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JEE Main 2025 (7 Apr, Shift 1) · Energy of the Electron & Energy Levels

Energy of the Electron & Energy Levels question from JEE Main 2025 (7 Apr, Shift 1)

Q10JEE Main 2025 · 7 APR · SHIFT 1Medium

Energy of the Electron & Energy Levels

In a hydrogen like ion, the energy difference between the 22nd excitation energy state and ground is 108.8 eV. The atomic number of the ion is:

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Answer: (c)

  1. Second excited state is n=3n = 3.
  2. ΔE=13.6 Z2(1−19)=12.09 Z2\Delta E = 13.6\,Z^2\left(1 - \frac{1}{9}\right) = 12.09\,Z^2 eV
  3. 12.09 Z2=108.8⇒Z2=9⇒Z=312.09\,Z^2 = 108.8 \Rightarrow Z^2 = 9 \Rightarrow Z = 3
  4. So the answer is (c) 3.
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