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

Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of $6000 \ K$. Maximum intensity is emitted at a wavelength of about $4800 \ \mathring{A}$. If the sun were to cool down from $6000 \ K$ to $3000 \ K$,then the peak intensity would occur at a wavelength of ....... $\mathring{A}$.

$A$ black body is at a temperature of $2880\;K$. The energy of radiation emitted by this object with wavelength between $499\;nm$ and $500\;nm$ is ${U_1}$,between $999\;nm$ and $1000\;nm$ is ${U_2}$ and between $1499\;nm$ and $1500\;nm$ is ${U_3}$. The Wien's constant $b = 2.88 \times {10^6}\;nm\,K$. Then

Two stars $A$ and $B$ radiate maximum energy at wavelengths $3.9 \times 10^{-7} \text{ m}$ and $5.2 \times 10^{-7} \text{ m}$ respectively. The ratio of the temperature of star $A$ to that of star $B$ will be

$A$ black body emits radiation of maximum intensity at wavelength $\lambda$ at temperature $T \ K$. Its corresponding wavelength at temperature $1.5 \ T \ K$ will be

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