Question

Why potential energy and total energy of an electron is taken as negative while it's kinetic energy as positive

Answer 1

Actually the electrostatic potential energy of a stationary electron at the infinite distance from the nucleus is taken as zero and as the electron approaches towards the nucleus, the electrostatic attraction is in the same direction as the motion, which means the potential energy of the electron starts to decrease so lesser than zero that make it negative.

Now, if the electron just “fell” straight in toward the nucleus, it would gain kinetic energy and the total energy (potential plus kinetic) would stay zero. But some of that kinetic energy gets lost to photons emitted by the atom as the electron drops into lower and lower orbitals and its total energy becomes negative.

The electron also has kinetic energy. Kinetic energy can never be negative (because in K.E expression we have squared of velocity which is always positive) and it is smaller in magnitude than the potential energy.