Question

The wavelength ${\lambda }_m=5.5\times 10^{-7}m$ corresponds to a temperature of the sun of $5500K$. If the furnace has wavelength ${\lambda }_m$ equal to $11\times 10^{-7}m$, then temperature of furnace is

• A. $5000K$
• B. $1750K$
• C. $3750K$
• D. $2750K$

Answer 1

Answer: (D)

According to Wien's displacement law,
${\lambda }_{m}T=b$ or ${\lambda }_m\propto \frac{1}{T}...(i)$
where, $b$ is Wien's constant, whose value is $2.9\times 10^{-3}mK$
Using the relation given by Eq. (i), we get
$\frac{{\left({\lambda }_m\right)}_s}{{\left({\lambda }_m\right)}_f}=\frac{T_f}{T_s}$
or $T_f=T_s\times \frac{{\left({\lambda }_m\right)}_S}{{\left({\lambda }_m\right)}_f}$
$=5500K\times \frac{\left(5.5\times 10^{-7}m\right)}{\left(11\times 10^{-7}m\right)}=2750K$