question_answer

The radii of first and second orbit of Helium atom are\[{{r}_{1}}\]and\[{{r}_{2}}\]respectively. The ratio of the velocities of the electrons revolving in their orbits is ___.

Answer:

First orbit	Second orbit
\[{{n}_{1}}=1\]	\[{{n}_{2}}=2\]
\[{{r}_{1}}={{r}_{1}}\]	\[{{r}_{2}}={{r}_{2}}\]
\[{{v}_{1}}:{{v}_{2}}=?\]

 We know that \[mvr=\frac{nh}{2\pi }\] \[\Rightarrow \]\[V=\frac{nh}{2\pi }\times \frac{1}{mr}\]\[\Rightarrow \]\[v\propto \frac{n}{r}\] (\[\because \] ‘h’ and ‘m’ are constants) \[\Rightarrow \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{n}_{1}}}{{{n}_{2}}}\times \frac{{{r}_{2}}}{{{r}_{1}}}\] \[\Rightarrow \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1}{2}\times \frac{{{r}_{2}}}{{{r}_{1}}}=\frac{{{r}_{2}}}{2{{r}_{1}}}\]