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scott_alexsk
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Why is the relation between an electrons rest mass inversely proportional to its distance from the nucleus (sp)?
Thanks,
-scott
Thanks,
-scott
scott_alexsk said:Why is the relation between an electrons rest mass inversely proportional to its distance from the nucleus (sp)?
Thanks,
-scott
scott_alexsk said:Really, are you sure? I was just looking up relativistic contraction which was used to explain why mercury is a liquid. The site that I looked at said that because the rest mass increases, since the atom moves faster since it weighs more, the electrons are held more closely to the nueclus causing Mercury to somewhat obtain a nobel gas configuration. This is my own phrasing but the site that I looked at phrased it in the same way that my question is phrased by saying that the distance to the nucleus in inversly proportional to the electron's rest mass.
Thanks,
-scott
What does one mean?scott_alexsk said:Thanks for clearing that up Doc. Now what would your explanation be for the electron getting closer to the nucleus?
I don't think I can do it justice, but here's a handwaving, semi-classical argument that might help. Since the effective mass of the electron increases (it's "relativistic" mass), and since the radius of a Bohr orbit is inversely proportional to the mass of the electron, the average radius of the "orbit" will be smaller.scott_alexsk said:Now what would your explanation be for the electron getting closer to the nucleus?
Mercury atoms are not traveling at relativistic velocities. They are not even vibrating at relativistic velocities. It has to do with the s-electron wave function.scott_alexsk said:the idea is that the relativistic effects caused by the fast speed of the mercury atoms causes somehow, according to several sources, . . .
The s-electron wave functions show a higher probability of being 'in the vicinity' of the nucleus.All s-electrons are affected in this way since they spend appreciable time near the nucleus. The contraction of p-orbitals and particularly d and f-orbitals is somewhat less as the time spent near the nucleus decreases as the orbital angular momentum increases.
As the electrons are pulled closer to the nucleus by this effect, they are stabilized and harder to ionize.
I believe that one will find gravitational forces between electrons and nuclei are insignificant. There is neglible attraction between neutrons (neutral, or no charge), but there is significant coulombic interaction (EM) between protons (+ charge) and electrons (- charge).imaginary said:in heavier atoms.. we see the nucleus is heavier and has charge opposite to that of an electron.. and since all the protons plus the neutron together attract the electron.. the electron faces a larger force on it.. too overcome this gravitaional and electomagnetic interaction.. the electron must have more centrifugal force.. which is obtained by revolving faster.
In gases, molecular speeds are governed by statistical thermodynamics - http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/disfcn.html.By the way does anyone know why heavier molocuels/atoms travel at faster speeds then lighter ones?
By asking this question, you have shown that you really didn't understand the explanation. Go back, and read the first 2 lines in Doc Al's earlier post #8. If there's some part of this that you don't understand, ask.scott_alexsk said:Thanks astronauc,
By the way does anyone know why heavier molocuels/atoms travel at faster speeds then lighter ones?
Please provide the reference (url, or citation). The 'electrons' move faster, not the atom. It is the 'relativistic mass' of the electron which increases with speed.scott_alexsk said:Well no according to one of the articles, the other did not go into much detail, because the rest mass of Mercury is greater it moves faster, . . .
scott_alexsk said:Well I think I understand all but that part of it. Tell me if this interpretation is correct. Because of the high speed of the Mercury atom, the relativistic mass of the electrons increases. As a result the energy those electrons have is no longer adequate to keep them in their current energy state, so they fall back, towards the nucleus, to a lower energy state. Now if this is correct than the only missunderstanding that I need to get through is why heavier atoms travel faster than lighter ones. Gokul, I think I know what you are getting at. When I am referring to heavier atoms, I am implying a heavier rest mass, not heavier relativistic mass. I know that the mass of an atom is not only determined by its speed.
Thanks,
-scott
While the fully filled 6s subshell is itself important, the relativistic correction to the 6s energy is quite significant and is largely responsible for the difference between Hg and its lighter relatives, Zn & Cd.Astronuc said:I need to do some more digging around, but I think the property of mercury has more to do with the pairing and filling of the d and s electrons, particulary the 6s, than it does 'relativistic correction' (or contraction).
scott_alexsk said:Why is the relation between an electrons rest mass inversely proportional to its distance from the nucleus (sp)?
Thanks,
-scott
I now think the above estimate for the relativistic correction is wrong - I didn't consider screening! If I account for screening using Slater's approximation, I get a number closer to 5%. In addition, I now think that, possibly "as important" as this relativistic correction, is the fact the the 6s electrons are very poorly screened by 5d and 4f electrons - the same phenomenon that is responsible for the Lanthanide contraction (and related effects).Gokul43201 said:A rough estimate of this correction is not too hard to do. The number I get says that the energies in Hg are about 30% lower than the non-relativistic estimates.
The inverse proportionality between electron rest mass and nuclear distance is a fundamental concept in the field of quantum mechanics. It describes the relationship between the mass of an electron and its distance from the nucleus of an atom. As the distance between an electron and the nucleus decreases, the electron's rest mass increases, and vice versa.
The inverse proportionality between electron rest mass and nuclear distance is directly related to atomic stability. As the distance between an electron and the nucleus increases, the electron's rest mass decreases, making the atom less stable. Conversely, as the distance decreases, the electron's rest mass increases, making the atom more stable.
The mathematical equation for the inverse proportionality between electron rest mass and nuclear distance is m_e = k/d^2, where m_e is the electron's rest mass, k is a constant, and d is the distance between the electron and the nucleus.
The inverse proportionality between electron rest mass and nuclear distance has a significant impact on the energy levels of an atom. As the distance between the electron and the nucleus changes, the energy levels of the electron also change. This is because the electron's energy is directly related to its rest mass, which is affected by the distance from the nucleus.
The inverse proportionality between electron rest mass and nuclear distance has been extensively studied and verified through various experimental evidence. This includes the observation of the energy levels of electrons in atoms, the calculation of atomic spectra, and the measurement of the radius of an atom. Additionally, the mathematical equations and theories derived from this concept have been consistently accurate in predicting the behavior of atoms and subatomic particles.