Considering the Bohr model of hydrogen like atoms, the ratio of the radius 5^mathrmth$5^{\mathrm{th}}$ orbit of the electron in mathrmLi^2+$\mathrm{Li}^{2+}$ and mathrmHe^+$\mathrm{He}^{+}$ is

### Related Formula Bohr orbit radius expression: r_n propto fracn^2Z$$r_n \propto \frac{n^2}{Z}$$ For a constant orbit index (n = 5$n = 5$): r_5 propto frac1Z$$r_5 \propto \frac{1}{Z}$$ where Z$Z$ is the atomic atomic number identifier. ### Core Logic Identify the atomic values: * For mathrmLi^2+ implies Z_mathrmLi = 3$\mathrm{Li}^{2+} implies Z_{\mathrm{Li}} = 3$ * For mathrmHe^+ implies Z_mathrmHe = 2$\mathrm{He}^{+} implies Z_{\mathrm{He}} = 2$ ### Step 1: Compute Ratio Set up the inverse scaling ratio format: fracr_mathrmLi^2+r_mathrmHe^+ = fracZ_mathrmHeZ_mathrmLi = frac23$$\frac{r_{\mathrm{Li}^{2+}}}{r_{\mathrm{He}^{+}}} = \frac{Z_{\mathrm{He}}}{Z_{\mathrm{Li}}} = \frac{2}{3}$$ ### Pattern Recognition Since orbit numbers are identical, the radius is purely inversely proportional to the atomic nuclear charge Z$Z$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Atoms