An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transition. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transition. The ratio of the velocities of the electron in these two orbits is

Number of spectral lines obtained due to transition of electrons from \(n\)th orbit to lower orbit is,
\(\begin{array}{ll} & \mathrm{N}=\frac{\mathrm{n}(\mathrm{n}-1)}{2} \\ \text { I case } & 6=\frac{\mathrm{n}_{1}\left(\mathrm{n}_{1}-1\right)}{2} \\ \Rightarrow & \mathrm{n}_{1}=4 \\ \text { II case } & 3=\frac{\mathrm{n}_{2}\left(\mathrm{n}_{2}-1\right)}{2} \\ \Rightarrow & \mathrm{n}_{2}=3\end{array}\)
Velocity of electron in hydrogen atom in \(n\)th orbit
\[
\begin{aligned}
\mathrm{v}_{\mathrm{n}} & \propto \frac{1}{\mathrm{n}} \\
\frac{\mathrm{v}_{\mathrm{n}}}{\mathrm{v}_{\mathrm{n}}} &=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}} \\
\Rightarrow \quad \frac{\mathrm{v}_{6}}{\mathrm{v}_{3}} &=\frac{3}{4}
\end{aligned}
\]