Q. A black body emits radiations of maximum intensity for the wavelength of 5000$\mathring{\mathrm{A}}$ when the temperature of the body is 1227$℃$. If the temperature of the body is increased by 1000$℃$, the maximum intensity would be observed at
A) 1000$\mathring{\mathrm{A}}$
B) 2000$\mathring{\mathrm{A}}$
C) 5000$\mathring{\mathrm{A}}$
D) 3000$\mathring{\mathrm{A}}$
Explanation
(d) According to Wien’s displacement law,
$\lambda_{m}T = constant$
or $\lambda_{m} \propto \frac{1}{T}$
or $\frac{\left( \lambda_{m} \right)_{1}}{\left( \lambda_{m} \right)_{2}} = \frac{T_{2}}{T_{1}}$
$\therefore$ $\frac{5000}{\left( \lambda_{m} \right)_{2}} = \frac{2227 + 273}{1227 + 273}$
or $\frac{5000}{\left( \lambda_{m} \right)_{2}} = \frac{2500}{1500}$
$\therefore$ $\left( \lambda_{m} \right)_{2} = 3000\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.