A few questions about momentum and energy of electrons in the quantum mechanical model of the electron

Question

I was learning about the quantum model of the electron and how thinking about electrons as standing waves explains orbitals, since certain radii will produce constructive interference and other will produce destructive interference. However, if the circumferences of the energy levels are multiples of the lowest one, does this mean that the De Broglie wavelength of the electron remains constant regardless of energy level, and therefore its magnitude of momentum is constant?

Does this mean that the energy an electron obtains by absorbing a photon does not increase its kinetic energy at all, instead only increasing its electric potential energy as it is pulled farther away from the positive nucleus? Is this need to keep kinetic energy constant why electrons moving between energy levels must absorb specific amounts of energy, whereas electrons escaping a metal through the photoelectric effect or an atom through ionization can absorb any amount of energy above a certain threshold, with the excess becoming kinetic energy?

Would this mean that energy levels are evenly spaced in terms of radius, but the energy needed to move an electron between them decreases as you get farther from the nucleus since the difference in electric potential will diminish as you get further from the nucleus?

Finally, if it is true that the momentum is constant, why? Is there a specific momentum needed? Is it somehow related to the force between the electron and nucleus?

Answer 1

You have a large number of questions that show you are trying to understand quantum mechanical entities in terms of classical physics.

The Bohr model of the atom, the de Broglie wavelength, the Heisenberg uncertainty principle, were developed and led the way to the full quantum mechanical theory, and it is misleading to depend on them now for understanding quantum mechanical systems.

The electrons in their energy levels are not orbiting, they are in orbitals. Orbitals give the probability of finding an electron at a specific (x,y,z) about the center of mass system of the atom. See the possible orbitals of the hydrogen atom here.

These are the basics or quantum mechanics.

The orbitals come from the solutions of the quantum mechanical wave equation where the potential defines the solutions, and the function $Ψ$ gives the probability as $Ψ^*Ψ$, the complex conjugate squared.

Individual free electrons are not waves in space, they are points, as can be seen in the double slit experiment one electron at a time.

What behaves as a wave is the probability , showing the interference pattern of a wave in the accumulation of electrons.

Finally you ask:

if it is true that the momentum is constant, why? Is there a specific momentum needed? Is it somehow related to the force between the electron and nucleus?

It is not the momentum that defines the energy level differences (it has three components) it is the energy of the incoming photon that should be same as the energy difference between two levels so that the atom, note the whole atom, can absorb it and have the electron in a higher energy level orbital.