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, ${\lambda }_1=140,$
${\lambda }_2=4200\mathring{A}$
$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{T_2}{T_1}=\frac{140}{4200}$
$\Rightarrow \frac{T_2}{T_1}=\frac{1}{30}$
$\Rightarrow \frac{T_1}{T_2}=\frac{30}{1}$