What is the ratio of the radius of the third stationary orbit of a...

According to Bohr's model, the radius of the $n^{\text{th}}$ stationary orbit of a hydrogen-like species is given by:
$r_n \propto \dfrac{n^2}{Z}$

For the third stationary orbit, $n = 3$ is constant for both ions. Thus, the radius is inversely proportional to the atomic number $Z$.
$r \propto \dfrac{1}{Z}$

For $\text{Li}^{2+}$, $Z = 3$. For $\text{He}^{+}$, $Z = 2$.
The ratio of their radii is:
$\dfrac{r_{\text{Li}^{2+}}}{r_{\text{He}^{+}}} = \dfrac{Z_{\text{He}^{+}}}{Z_{\text{Li}^{2+}}} = \dfrac{2}{3}$

Therefore, the required ratio is $2:3$.

Answer: $2:3$