Q. The wavelength $\lambda_{m} = 5.5 \times 10^{- 7}$ m when temperature of sun is 5500 K. If the furnace has wavelength $\lambda_{m}$ equal to $11 \times 10^{- 7}$m, then temperature of furnace is
A) 5000 K
B) 1750 K
C) 3750 K
D) $2750$ K
Explanation
(d) According to Wien’s displacement law,
$\lambda_{m}T = b\ or\ \lambda_{m\ } \propto \frac{1}{T}$
Where $b$ is Wien’s constant whose value is $29 \times 10^{- 3}$ mK
$\frac{{{(\lambda}_{m)}}_{S}}{{(\lambda_{m)}}_{F}} = \ \frac{T_{F}}{T_{S}}$
Or $T_{F}$=$T_{S} \times \frac{{{(\lambda}_{m)}}_{S}}{{(\lambda_{m)}}_{F}}$ = 5500 K$\ \times \ \frac{(5.5 \times 10^{- 7\ }m)}{(11 \times 10^{- 7\ }m)}$
= 2750 K
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.