Question

The maximum emission wavelength at temperature 2000K is $4\mu m$. The maximum wavelength corresponding to temperature 2400K will be

• A. $0.66\times {10}^{-6}$ m
• B. 1 m
• C. $3.33\times {10}^{-6}$ m
• D. ${10}^{-6}$ m

Answer 1

Answer: (C)

$3.33\times {10}^{-6}$ m

According to Wein's displacement law:
$\lambda T=b=constant$
$T_1=2000K$
${\lambda }_1=4\times {10}^{-6}m$
Given that
$T_2=2400K$
${\lambda }_1{T}_1={\lambda }_2{T}_2$
i.e.
${\lambda }_2=\frac{T_1}{T_2}{\lambda }_1=\frac{2000}{2400}\times 4\times {10}^{-6}m=3.33\times {10}^{-6}m$