If radius of second Bohr orbit of the He + ion is 105 . 8 pm , what is the radius of third Bohr orbit of Li…

According to bohr's model, radius of nth orbit is given by

$$\begin{gathered} {\mathrm{r}}_{\mathrm{n}}={\mathrm{a}}_0\frac{{\mathrm{n}}^2}{\mathrm{Z}} \\ {\mathrm{r}}_{\mathrm{n}}=52.9\frac{{\mathrm{n}}^2}{\mathrm{Z}}\mathrm{in} \mathrm{pm} \\ {\mathrm{a}}_0=52.9\mathrm{pm} \end{gathered}$$

^{$$\begin{gathered} \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{{\mathrm{r}}_{{\mathrm{He}}^{+}}}{{\mathrm{r}}_{{\mathrm{Li}}^{2+}}} \\ \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{n_1^2}{n_2^2}\frac{Z_2}{Z_1} \\ =\frac{2^2}{3^2}\frac{3}{2}=\frac{2}{3} \\ \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{{\mathrm{r}}_{{\mathrm{He}}^{+}}}{{\mathrm{r}}_{{\mathrm{Li}}^{2+}}}=\frac{2}{3} \\ {\mathrm{r}}_{{\mathrm{He}}^{+} } \mathrm{of} \mathrm{second} \mathrm{orbit}=105.8\mathrm{pm} \\ {\mathrm{r}}_{{\mathrm{Li}}^{2+}} \mathrm{of} \mathrm{third} \mathrm{orbit}=\frac{105.8 \mathrm{x} 3}{2}=158.7\mathrm{pm} \end{gathered}$$}