Q. What will be the ratio of temperatures of sun and moon, if the wavelengths of their maximum emission radiations rates are 140 $\mathring{\mathrm{A}}$ and 4200 $\mathring{\mathrm{A}}$ respectively?
A) 1:30
B) 30:1
C) 42:14
D) 14:42
Explanation
(b) From Wien’s law
$\lambda_{m}T = constant$
Where $\lambda_{m}$ is maximum wavelength and $T$ the absolute temperature.
Given, $\lambda_{1} = 140,\ \ \ \ \ \lambda_{2} = 4200\mathring{\mathrm{A}}$
$\therefore$ $\frac{\lambda_{1}}{\lambda_{2}} = \frac{T_{2}}{T_{1}} = \frac{140}{4200}$
$\Rightarrow$ $\frac{T_{2}}{T_{1}} = \frac{1}{30}$
$\Rightarrow$ $\frac{T_{1}}{T_{2}} = \frac{30}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.