Do Electrons in Higher Energy Orbitals Move Faster Than Those in Lower Ones?

[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..).

Please see the link http://en.wikipedia.org/wiki/Relativistic_quantum_chemistry

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]

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 it`s way small compared to the electron`s orbit.
Let`s 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 doesn`t 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]

Any ideas of what`s 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 Newton`s 2nd law, in the first place?