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

Question

A black body at 1373 ℃ emits maximum energy corresponding to a wavelength of 1.78 microns. The temperature of the moon for which λ m=14 micron would be (A) 62.6℃ (B) -58.9℃ (C) -63.7℃ (D) 64.2℃

Tardigrade Admin · Accepted Answer

(T2/T1)= (λ m1/λ m2)=(1.78/14) T2=(1.78/14) × T1=(1.78/14)(1373 + 273) =209.3K=209.3 -273=-63.7â

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

$62.6℃$

$- 58.9℃$

$- 63.7℃$

$64.2℃$

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

Q. A black body at 1373 ℃ emits maximum energy corresponding to a wavelength of 1.78 microns. The temperature of the moon for which λm​=14 micron would be

62.6℃

−58.9℃

−63.7℃

64.2℃