Consider the Bohr model of hydrogen like atoms, the ratio of the radius of orbit of the electron in and is [2025]

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Solution

Q.
Consider the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{th}$ orbit of the electron in ${Li}^{2 +}$ and ${He}^{+}$ is [2025]

1 $\frac{3}{2}$

2 $\frac{4}{9}$

3 $\frac{9}{4}$

4 $\frac{2}{3}$

Ans.
(4)

$r = a_{0} \cdot \frac{n^{2}}{Z}$

For ${Li}^{2 +}$ : $r_{5} = a_{0} \cdot \frac{25}{3}$

for ${He}^{+}$ : $r_{5} = a_{0} \cdot \frac{25}{2}$

$∴ \frac{r_{{Li}^{2 +}}}{r_{{He}^{+}}} = \frac{2}{3}$

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