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What is the energy of the first excited state of hydrogen atom?

What is the energy of the first excited state of hydrogen atom? How high is it above the ground state if the ground state is at −13.61 eV?

Answer:
Well, the ground state is the \(1 s^{1}\) configuration… the first excited state (search \(\text { “H I” }\)) is the \(1 s^{0} 2 p^{1}\) configuration.
What is the energy of the first excited state of hydrogen atom Img 1
The energy for this hydrogen-like atom is given by:
\(E_{n}=-Z^{2} \cdot \frac{13.61 \mathrm{eV}}{n^{2}}\)

where \(Z\) is the atomic number and \(n\) is the energy level of the orbital the electron is in.

\(E_{2}=-1^{2} \cdot \frac{13.61 \mathrm{eV}}{2^{2}}\)
\(=-3.40 \mathrm{eV}\)

[You could have wrongly chosen the \(1 s^{0} 2 s^{1}\) configuration and coincidentally gotten the “right” answer, because to a first approximation \(E_{2 p}=E_{2 s}\) in hydrogen atom.]

How many electrons does hydrogen have? What is its atomic number?

From the reference above,
What is the energy of the first excited state of hydrogen atom Img 2
which says that the first excited state lies \(10.20 \mathrm{eV} \text { above }\) the ground state. And in fact,
What is the energy of the first excited state of hydrogen atom Img 3

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