Question

If the scattering intensity of a liquid is $8$ units at a wavelength of $500\, nm$, then the scattering intensity at a wavelength of $400\, nm$ will be approximately

• A. 13 units
• B. 16 units
• C. 20 units
• D. 24 units

Answer 1

Answer: (C)

20 units

Answer 2

Intensity,
$I \propto \frac{1}{\lambda^{4}}$
$\therefore \frac{I_{2}}{I_{1}} =\left(\frac{\lambda_{1}}{\lambda_{2}}\right)^{4}$
$\frac{I_{2}}{I_{1}} =\left(\frac{500}{400}\right)^{4} \cong 2.5$
$I_{2} =2.5 I_{1}=2.5 \times 8$
$I_{2} =20.5 \approx 20$ units