Question

A black body at $1373$ $℃$ emits maximum energy corresponding to a wavelength of $1.78$ microns. The temperature of the moon for which $\lambda _{m}=14$ micron would be

• A. $62.6℃$
• B. $-58.9℃$
• C. $-63.7℃$
• D. $64.2℃$

Answer 1

Answer: (C)

$\frac{T_{2}}{T_{1}}= \, \frac{\lambda _{m_{1}}}{\lambda _{m_{2}}}=\frac{1.78}{14}$
$T_{2}=\frac{1.78}{14} \, \times T_{1}=\frac{1.78}{14}\left(1373 + 273\right)$
$=209.3K=209.3$ $-273=-63.7℃$