Which one of the following is the energy of an electron in the n = 5 level of a hydrogen atom?

Question

Which one of the following is the energy of an electron in the n = 5 level of a hydrogen atom?

BlackTom AI · Accepted Answer

The question asks for the energy of an electron in the n = 5 level of a hydrogen atom.

First, recall the energy formula for a hydrogen atom: E_n = -13.6 eV / n^2. This is the energy of the bound electron relative to zero energy at infinite separation.

Plugging in n = 5 gives E_5 = -13.6 eV / (5^2) = -13.6 eV / 25 = -0.544 eV.

To express this in joules, convert using 1 eV = 1.602 × 10^-19 J: E_5 = -0.544 eV × 1.602 × 10^-19 J/eV ≈ -8.72 × 10^-20 J.

Thus, the energy value in joules is approximately -8.72 × 10^-20 J.

Note on absent answer options: since no list of choices is provided in the prompt, there is no alternative option to compare or evaluate for correctness. The calculation above directly yields the numerical energy value for n = 5 in the hydrogen atom.

Which one of the following is the energy of an electron in the n = 5 level of a hydrogen atom?

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