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Working with ionization of Hydrogen atom

Find the maximum wavelength of the photon that a hydrogen atom in its ground state must absorb in order for the ionization to occur.

Solution Preview

Maximum wavelength means minimum frequency (or minimum energy).

The ionization potential of hydrogen atom is 13.6 eV. That is you must give 13.6 eV to an electron in this atom so that it can come out leaving the atom ionized.

Thus the minimum energy that our photon must have is 13.6eV right ?

We will convert ...

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Answer with all mathematical steps and explanations.

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