Separation energy of a hydrogen like ion from its third excited state is 2.25 times the separation energy of hydrogen ion from its first excited state. Find out the atomic number of this hydrogen like ion.

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answer is 3.

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Detailed Solution

Let the separation energy of the ion be E. Then $E = 13 .6 \times Z^{2} \times \frac{1}{16} eV and E_{H} = 13 .6 \times \frac{1}{4} eV$
$\Rightarrow \frac{E}{E_{H}} = Z^{2} \times \frac{4}{16} \Rightarrow \frac{2 .25 E_{H}}{E_{H}} = \frac{Z^{2}}{4} \Rightarrow Z^{2} = 9 \Rightarrow Z = 3$

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