KCET · Physics · Waves and Sound
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
- A 13 units
- B 16 units
- C 20 units
- D 24 units
Answer & Solution
Correct Answer
(C) 20 units
Step-by-step Solution
Detailed explanation
Intensity,
\(I \propto \frac{1}{\lambda^{4}} \)
\(\frac{I_{2}}{I_{1}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right)^{4} \)
\(\frac{I_{2}}{I_{1}}=\left(\frac{500}{400}\right)^{4} \cong 2.5 \)
\(I_{2}=2.5 I_{1}=2.5 \times 8 \)
\(I_{2}=20.5 \approx 20 \text { units}\)
\(I \propto \frac{1}{\lambda^{4}} \)
\(\frac{I_{2}}{I_{1}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right)^{4} \)
\(\frac{I_{2}}{I_{1}}=\left(\frac{500}{400}\right)^{4} \cong 2.5 \)
\(I_{2}=2.5 I_{1}=2.5 \times 8 \)
\(I_{2}=20.5 \approx 20 \text { units}\)
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