Probably, your book considers the promotion of the electron to the 5th level. If the value of the energy is correct, consider the exercise solved

I thought so, too

Thank you

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The sign of the answer really depends on the wording of the question, and unfortunately some authors are a little sloppy in the way they word questions. Are they asking for the energy released when an electron falls from the 5th to the 2nd level (which would be positive) or the change in energy of the atom when an electron falls from the 5th to the 2nd level (which would be negative)?

Thank you! I got what you've said ..

so if the question is asking for the released energy, we should take into account that n1 < n2 so the value is positive

and if it's asking about the change in energy, so it depends on the problem "5th to 2nd" or "2nd to 5th", right ?

or I can solve it as I did and take the absolute value if it's about the released energy

*actually I committed a mistake when I translated the question, the author is asking about the released energy but I didn't pay attention for it

Thank you very much