Answer
$1.017$
Work Step by Step
According to the classical radiation law,
$I_c=\frac{2\pi ckT}{\lambda^4}$
and according to the Planck’s radiation law,
$I_p=\frac{2\pi c^2h}{\lambda^5}\frac{1}{e^{\frac{hc}{\lambda kT}}-1}$
Therefore, the ratio of $\frac{I_c}{I_p}$ is given by
$\frac{I_c}{I_p}=\frac{\lambda kT}{hc}(e^{\frac{hc}{\lambda kT}}-1)$
Given, $T=2000$ $K$, $\lambda=200$ $\mu m$ $=200\times 10^{-6}$ $m$
$\therefore \lambda kT=200\times 10^{-6}\times 1.38\times 10^{-23}\times 2000$ $J.m$
or, $\lambda kT=5.52\times 10^{-24}$ $J.m$
and $hc=6.63\times 10^{-34}\times 3\times 10^{8}$ $J.m$
or, $hc=1.989\times 10^{-25}$ $J.m$
$\therefore \frac{\lambda kT}{hc}\approx 27.75$ and $\frac{hc}{\lambda kT}\approx 0.036$
Therefore,
$\frac{I_c}{I_p}=27.75\times(e^{0.036}-1)\approx 1.017$
