Question
What does the negative sign of electron energy convey?

Answer

Negative sign for the energy of an electron in any orbit in a hydrogen atom indicates that the energy of the electron in the atom is lower than the energy of a free electron at rest. A free electron at rest is an electron that is infinitely far away from the nucleus and is assigned the energy value of zero.
As the electron gets close to the nucleus, value of ‘n’ decreases and $E_n$​​​​​​​ becomes large in absolute value and more negative. The negative sign corresponds to attractive forces between electron and nucleus.

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