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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.

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  • $\begingroup$ Please clarify if the above claim is true. $\endgroup$ – Tejas P Mar 13 '17 at 11:24
  • $\begingroup$ What exactly do you mean by statement like "some quantity is quantized"? $\endgroup$ – Ruslan Mar 13 '17 at 15:03
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In QM, a particle is described by its wavefunction. Each state of the hydrogen atom has a particular wavefunction and a particular energy. Since you can count the number of different wavefunction, the energy is quantized.

It is important to understand that the wavefunction does not tell you where the electron is, it can only tell the probability to find the electron in a certain region. Thus, if you try to locate the electron, you will always get different results. But, if you measure the average distance to the nucleus, your result will approach the bohr radius. Because of this, it looks like the electron is present everywhere in space because the wavefunction is defined everywhere.

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.

So, to answer your question, the electron's energy is quantized in the hydrogen atom. But, you cannot know the position of the particle and its energy with great precision at the same time.

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