Q180 / 180 · KCET 2011 · Physics
If the scattering intensity of a liquid is 8 units at a wavelength of $500 \mathrm{~nm}$, then the scattering intensity at a wavelength of $400 \mathrm{~nm}$ will be approximately
- A13 units
- B16 units
- Correct answerC20 units
- D24 units
Solution
Intensity,
$$
\begin{aligned}
&I \propto \frac{1}{\lambda^{4}} \\
&\frac{I_{2}}{I_{1}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right)^{4} \\
&\frac{I_{2}}{I_{1}}=\left(\frac{500}{400}\right)^{4} \cong 2.5 \\
&I_{2}=2.5 I_{1}=2.5 \times 8 \\
&I_{2}=20.5 \approx 20 \text { units }
\end{aligned}
$$
Hence, the correct answer is option: 'C'.