# Quantization of kinetic and potential energy of electron in H atom

The total energy of electron in an hydrogen atom is quantized.The Bohr radius in the ground state is just an average value of the distance of the electron from the nucleus. This means that the electron can be found closer to the nucleus than the Bohr radius. As the electron comes closer to the nucleus its potential energy decreases and since total energy is quantized, its kinetic energy has to increase. Since the position of electron is not quantized, the kinetic and potential energies of the electron must not be quantized. Is this a valid reasoning?

Is it really the fact that kinetic and potential energies of an electron in the H atom are not quantized?

Thanks for the help.

• Please clarify if the above claim is true. – Tejas P Mar 13 '17 at 11:24
• What exactly do you mean by statement like "some quantity is quantized"? – Ruslan Mar 13 '17 at 15:03

The wavefunction also contains information about the energy of the system. If the electron is in the ground state, its energy will be definite (the Rydberg energy). Since you do not know where the electron is exactly, you cannot compute its energy classicaly. If you try to measure the location of the particle and compute the energy from the position you get, you will not know its kinetic energy because of the Heisenberg uncertainty principle ($\Delta x\Delta p \geq\hbar$). Indeed, if you locate the particle, the uncertainty of its position will be small, but because of the principle, there will be a great uncertainty on its momentum and thus, its kinetic energy. It is possible to measure the energy of a particle with great precision, but because of this same principle, you won't know exactly where the particle is.