1. Tardigrade
  2. Question
  3. Physics
  4. 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.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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.

NTA AbhyasNTA Abhyas 2020Atoms

Solution:

Let the separation energy of the ion be $E$ . Then
$E \, = \, 13.6\times Z^{2}\times \frac{1}{16} \, eV$
and $E_{H}=13.6\times \frac{1}{4} \, eV$
⇒ $\frac{E}{E_{H}}=Z^{2}\times \frac{4}{16}$
⇒ $\frac{2.25 E_{H}}{E_{H}}=\frac{Z^{2}}{4}$
$\Rightarrow Z^{2}=9\Rightarrow Z=3$