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What is the significance of negative sign of electronic energy?

Answer 1

Isabella Alvarez

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

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.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.