Question

Given that the amplitude A of scattered light is : (A₀) of incident light.

(ii) Directly proportional to the volume (V) of the scattering particle

(iii) Inversely proportional to the distance (r) from the scattered particle

(iv) Depend upon the wavelength ($\lambda$) of the scattered light. then:

• A. $A \propto \frac{1}{\lambda}$
• B. $A \propto \frac{1}{\lambda^{2}}$
• C. $A \propto \frac{1}{\lambda^{3}}$
• D. $A \propto \frac{1}{\lambda^{4}}$

Answer 1

Answer: (B)

$A \propto \frac{1}{\lambda^{2}}$

Answer 2

Let $A = \frac{KA_{0}V\lambda^{x}}{r}$

By substituting the dimension of each quantity in both sides

$\Rightarrow \lbrack L\rbrack = \frac{\lbrack L\rbrack.\lbrack L^{3}\rbrack\lbrack L^{x}\rbrack}{\lbrack L\rbrack}$

$\therefore\lbrack L\rbrack = \lbrack L^{3 + x}\rbrack$; $\Rightarrow 3 + x = 1$ or $x = - 2$

$\therefore A \propto \lambda^{- 2}$