We have to calculate the binding energy of the hydrogen atom in the first excited state.

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The allowed energy of the stationary states of the hydrogen atom are given by the equation

The first excited state of the hydrogen atom corresponds to the principal quantum number . Therefore, the energy of the first excited state of hydrogen atom will be

The binding energy by definition is the minimum energy required for making electron from the atom free. The energy of a free electron is zero. Therefore, the binding energy of the first excited state of hydrogen atom will be