Question

A rectangular body has maximum wavelength ${\lambda }_m$ at $2000K$. Its corresponding wavelength at $3000K$ 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 $\frac{2}{3}{\lambda }_m$

According to Wien's law
${\lambda }_m\propto \frac{1}{T}$

The ratio of the change in wavelength is given by:

$\frac{{\lambda }_{m1}}{{\lambda }_{m2}}=\frac{T_2}{T_1}$

${\lambda }_{m2}=\frac{{\lambda }_m\times 2000}{3000}$

When the temperature becomes $3000K$, ${\lambda }_m$ becomes $\frac{2}{3}$ times time initial maximum wavelength of the radiation.