A black body at ${1227}^{0}C$ emits radiation with maximum intensity at a wavelength of 5000 $\stackrel{0}{A}$. If the temperatures of the body is increased by ${1000}^0 c$, the maximum intensity will be observed at

The product of wavelength corresponding to maximum intensity of radiation and temperature of the body in Kelvin is constant.

According to Wien's law,

             ${\mathrm{\lambda }}_{\mathrm{m}}\mathrm{T} = \mathrm{constant} (\mathrm{say} \mathrm{b})$

Where ${\mathrm{\lambda }}_{\mathrm{m}}$ is a wavelength corresponding to maximum intensity of radiation and T is temperature of the body in Kelvin.

         $\frac{{\mathrm{\lambda }}_{{\mathrm{m}}^{\text{'}}}}{{\mathrm{\lambda }}_{\mathrm{m}}}= \frac{\mathrm{T}}{{\mathrm{T}}^{\text{'}}}$

Given, $\mathrm{T} = 1227 + 273 = 1500 \mathrm{K},$

           ${\mathrm{T}}^{\text{'}} = 1227 + 1000 +273 = 2500 \mathrm{K}$

            ${\mathrm{\lambda }}_{\mathrm{m}} = 5000$$\stackrel{0}{A}$

Hence, ${\mathrm{\lambda }}_{{\mathrm{m}}^{\text{'}}} = \frac{1500}{2500}\times 5000 = 3000$$\stackrel{0}{A}$