Two oil drops in Millikan’s experiment are falling with terminal velocities in the ration 1:4 The ration of their de-Brogile wave length is

Q: Two oil drops in Millikan’s experiment are falling with terminal velocities in the ration 1:4 The ration
of their de-Brogile wave length is

Sol: $\large v_T \propto r^2 \Rightarrow r \propto \sqrt{v_T}$

$\large \frac{r_1}{r_2} = \sqrt{\frac{v_1}{v_2}} = \frac{1}{2} $

$\large \frac{m_1}{m_2} = \frac{1}{8} $

$\large \frac{\lambda_1}{\lambda_2} = \frac{m_2}{m_1}.\frac{v_2}{v_1} $

$\large \frac{\lambda_1}{\lambda_2} = \frac{8}{1}.\frac{4}{1} $

= 32:1