Question

The wavelength $\lambda_{m}=5.5 \times 10^{-7} m$ corresponds to a temperature of the sun of $5500\, K$. 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. $2750\, K$

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}}$
$=5500 K \times \frac{\left(5.5 \times 10^{-7} m \right)}{\left(11 \times 10^{-7} m \right)}=2750\, K$