JEE Main 2025 Apr 4 Shift 1, Physics Q20: Bohr Model of the Hydrogen Atom

JEE Main2025Apr 4, Shift 1Physics

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

Solution

In the Bohr model for a hydrogen-like ion, $r_{n} = a_{0} \frac{n ^{2}}{Z}$ .

For Li $^{2 +}$ : $Z = 3$ , so $r_{5} (Li^{2 +}) = a_{0} \cdot \frac{25}{3}$ .

For He $^{+}$ : $Z = 2$ , so $r_{5} (He^{+}) = a_{0} \cdot \frac{25}{2}$ .

Ratio: $\frac{r _{5} ( Li ^{2 +} )}{r _{5} ( He ^{+} )} = \frac{25/3}{25/2} = \frac{2}{3}$ .

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