Question

A black body at a temperature of $1640$ K has the wavelength corresponding to maximum emission equal to $1.75$$\mu$m. Assuming the moon to be a perfectly black body, the temperature of the moon, if the wavelength corresponding to maximum emission is $14.35$$\mu$m, is

• A. $100$ K
• B. $150$ K
• C. $200$ K
• D. $250$ K

Answer 1

Answer: (C)

$200$ K

According to Wein's displacement law, the peak wavelength is inversely proportional to absolute temperature.
So, the ratio of temperatures will be inverse of ratio of wavelengths.
So, $\frac{T_1}{T_2}=\frac{{\lambda }_2}{{\lambda }_1}$
Now,
$T_1$ = $1640$K,
${\lambda }_1=1.75\mu m$
${\lambda }_2=14.35\mu m$
Putting the values, we get $T_2$ = $200$ K