# Electron speeds in orbitals

#### condorino

Do electrons in higher energy orbitals move faster than ones in lower energy orbitals?
Maybe there's an easy answer, but I don't know if it's what you were looking for.

The answer is written in the Uncertainty Principle: if you "confine" the "motion" of a particle, then its "momentum" will increase. Now, higher energy of the orbital means that is more bounded to the nucleus, and the probability of finding the electron is a function that drops to zero rapidly: The "Box" that contains the electron is small so its momentum will be high.

#### RonL

Gold Member
Do electrons in higher energy orbitals move faster than ones in lower energy orbitals?
Hello Quantom,
Being as these guys wrecked my old image of electron movement, everyone gets to see my new one. I still can't get any kind of picture in my mind about valance shells, and my hardest thing to see was the single electron, but here is my new thinking.
If I recall correctly the electron has different energy states and on a quantom scale, time and distance all but disappear.

The electromagnetic field at any level is a little springy so at any state, and at any point the electron is actually bumping it's own field, thus creating what is called the cloud (it's everywhere at the same time, if it could be viewed) this constant contact of it's own force causes it to average out all around the nucleus.

What prevents it from hitting the nucleus, might be the average of the magnetic field being converged, but I can't picture what would prevent it's going beyond a certain distance away from the nucleus.

For what it's worth that is what comes to my mind, so anyone can tear it to sherds, I will gain from whatever is said, no matter what.

Thanks
Ron

#### ytuab

Maybe there's an easy answer, but I don't know if it's what you were looking for.

The answer is written in the Uncertainty Principle: if you "confine" the "motion" of a particle, then its "momentum" will increase. Now, higher energy of the orbital means that is more bounded to the nucleus, and the probability of finding the electron is a function that drops to zero rapidly: The "Box" that contains the electron is small so its momentum will be high.
In higher energy orbital, the electrons move slower than in lower energy orbital, do they?

The energy of Helium ion is lower than Hydrogen atom.
The electron of Helium ion is closer to the nucleus by the stronger Coulomb force, So the velocity of the electron is faster than Hydrogen atom.

This difference of the velocity is showed by the difference of "the relativistic energy" between Helium ion and Hydrogen atom.

#### alxm

In higher energy orbital, the electrons move slower than in lower energy orbital, do they?

The energy of Helium ion is lower than Hydrogen atom.
The electron of Helium ion is closer to the nucleus by the stronger Coulomb force, So the velocity of the electron is faster than Hydrogen atom.
That doesn't address the point condorino was making at all. A hydrogen atom and helium ion are different potentials. Naturally the electron will have different energies.

The energy does increase if the electron is confined to a smaller space. That's easily shown from the solution to the hydrogen atom. Keeping the charge the same, the energy scales as $$\frac{1}{a_0^2}$$.

This difference of the velocity is showed by the difference of "the relativistic energy" between Helium ion and Hydrogen atom.
The relativistic energy of an electron is its energy when relativistic momentum is taken into account, i.e. solving the Dirac equation. It has a precise meaning. If you don't know what the term means I suggest you stop using it. It makes no sense to invoke it here.

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#### alxm

The electromagnetic field at any level is a little springy so at any state, and at any point the electron is actually bumping it's own field, thus creating what is called the cloud (it's everywhere at the same time, if it could be viewed) this constant contact of it's own force causes it to average out all around the nucleus.
Electrons do not self-interact.

What prevents it from hitting the nucleus, might be the average of the magnetic field being converged, but I can't picture what would prevent it's going beyond a certain distance away from the nucleus.
Electrons 'hit' the nucleus all the time. (e.g. K-shell capture)

#### ytuab

That doesn't address the point condorino was making at all. A hydrogen atom and helium ion are different potentials. Naturally the electron will have different energies.

The energy does increase if the electron is confined to a smaller space. That's easily shown from the solution to the hydrogen atom. Keeping the charge the same, the energy scales as $$\frac{1}{a_0^2}$$.

The relativistic energy of an electron is its energy when relativistic momentum is taken into account, i.e. solving the Dirac equation. It has a precise meaning. If you don't know what the term means I suggest you stop using it. It makes no sense to invoke it here.
I just said that when the electrons are closer to the nucleus (the energy becomes lower),
the change of the relativistic mass is bigger (this means electrons becomes faster).

Actually, the relativistic correction of energy is more important when the electrons are closer to the nucleus (He +, Li++ is bigger than hydrogen)

#### condorino

I just said that when the electrons are closer to the nucleus (the energy becomes lower),
the change of the relativistic mass is bigger (this means electrons becomes faster).
Of course, higher energy orbitals are less bounded to the nucleus, they have big boxes and are slower. Sorry.

#### alxm

I just said that when the electrons are closer to the nucleus (the energy becomes lower),
And that is wrong. The energy increases if the electrons are closer to the nucleus than in the ground state. The ground state is the lowest-energy state. By definition, but also mathematically provable by the variational theorem.

the change of the relativistic mass is bigger (this means electrons becomes faster).
Uh, no. If their mass is bigger their velocity is slower for a given energy/momentum.

Actually, the relativistic correction of energy is more important when the electrons are closer to the nucleus (He +, Li++ is bigger than hydrogen)
So what? The relativistic correction to the electronic energy for He+ is less than 0.01% You don't know what you're talking about if you're invoking such a minuscule factor as an explanation here. You're side-tracking the discussion.

#### ytuab

And that is wrong. The energy increases if the electrons are closer to the nucleus than in the ground state. The ground state is the lowest-energy state. By definition, but also mathematically provable by the variational theorem.

Uh, no. If their mass is bigger their velocity is slower for a given energy/momentum.

So what? The relativistic correction to the electronic energy for He+ is less than 0.01% You don't know what you're talking about if you're invoking such a minuscule factor as an explanation here. You're side-tracking the discussion.
In the relativistic theory, If the velocity is faster, the mass is bigger. (The Dirac equation contains this effect. (So the velocity is not slower for given energy. Do you know the origin of Dirac equation ? Dirac equation(K-G equation) is made from relativistic momentum and relativistic energy(both contains relativistic mass))

The difference between the energy by Shrodinger equation and experimental value(ground state energy) is bigger in Helium ion(about 0.002ev) than Hydrogen(0.000..).

It is written as follows (in the middle part)

A nucleus with a large charge will cause an electron to have a high velocity (But the total energy becomes lower(By Shrodinger equation). A higher electron velocity means an increased electron relativistic mass, as a result the electrons will be near the nucleus more of the time and thereby contract the radius for small principal quantum numbers

Many of the chemical and physical differences between the 6th Row (Cs-Rn) and the 5th Row (Rb-Xe) arise from the larger relativistic effects for the former. These relativistic effects are particularly large for gold and its neighbors, platinum and mercury.

#### JK423

Gold Member
Suppose we place ena electron in the LHC and we accelerate it.
Say that we "launch it" at t=0. For t>0 we know "exactly" the position of the electron because it follows the classical laws. Ofcourse we have an inaccuracy Δx but its way small compared to the electrons orbit.
Lets say that the electrons wavefunction is Ψ. What will happen?
1)Starting at the point of launch, it will start spreading all the way of the 27km perimeter? That doesnt make sense because then we would have no idea where the electron is.
What is really happening?
2)Ψ is like i.e. a gaussian packet that moves in space with a specific velocity?

#### JK423

Gold Member
Any ideas of whats happening in this case?
If the concept of speed has no meaning in quantum mechanics, then how does an electron move, in classic orbits governed by newtons 2nd law, in the first place?

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