Question

A black body has wavelength corresponding to the maximum energy equals to ${\lambda }_m$ at $2000\text{K}$. Its corresponding wavelength at $3000\text{K}$ 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

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

Here, ${\lambda }_{m_1}={\lambda }_m,T_1=2000\text{K}$
${\lambda }_{m_2}=?,T_2=3000\text{K}$
According to Wein's displacement law,
${\lambda }_{m_2}{T}_2={\lambda }_{m_1}{T}_1$
${\lambda }_{m_2}={\lambda }_{m_1}\frac{T_1}{T_2}={\lambda }_m\times \frac{2000}{3000}=\frac{2}{3}{\lambda }_m$