The minimum energy required to free the electron from the ground state of the hydrogen atom is: A). $3.4\text{ eV}$ B). less than $3.4\text{ eV}$ C). $13.6\text{ eV}$ D). between $13.6\text{ eV}$ and $3.4\text{ eV}$

The correct answer is $13.6\text{ eV}$. The energy of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is given by:\n\n$$E_n = -\frac{13.6}{n^2}\text{ eV}$$\n\nFor the ground state, $n = 1$. The energy is:\n\n$$E_1 = -13.6\text{ eV}$$\n\nTo free the electron completely, it must be removed to infinity where its energy is $0\text{ eV}$. The minimum energy required (ionization energy) is:\n\n$$E_{\text{required}} = E_\infty - E_1 = 0 - (-13.6\text{ eV}) = \boxed{13.6\text{ eV}}$$ \n\n> The ionization energy is equal to the binding energy of the electron in the ground state.

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