Atoms And Nuclei Question 267

Question: Excitation energy of a hydrogen like ion in its excitation state is 40.8 eV. Energy needed to remove the electron from the ion in ground state is

Options:

A) 54.4 eV

B) 13.6eV

C) 40.8 eV

D) 27.2 eV

Show Answer

Answer:

Correct Answer: A

Solution:

  • Excitation energy $ \Delta E=E_{2}-E_{1}=13.6Z^{2} $

$ [ \frac{1}{1^{2}}-\frac{1}{2^{2}} ] $

$ \Rightarrow 40.8=13.6\times \frac{3}{4}\times Z^{2}\Rightarrow ,=2. $

Now required energy to remove the electron from ground state $ =\frac{+13.6Z^{2}}{{{( 1 )}^{2}}}=13.6{{( Z )}^{2}}=54.4eV. $



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