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for it to change at the K- edge, and since the normal absorption coefficient is small compared to it, the K-edge in the picture should scarcely be noticeable. Since Bragg had already noted qualitatively that this edge shows strongly Darwin continued that real crystals might fulfill the sharp angle relations so incompletely that only little detached clods scattered at different depths would produce the real reflection, whose weakening would depend on the normal absorption of the rest of the material, so that this latter would be effective for the intensity of reflection. Our above considerations seem to show that the intensity relation corresponds entirely quantitatively with the effect of normal absorption. In investigting this pehenomenon it would next be of interest to consider cases where the jump would be especially high. One calculates the forCu2O cuprite on account of the copper would show a higher jump (7.3) than Cs and I (5.2) but since the light O is present in small amount the intensity at the Cu edge should jump 6.86 fold. The strong intensity drop beyond this edge which the American authors attribute to a very strong Beta line and which makes the measurement of the jump inexact, depends probably on the experimental arrangement and isn't found photographically by Walter.2 {2Under Sommerfeld, who read this, Dr. Ott has started checking these effects quantitatively at the Münchener first. für Theor. Phys.}
A further Testingtheoretically interesting question accompanies the verification of theincreasing accuracy in measuring absorption jumps. We calculate above with a constant scattering coefficient sigma-- as though there were the same number of electrons scattering in the atom before and after the jump. It is to be remembered, though, that the K-electrons undergo a change in scattering power just at the K-edge, as we observe here. The classical scattering theory postulates frequencies high with respect to the characteristic frequency; here we are dealing with one such, part for outside effects. One might directly state that the property of light of knocking K electrons out photoelectrically
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departs suddenly for longer waves-- might not, just as sharply and at the same place, the property of setting them in vibration vanish?-- The two K electrons are for Cu 1/15, for I 1/27 of the total number. A somewhat greater accuracy in measuring the jump than that of Clark and Duane might permit a decision to be made as to whether the K- electrons are suddenly prevented from scattering at the K- edge.
Obviously this absorption phenomenon in which the intensity depends so simply on the absorption coefficients can be used for the investigation of the fine structure of the edge. The result1drawn theoretically that this must depend on the outside {1 x.f.P. 1,125 (1920)} condition of the atom, especially to degree of ionization could be is experimentally verified.2 {2. J. Bergengren ZfP 3, 247(1920 A Lindh ibid 6 303 (1921) also [Dis. Lund 1923]}
For further development it is worth using cases in which the effect for similar atoms is the same and well-defined. This is well fulfilled in a crystal; better for example than for dissolved molecules radiated through paper supports. In case, as is easier, this cr reflecting crystals of any thickness are used as absorption leaves, here also observations for might serve for the investigation of the fine structure of the edge.
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{May 10, 1925 (Linus 2 months old)}
The Canonical Distribution
Let the chance (time chance t/T) that one system be in region i , δq1....δpn be pi(ε) δq1....δpn = piδσi
Let there be N identical systems, with N very large.
At any instant these will be distributed wioth Ni systems in the i th region.
We shall put the following restrictions on the set.
constant total energy
constant number
Nε = Σ Ni εi (1)
N = Σi Ni , and (2)
hence Σ δNi = 0 (3)
The chance of one system being in region δ σi is
pi δσi.
The chance of the first Ni being there is [pi δσi]Ni
The chance of the systems having a given configuration is hence
πi [piδσi]Ni (4)
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2
The chance of knowing one of the identical [?] obtained by [?] is
If we assume dσi = dσ , a constant,
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