Question

Distribution of intensity of emitted energy as a function of wavelength is shown in the figure. Point $A$ corresponds to the peak wavelength emitted by a body at certain temperature. Find the correct option when the temperature of the body increases.

• A. Intensity of $A$ increases, wavelength decreases
• B. Intensity of $A$ decreases, wavelength decreases
• C. Intensity of $A$ increases, wavelength increases
• D. Intensity of $A$ decreases, wavelength increases

Answer 1

The correct option is A Intensity of $A$ increases, wavelength decreases

We know from Wien's Displacement Law, ${\lambda }_{m}T=b=$constant.
$\Rightarrow {\lambda }_m\propto \frac{1}{T}$
As temperature increases, wavelength decreases.
Also, Intensity, $I=\frac{E}{tA}=\frac{hc}{\lambda tA}$
$\Rightarrow I\propto \frac{1}{\lambda }$
As wavelength decreases, Intensity increases.
Hence, as temperature increases, wavelength decreases and intensity increases.
Option $\left(a\right)$ is correct.