The radiation energy density per unit wavelength at temperature $T$ is maximum at a wavelength $\lambda_0$. At temperature $2T$,it will have a maximum at a wavelength

We consider the radiation emitted by the human body. Which of the following statements is true?

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 $2.8 \times 10^{-6} \ m$?

The variation of radiant energy emitted by the Sun, the filament of a tungsten lamp, and a welding arc as a function of its wavelength is shown in the figure. Which of the following options is the correct match?

$A$ piece of iron is heated in a flame. It first becomes dull red, then becomes reddish yellow, and finally turns to white hot. The correct explanation for the above observation is possible by using

The spectral emissive power $E_\lambda$ for a body at temperature $T_1$ is plotted against the wavelength and the area under the curve is found to be $A$. At a different temperature $T_2$,the area is found to be $9A$. Then $\lambda_1/\lambda_2 =$