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

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Modern Physics

Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius

5^{th}

orbit of the electron in

Li^{2 +}

and

He^{+}

(A) $\frac{3}{2}$
(B) $\frac{4}{9}$
(C) $\frac{9}{4}$
(D) $\frac{2}{3}$ ✓ Correct

Answer: (D)

Solution

In the Bohr model the orbital radius is

r_{n} = r_{0} \frac{n ^{2}}{Z}

. For the same orbit

n = 5

, the radius is inversely proportional to the nuclear charge, so

\frac{r _{5} ( Li ^{2 +} )}{r _{5} ( He ^{+} )} = \frac{Z _{H e}}{Z _{L i}} = \frac{2}{3} .

The ratio of the radii is

2/3

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Single correct option

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