Sciencemadness Discussion Board

When does an electron have kinetic energy as opposed to potential energy?

dolimitless - 28-6-2009 at 01:01

Do electrons only exhibit potential energy when they are confined a stable electron energy level? I am reviewing Bohr's model of the atom in my textbook and there is an equation that shows the potential energy of an electron in a certain energy level is given by the equation e = - Rhc / n^2. Is there no kinetic energy factor to an electron when it is in a bound state, but only when in an unbound, free state? I am confused.

bquirky - 28-6-2009 at 10:31

im not relly qualified to answer but wouldn't it be that an electron cant really kick around at high speed while its stuck to an atom ?

an electron darting down a CRT tube whould surly have some notable kinetic energy but it isnt draging a whole atom along for the ride.

whereas a bunch of electrons sitting on a charged capacitor plate arnt moving and whould mainly have potential energy


thats my guess :)

hodges - 28-6-2009 at 13:45

When an electron is part of an atom, it is not really "moving" in the classical sense. The old "solar system" model of electrons orbiting the nucleus is not correct. A better model is to imagine the electron "smeared out" over the surface of each orbit.

Since the electron is not moving, it has no kinetic energy. Once the atom is ionized and the electron thus removed, it can then acquire kinetic energy by being accelerated (for example, by an electric field).

Hodges

entropy51 - 28-6-2009 at 15:03

Why would you think that an electron moving with velocity v had no kinetic energy?

The KE in the nth orbit is K.E = mv**2/2 = mZ**2e**4/[8(eps) 2h**2n**2 ]

where eps is the permittivity of free space

Quantum mechanics says that you have to take an average over the wave function to find the expectation value of v, it doesn't say that v = 0

[Edited on 28-6-2009 by entropy51]

[Edited on 28-6-2009 by entropy51]

dolimitless - 28-6-2009 at 16:10

Is the kinetic energy associated with electrons the photon it releases when jumping back to its energy level, and thus assuming a fixed, lower potential energy?

entropy51 - 28-6-2009 at 16:48

The photon energy is the difference in the TOTAL energy of the initial and final states. The total energy is E = K + U, where K = kinetic energy and U = potential energy.

See here https://www.sciencemadness.org/whisper/viewthread.php?tid=12...

This forum is devoted to amateur science, and your questions seem more general and somewhat off topic. You might want to ask general questions at a forum devoted to answering general questions, such as http://www.chemicalforums.com/

[Edited on 29-6-2009 by entropy51]

[Edited on 29-6-2009 by entropy51]

dolimitless - 28-6-2009 at 21:38

Quote: Originally posted by entropy51  
The photon energy is the difference in the TOTAL energy of the initial and final states. The total energy is E = K + U, where K = kinetic energy and U = potential energy.

See here https://www.sciencemadness.org/whisper/viewthread.php?tid=12...

This forum is devoted to amateur science, and your questions seem more general and somewhat off topic. You might want to ask general questions at a forum devoted to answering general questions, such as http://www.chemicalforums.com/

[Edited on 29-6-2009 by entropy51]

[Edited on 29-6-2009 by entropy51]


I am sorry if the "begginings" section of this forum is too accelerated and amatueur for my basic questions. Why would you direct me to another forum? Why would you post a link to a thread advocating a homework section for this website? This is not a homework question. I am a beginner in chemistry and merely had a question.

And you didn't even answer my question as posed by my first post, thanks.

[Edited on 29-6-2009 by dolimitless]

dolimitless - 28-6-2009 at 21:43

So can anybody clairfy for me.... Is there no kinetic energy factor to an electron when it is in a bound state, but only when in an unbound, free state? I am confused. :(

12AX7 - 29-6-2009 at 09:35

In QM, there is neither KE nor PE, only E.

Tim

dolimitless - 29-6-2009 at 12:14

So neither? lol if this is such a basic question, why cant anyone give a straight answer?

entropy51 - 29-6-2009 at 13:54

Quote: Originally posted by 12AX7  
In QM, there is neither KE nor PE, only E.

Tim


That's an interesting point of view. Last I looked the Schrodinger equation contains a term V(r), the potential energy. KE has also not been forgotten in QM.

You might want to refresh your memory of Schrodinger's equation, at Wiki for example. I wasn't able to copy the link to post here.

But the original poster asked the question in the context of the Bohr atom, I do believe.

[Edited on 29-6-2009 by entropy51]

[Edited on 29-6-2009 by entropy51]

chemrox - 29-6-2009 at 15:07

An electron always has kinetic energy. When it ceases to have kinetic energy it ceases to be an electron. This is so fucking obvious I shouldn't have to post it.

[Edited on 29-6-2009 by chemrox]

PainKilla - 29-6-2009 at 15:52

If you are approaching Bohr's model, you need to understand the underlying physical principles and assumptions behind this model (not outlined in any real detail here).

Realize that the Bohr model was not developed specifically to explain all aspects of atoms, rather it was developed to explain the emission spectrum of hydrogen (based on the Rydberd formula, which was empirical in nature) - and it worked well for this, but not for the other atoms. The quantization of energy based on the conclusions of Einstein with respect photoelectric effect had Bohr postulate that electrons jump in discrete intervals (hence the energy levels). This also provided a foundation for the discrete spectral lines of hydrogen (and other atoms). The major step forward was the quantization of orbits by making discrete the values of angular momentum that an electron could have.

Read Bohr's original paper for the assumptions taken in his model, but long story short, the kinetic energy is equal to potential energy, because the centripetal velocity of the electron is equal to the Coulombic attraction of the electron and the proton... IE:

electrostatic force = (k*charge1*charge2) / (r^2) , where k is Coulomb's constant and r is radius.

centripetal force = (m*(v^2)) / r , where m is mass, v is velocity, r is radius

and then the actual energies given by:

PE = k*charge1*charge2 / r
and
KE = (1/2)*m*(v^2)

and KE = PE

You can read Bohr's original derivation here.

To answer the thread's original question, an electron will always have kinetic energy in principle, since the Coulombic attraction will exist infinitely far away, just the kinetic energy will be infinitely small.

[Edited on 29-6-2009 by PainKilla]

dolimitless - 29-6-2009 at 19:06

Painkilla, thanks for the great explanation. Cheers to you.

chemrox - 30-6-2009 at 13:02

The above is indeed very nice but I don't understand why anyone would still want to place an electron in a Newtonian framework. Explaining electrons was the beginning of quantum chemistry.

12AX7 - 30-6-2009 at 19:17

Because Bohr did it before QM. It is astonishing that his model manages to produce the correct results.

Tim