A black body at a temperature of $1640\,\,K$ has the wavelength corresponding to maximum emission equal to $1.75 \,\,\mu m.$ Assuming the moon to be a perfectly black body, the temperature of the moon, if the wavelength corresponding to maximum emission is $14.35\,\,\mu m$ is.......$K$
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$\frac{{{T_2}}}{{{T_1}}}\, = \,\frac{{{\lambda _{{m_1}}}}}{{{\lambda _{{m_2}}}}}\, = \,\frac{{1.75}}{{14.35}}\, \Rightarrow \,{T_2}\, = \,\frac{{1.75}}{{14.35}}\, \times \,1640\, = \,200\,K$
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