Q. Excitation energy of a hydrogen like ion in its first excitation state is $40.8\ eV$. Energy needed to remove the electron from the ion in ground state is
A) $54.4\ eV$
B) $13.6\ eV$
C) $40.8\ eV$
D) $27.2\ eV$
Explanation
(a) Excitation energy $\mathrm{\Delta}E = E_{2} - E_{1} = 13.6\ Z^{2}\left\lbrack \frac{1}{1^{2}} - \frac{1}{2^{2}} \right\rbrack$
$\Rightarrow 40.8 = 13.6 \times \frac{3}{4} \times Z^{2} \Rightarrow Z = 2$
Now required energy to remove the electron from ground state $= \frac{+ 13.6Z^{2}}{(1)^{2}} = 13.6(Z)^{2} = 54.4\ eV$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.