at a temperature of $2000 \ K$. Its corresponding wavelength at a temperature of $3000 \ K$ will be: