Question

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

• A. $\frac{3}{2}$
• B. $\frac{4}{9}$
• C. $\frac{9}{4}$
• D. $\frac{2}{3}$

Hint:

The radius of an orbit in the Bohr model depends on the principal quantum number and the atomic number.

Answer 1

The Correct Option is D

1. Radius of the $5^{\text{th}}$ orbit for $\mathrm{Li}^{2+}$: \[ r_{5} = \frac{5^2}{3} a_0 \]
2. Radius of the $5^{\text{th}}$ orbit for $\mathrm{He}^{+}$: \[ r_{5} = \frac{5^2}{2} a_0 \]
3. Ratio of the radii: \[ \frac{r_{\mathrm{Li}^{2+}}}{r_{\mathrm{He}^{+}}} = \frac{2}{3} \]Consequently, the correct answer is (4) $\frac{2}{3}$.