Question

An ideal black body emits maximum intensity of radiation of wavelength $5000\dot{A}$ at temperature ${1227}^{o}C$. If its temperature is increased by ${10}^3{}^{o}C$ then the maximum emission wavelength will be:

• A. $5000\dot{A}$
• B. $4000\dot{A}$
• C. $3500\dot{A}$
• D. $3000\dot{A}$

Answer 1

The correct option is D $3000\dot{A}$

According to Wein's displacement law:
$\lambda T=b=constant$
$T_1=1500K$
${\lambda }_1=5000\dot{A}$
Given that temperature increases by ${1000}^{\circ }C$
$T_2=2500K$
${\lambda }_1{T}_1={\lambda }_2{T}_2$
${\lambda }_2=\frac{T_1}{T_2}{\lambda }_1=\frac{1500}{2500}\times 5000=3000\dot{A}$