I am wondering how fast electrons travel inside of atomic electron orbitals. Surely there is a range of speeds? Is there a minimum speed? I am not asking about electron movement through a conductor.
Tell me more
×
Physics Stack Exchange is a question and answer site for
active researchers, academics and students of physics. It's 100% free, no registration required.
|
|
So, what about this? "It takes about 150 attoseconds for an electron to circle the nucleus of an atom. An attosecond is $10^{-18}$ seconds long, or, expressed in another way: an attosecond is related to a second as a second is related to the age of the universe," says Johan Mauritsson, an assistant professor in atomic physics at the Faculty of Engineering, Lund University. He is one of seven researchers behind the study, which was directed by him and Professor Anne L'Huillier." Doesn't that give us a defined speed? Or does that make the 'orbit' totally unreliably uncertain? |
|||||
|
|
Please look at http://www.colutron.com/download_files/Quantum.pdf It might be controversal but contains exact solutions and the numbers come out right. |
|||||
|
|
The state of an electron (or electrons) in the atoms isn't an eigenstate of the velocity (or speed) operator, so the speed isn't sharply determined. However, it's very interesting to make an order-of-magnitude estimate of the speed of electrons in the Hydrogen atom (and it's similar for other atoms). The speed $v$ satisfies $$ \frac{mv^2}2\sim \frac{e^2}{4\pi\epsilon_0 r}, \qquad mv\sim \frac{\hbar}{r} $$ The first condition is a virial theorem – the kinetic and potential energies are comparable - while the second is the uncertainty principle. The second one tells you $r\sim \hbar / mv$ which can be substituted to the first one (elimination of $r$) to get (let's ignore $1/2$) $$ mv^2 \sim \frac{e^2 \cdot mv}{4\pi\epsilon_0\hbar},\qquad v \sim \frac{e^2}{4\pi\epsilon_0\hbar c} c = \alpha c $$ so $v/c$, the speed in the units of the speed of light, is equal to the fine-structure constant $\alpha$, approximately $1/137.036$. The smallness of this speed is why the non-relativistic approximation to the Hydrogen atom is so good: the relativistic corrections are suppressed by higher powers of the fine-structure constant! One could discuss how the speed of inner-shell electrons and valence electrons is scaling with $Z$ etc. But the speed $v\sim \alpha c$ would still be the key factor in the formula for the speed. |
|||||||||||||
|
|
This is the realm of quantum mechanics and classical notions about point like electrons travelling at certain speeds don't really apply in this domain. So there isn't an average speed or a minimum speed or even a maximum speed (except for the speed of light which is the maximum speed for any particle with mass). The closest you can come to having any concept of speed for an electron in an orbital would be to apply the Heisenberg uncertainty relation which states that $$\Delta x \Delta p \geqslant \hbar$$ So if you plug the size of the orbital in for $\Delta x $ and solve for $ \Delta p $ you would have an estimate for the uncertainty in the momentum which you could then relate to the uncertainty in speed. |
|||
