Question

On decreasing the wavelength of incident light from $8000\stackrel{o}{A}$ to $4000\stackrel{o}{A}$. The intensity of the scattered light in Rayleigh scattering will become ___________ times the initial scattered intensity.

• A. $2$
• B. $4$
• C. $16$
• D. $8$

Answer 1

Answer: (C)

$16$

Rayleigh scattering intensity $I\propto \frac{1}{{\lambda }^4}$
$⟹\frac{I_2}{I_1}=\frac{{\lambda }_1^4}{{\lambda }_2^4}$
Or $\frac{I_2}{I_1}=(\frac{8000}{4000}{)}^4=16$
Thus decreasing the wavelength of light by a factor of $2$, Rayleigh scattering become $16$ times the initial scattered intensity.
Correct answer is option C.