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JEE Main 20254 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
4 April
Shift
Morning Shift
Subject
Physics
Chapter
Atomic Physics

JEE Main 2025 · 4 April · Morning Shift · Physics · Atomic Physics

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

Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius 5th 5^{\text{th }} orbit of the electron in Li2+\mathrm{Li}^{2+} and He+\mathrm{He}^{+} is

Options

  1. A32\frac{3}{2}
  2. B49\frac{4}{9}
  3. C94\frac{9}{4}
  4. D23\frac{2}{3}

Correct answer

D. 23\frac{2}{3}

Step-by-step solution

r=r⋅n22\mathrm{r}=\mathrm{r} \cdot \frac{\mathrm{n}^2}{2}
for Li2+\mathrm{Li}^{2+}
r5=r⋅253r_5=r \cdot \frac{25}{3}
for He+\mathrm{He}^{+}
<br/>r5=r⋅252∴rLi2+rHe+=23<br/>\begin{aligned}<br/>& \mathrm{r}_5=\mathrm{r} \cdot \frac{25}{2} \\ & \therefore \frac{\mathrm{r}_{\mathrm{Li}^{2+}}}{\mathrm{r}_{\mathrm{He}^{+}}}=\frac{2}{3}<br/>\end{aligned}
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