Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius \({5}^{\text{th }}\) orbit of th…

In Bohr's model, radius of \( n^\text{th} \) orbit in hydrogen-like atoms is given by:

\[
r_n \propto \frac{n^2}{Z}
\]

So for 5th orbit:

\[
r_5 \propto \frac{25}{Z}
\]

Now,
For Li\(^{2+}\), \( Z = 3 \Rightarrow r \propto \frac{25}{3} \)
For He\(^{+}\), \( Z = 2 \Rightarrow r \propto \frac{25}{2} \)

Taking ratio:

\[
\frac{r_{Li^{2+}}}{r_{He^+}} = \frac{25/3}{25/2} = \frac{2}{3}
\]