Question

A black body has a wavelength of $\lambda$ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be

• A. $\frac{2\lambda }{3}$
• B. $\frac{3\lambda }{2}$
• C. $\frac{4\lambda }{9}$
• D. $\frac{9\lambda }{4}$

Answer 1

The correct option is A $\frac{2\lambda }{3}$

Wien's displacement law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. The characteristic wavelength given is the wavelength with maximum intensity.

$⟹\lambda T=constant$

$⟹\lambda \times 2000K={\lambda }^{\prime }\times 3000K$

$⟹{\lambda }^{\prime }=\frac{2}{3}\lambda$