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Q.
If at temperature $T_{1}=1000\, K$, the wavelength is $2.2 \times 10^{-6} m ,$ then at what temperature the wavelength will be $4.4 \times 10^{-5} m ?$
Thermal Properties of Matter
Solution:
Wien's law states that $\lambda \propto \frac{1}{t}$
$\frac{\lambda_{1}}{\lambda_{2}}=\frac{ T _{2}}{ T _{1}} $
$\Rightarrow T _{2}=\frac{\lambda_{1}}{\lambda_{2}} \times T _{1}$
$=\frac{2.2 \times 10^{-6}}{4.4 \times 10^{-5}} \times 1000$
$\therefore T _{2}=50 K$
$\therefore 49 K$ is nearest to $50 .$