Re: Moseley's Plot and equation

["W. Barlow Newbolt" <wnewbolt@liberty.uc.wlu.edu>]

On 5 Apr 1996, ken fox wrote:

> Again I come for help.
>
> The IB Higher level curriculum expects a qualitative understanding of
> Moseley's equation that states:
>
> sqrt f = a(Z-b). 
>
> The plot is interesting and its historical value is clear. For the K series
> b=1 as photons are emited when L or M electrons fall to fill the hole left in
> the K shell. b =1, my reference(Tipler's Modern Physics) tells me as the one
> remaining electron in the K shell seems to "screen" the nucleus so that a
> nucleus Z acts as if it were Z - 1. I think (hope) I understand that.
>
> I ran into trouble by letting my mouth point out that for the L series, where
> the L shell is temporarily lacking an electron, the the value of b = 7.4.
> This value is apparently determined from his plot. One of my brighter
> students,Ben, who hopes to pursue theoretical Physics, argures that by the
> earlier reasoning, the value shouldbe at least 9. He argued it should exceed
> 9 but I could not follow his logic.
>
> I have never taught this part of Physics before and am insecure as the
> dickens. I am enjoying trying to learn it but....  Can anyone help me out
> with a reply forBen?
>
> Thanks in advance.
>
> Ken Fox
> Smoky Hill High School
> 16100 Smoky Hill Rd.
> Aurora, CO. 80015
> 303-693-1700
> ken_fox@shhs1.ccsd.k12.co.us
Unfortunately, life is never quite as simple as we would like. If we were 
to assume that in the L-case we would have the two K electrons near the 
nucleus and also the seven L electrons left when the vacany was created we 
would have (Z-9).  This is where the figure of nine comes from.  The L 
shell electrons do not all have spherially symmetric probability 
distributions, and may not be inside the orbit of the approaching electron
which will fill the vacancy.  For all these reasons the count electrons 
approach doesn't work any more.  Although I don't know what current 
theory and experiment gives, I would expect 7.4 would not be far off.

					Barlow Newbolt
					Washington and Lee