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Separation energy of a hydrogen like ion from its third excited state is 2 . 25 times the separation energy of hydrogen atom from its first excited state. Find out the atomic number of this hydrogen like ion.

Correct answer

3

Step-by-step solution

Let the separation energy of the ion be E . Then E = 13 . 6 × Z 2 × 1 16 eV and E H = 13 . 6 × 1 4 eV ⇒ E E H = Z 2 × 4 16 ⇒ 2.25 E H E H = Z 2 4 ⇒ Z 2 = 9 ⇒ Z = 3

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