Question

The ratio of temperatures of sun and moon, if the wavelengths of their maximum emission radiations rates are $140$ $Å$ and $4200$ $Å$ , will be

• 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 $T$ is the absolute temperature.
Given, $\lambda _{1}=140Å$ , $ \, \lambda _{2}=4200Å$
$\therefore $ $\frac{\lambda _{1}}{\lambda _{2}}=\frac{T_{2}}{T_{1}}=\frac{140}{4200}$
$\Rightarrow $ $\frac{T_{2}}{T_{1}}=\frac{1}{30}$
$\Rightarrow $ $\frac{T_{1}}{T_{2}}=\frac{30}{1}$