Question

A black body has wavelength ${\lambda }_m$ corresponding to maximum energy at 2000 K. Its wavelength corresponding to maximum energy at 3000 K will be : -

• A. $\frac{3}{2}{\lambda }_m$
• B. $\frac{2}{3}{\lambda }_m$
• C. $\frac{16}{81}{\lambda }_m$
• D. $\frac{81}{16}{\lambda }_m$

Answer 1

Answer: (B)

Key Idea: The relation between the wavelength corresponding to maximum intensity of radiation at any temperature is given by Wien's displacement law.
Wien's displacement law is given by
${\lambda }_{m}T=\text{cosntant}$
or ${\lambda }_1{T}_1={\lambda }_2{T}_2$ $or{\lambda }_2={\lambda }_1\left(\frac{T_1}{T_2}\right)$
Here, $T_1=2000K,T_2=3000K,{\lambda }_1=\lambda$
$\therefore {\lambda }_2=\lambda \times \frac{2000}{3000}=\frac{2}{3}\lambda$