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If the binding energy of an electron in a hydrogen atom is 13.6 eV, then the energy required to remove the electron from the first excited state of Li++ isA.30.6 eVB.13.6 eVC.3.4 eVD.122.4 eV

Question

If the binding energy of an electron in a hydrogen atom is 13.6 eV, then the energy required to remove the electron from the first excited state of Li++ isA.30.6 eVB.13.6 eVC.3.4 eVD.122.4 eV

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Solution

The energy levels of a hydrogen-like atom (an atom or ion with only one electron) are given by the formula:

E = -13.6 Z^2/n^2 eV

where Z is the atomic number and n is the energy level.

For a hydrogen atom (Z=1), the ground state (n=1) energy is -13.6 eV, which is the binding energy given in the question.

For Li++ (Z=3), the first excited state is n=2. Substituting these values into the formula gives:

E = -13.6 * 3^2 / 2^2 = -30.6 eV

The energy required to remove an electron is the absolute value of the energy level, so the energy required is 30.6 eV.

So, the correct answer is A. 30.6 eV.

This problem has been solved

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