Quantum Leap: Electrons and Instant Movement

[psuedoben]

Electrons can only exist at certain levels of orbit around the nucleus of an atom, meaning that when they leap, they skip the space in between the two orbitals all together. so if they do this instantly, there is no time between the electron being on one level of orbit to the other. I have seen somewhere that mathematically the number .9999... repeating is equivalent to the number 1 because you can't find a number between the two, then is it true that the electron is in two places at once during the leap because you cannot find a time when it is between the two orbitals? (I am aware that electrons are in fact able to exist in multiple places at once)

 

[Quantum Defect]

Electrons can only exist at certain levels of orbit around the nucleus of an atom, meaning that when they leap, they skip the space in between the two orbitals all together. so if they do this instantly, there is no time between the electron being on one level of orbit to the other. I have seen somewhere that mathematically the number .9999... repeating is equivalent to the number 1 because you can't find a number between the two, then is it true that the electron is in two places at once during the leap because you cannot find a time when it is between the two orbitals? (I am aware that electrons are in fact able to exist in multiple places at once)

The "orbits" are from the Bohr model of the Hydrogen atom. From solutions to the Schrödinger Equation, the wave functions for the electron are actually distributed in three dimensions.

 

[psuedoben]

i understand that the bohr model is flawed, but doesn't the same reasoning apply to the 3D model? the electrons move from one of the wave orbitals to another without passing through the space between? its more than likely that I'm wrong, so please point out the flaws in my logic!

 

[Quantum Defect]

i understand that the bohr model is flawed, but doesn't the same reasoning apply to the 3D model? the electrons move from one of the wave orbitals to another without passing through the space between? its more than likely that I'm wrong, so please point out the flaws in my logic!

There is actually spatial overlap in the wave functions. I.e. Look at a picture for the wavefunction of a 1s electron in Hydrogen. It will occupy some of the same space that would be occupied by a 2p electron.

People have modeled the interactions of electrons in atoms with electric fields in real time. There are some very interesting movies of atoms interacting with attosecond laser pulses to model how frequency up-conversion works. You can do the same kind of simulation with simpler electronic transitions.

 

[psuedoben]

ok cool, i studied general chemistry the previous quarter (I'm a freshman in college) so I'm familiar with these types of orbitals, my question is though, when the electrons are energized or emit energy and therefore move to the appropriate electron field, do they "jump" there? or do they move from one to another by following a path?

 

[jtbell]

There is actually spatial overlap in the wave functions. I.e. Look at a picture for the wavefunction of a 1s electron in Hydrogen. It will occupy some of the same space that would be occupied by a 2p electron.

See these diagrams, for example:
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html

 

[jtbell]

do they "jump" there? or do they move from one to another by following a path?

We . don't . know . (gasp! )

The mathematical formalism of QM is silent about what the electron "really really does," "inside" or "underneath" the probability distribution, between observations. That is the province of interpretations of QM. There are a number of interpretations that are consistent with the mathematics and with experimental observations. There is no general agreement about which one is best. It's a field of active research, speculation, and endless discussion in this forum.

 

[psuedoben]

See these diagrams, for example:
http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html

Ok, so what you're saying is that they don't necessarily "jump," their probability wave either just expands or shrinks?

 

[Quantum Defect]

ok cool, i studied general chemistry the previous quarter (I'm a freshman in college) so I'm familiar with these types of orbitals, my question is though, when the electrons are energized or emit energy and therefore move to the appropriate electron field, do they "jump" there? or do they move from one to another by following a path?

It is a bit more complicated than that. I think a better picture is that the wave function "morphs" as the atom changes state.

Here is a video for a simulation of a large porphyrin molecule being excited -- lots of "sloshing" of the electronic wave function!

 

[psuedoben]

It is a bit more complicated than that. I think a better picture is that the wave function "morphs" as the atom changes state.

Here is a video for a simulation of a large porphyrin molecule being excited -- lots of "sloshing" of the electronic wave function!

Ok, that actually makes a lot more sense. That's a very cool visual! It's funny to think of a student's evolution of their understanding of the shape of an atom/position of the electron. First, we learn they're like circles orbiting the nucleus, then they're more oval like and 3D, then we learn that they're probability wave functions.

 

[psuedoben]

We . don't . know . (gasp! )

The mathematical formalism of QM is silent about what the electron "really really does," "inside" or "underneath" the probability distribution, between observations. That is the province of interpretations of QM. There are a number of interpretations that are consistent with the mathematics and with experimental observations. There is no general agreement about which one is best. It's a field of active research, speculation, and endless discussion in this forum.

that makes sense and that's kind of what i figured the answer to my question would be! i think i am limited in that i am attempting to use what i see occur in the world around me to decipher what would happen on the quantum level, but reality is so much different there it doesn't necessarily translate.