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In Bohr's model I studied that energy of an electron in the $nth$ shell is given by:

$$E_{n}=-13.6 × \frac{Z^2}{n^2} eV.$$

Clearly, the energy of the electron comes out to be negative. But what is the meaning of negative energy? What is its significance? What is the negative sign trying to tell us? Please can someone explain? I am so confused. Please help.

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The electron is bound to the nucleus of the atom, due to it being attracted to its positive charge. This means that to 'release' the electron from the atom, you need to give it energy so that it can overcome this bound state. In other words, the zero on the energy scale is for an electron that is not bound to the nucleus. Therefore, the energy levels are all negative in value.

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    $\begingroup$ I think it should be mentioned that this is a consequence of convention; the energy technically doesn't need to be negative. $\endgroup$
    – BioPhysicist
    Commented Jun 6, 2021 at 16:54

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