Question

What is the significance of negative sign of electronic energy?

Answer 1

It means it is electro-statically bound to the nucleus and one must put energy to pluck it out.

Explanation:

It is just the same as gravitationally bound orbits. Total orbital energy is the sum of kinetic and potential energies.

`E = K + U`

Of these kinetic energy (`K`) is always positive (because of the `v^2` dependence and mass being positive definite)

The potential energy (`U`), for attractive interaction, is always negative.

Depending on which term is dominant, the total orbital energy can be positive, zero or negative.

`E < 0` : Bound orbit (elliptical or circular trajectories).
`E = 0` : Just unbound (parabolic trajectory)
`E > 0` : Unbound orbit (hyperbolic trajectory)

Electronic motion is more complicated and is explained by the rules of quantum mechanics. But still bound electrons have negative "orbital" energy.