Discovering Atomic Radii for Isotopes: A Comprehensive Guide

[elas]

So how do you allow for the difference in mass?

 

[damgo]

You use the reduced mass, m_e*m_nucleus/(m_e+m_nucleus) . Since the electron is so much lighter than the nucleus, this is a very small correction; and so the correction for different isotopes is a *very*-small second-order effect. Even for say hydrogen vs. tritium, where it will be most noticeable, you get

hydrogen: m_e*(1-0.00054)
tritium: m_e*(1-0.00018)

 

[elas]

I agree the difference is very small, but I found a method of determining the difference in radius caused by this small difference in mass. When I tried to discover if I had something new I was met with several replies stating that there is no change in radius. I still have not had any authoritive reference for this claim.
Meanwhile I am continueing with my work as I hope other structural relationships will come to light, but all replies are much appreciated,
elas

 

[Alexander]

well, because the difference between psi-function of various isotopes of the same element is in 5-th digit only, make sure that your semi - empirical formula can fetch that far.

 

[Creator]

Originally posted by elas

I seek to explain why element 92 is almost 300 times the mass of element 1 but only three times the size,...

Elas; there are several considerations that need to be addressed in trying to develope an empirical formula for atomic size, which make it almost prohibitive.

Ist, element 92, for example, has 92 positive charges accelerating each electron, which, you would think, should actually shrink the orbits. However, there is something else that you forgot to take into account.
There is something called "shielding".

This, in effect, is due to successive 'layers' of electron orbitals at various distances from the nucleus. The innermost electrons actually 'shield' successive outer electrons from the full electrostatic effect of the nucleus. This effect, the combined effect(and its magnitude) is probably the hardest thing to quantify especially at higher atomic numbers.

Creator

 

[elas]

I very much appreciate the advise particularly from those with professional training in Particle Physics. I have taken an amateur interest in cosmology for many years. As a follow on from this I ended up dealing with the question of the structure of fundamental particles; in the belief that the closer one reaches back to the beginning the simpler the problem should be, and the simple problems are all I can manage.
There is a very simple system for finding the radii (if they exist)of elements and isotopes, and I intend to finish finding them and then look to see if I can go any further. In this I am encouraged by the lack of firm reference on the subject matter.
Mant thanks
elas

 

[elas]

I have at last found an authoritive quote-

..."However,the nuclear and atomic properties of isotopes can be different. The electronic energy levels of an atom depend upon the nuclear mass. Thus corresponding atomic levels of isotopes are slightly shifted relative to each other."
(From an ancient science encyclopedia in our ancient library)

My method reveals the amount of shift per nucleon added or removed in terms of mass and radius. If anyone is aware of such a method already in existence I would like to have the details, otherwise you are going to be bored with my amateur version in the near future.

 

[elas]

Please go to "Vacuum force model in "theory Developement