Question

What will be the ratio of temperatures of sun and moon, if the wavelengths of their maximum emission radiations rates are $140\,\mathring{A}$ and $4200\ ,\mathring{A}$ respectively?

• A. $ 1:30 $
• B. $ 30:1 $
• C. $ 42:14 $
• D. $ 14:42 $

Answer 1

Answer: (B)

From Wien's law $\lambda_{m} T=$ constant
where $\lambda_{m}$ is maximum wavelength and $T$ the absolute temperature.
Given, $\lambda_{1}=140,$
$\lambda_{2}=4200\,\mathring{A}$
$\therefore \frac{\lambda_{1}}{\lambda_{2}}=\frac{T_{2}}{T_{1}}=\frac{140}{4200}$
$\Rightarrow \frac{T_{2}}{T_{1}}=\frac{1}{30}$
$\Rightarrow \frac{T_{1}}{T_{2}} =\frac{30}{1}$