Question

A black body has a wavelength of $\lambda$ at temperature $2000K$. Its corresponding wavelength at temperature $3000K$ 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 $\frac{2\lambda }{3}$

By Wien's displacement law, we have:

$\Rightarrow {\lambda }_{max}T=const$

$\Rightarrow \frac{{\lambda }_{max,1}}{{\lambda }_{max,2}}=\frac{T_2}{T_1}=\frac{3}{2}$

On substituting, we get the required wavelength as $\frac{2\lambda }{3}$.