Where It Isn't

One way to proof the validity of $f_{osc}$ and the associated $I_{osc}=q_e*f_{osc}$ where $q_e$ is the electron charge, is to pass such a current, $I_{osc}$, through a metal whose photoelectric threshold frequency cannot be obtained (usually where the expected threshold frequency is at the edge of the producible light spectrum) during the experiment to obtain the threshold frequency.

In another words, repeat the experiment to obtain $f_{threshold}$ with $I_{osc}$ following through the metal.

To find where there was none...

I Found The Rabbit Hole

This is being thick skin about why $f_{osc}$ is not the photoelectric emission threshold frequency.

This line of best fit has gradient$\rightarrow\infty$ as $x\rightarrow\infty$.  For any such line fitted closer to the origin, it has gradient $\lt\infty$.  "Threshold", the x-intercept of this line is not unique.

This is a line to fit V-I characteristics of a gas discharge tube at the onset of glow discharge,

where $x=log(I)$.  The drop in voltage here is attributed to negative charges created.

This should not be confused with,

$K_{max}=hf-\Phi$

where $K_{max}$ is the maximum kinetic energy of ejected electrons and $\Phi=hf_o$ the Work Function defined by $f_o$, the threshold frequency.   This relation answers the question: "What happens to the excess energy of the photon beyond $\Phi$ after impact?"

Using sodium, $Na$

$f_o=4.39*10^{14}\,Hz$

If we reverse and find $a_{\psi}$ using

$f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}$ --- (*)

with a change in notation,

$f_{hole}=c\sqrt{\cfrac{2\pi}{a_{\psi\,hole}}}$

$a_{\psi\,hole}=2\pi\left(\cfrac{c}{f_{hole}}\right)^2=2.93\text{e-}12\,m$

What is this small hole?

Could it be that $f_{osc}$ of sodium, opens up this small hole and subsequent photons that falls into it, is split into two parts,

$K_{max}=hf-\Phi$

$\Phi=hf_{hole}$, $f$ is the frequency of the impacting photons and $K_{max}$ is the maximum kinetic energy of the ejected particles.  $f_{osc}$ of sodium is given by,

$f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi\,Na}}}$

where $a_{\psi\,Na}$ is the size of sodium $\psi$ cloud.

$f_{osc}$ opens up a hole denoted by $a_{\psi\,hole}$, and all photons at greater size than $a_{\psi\,hole}$ (lower frequency than $f_{hole}$, as indicated by (*)) are rejected by the hole.  If this is the role of $f_{osc}$, then using a narrow bandwidth of photons at $f_{osc}$ and illuminating the metal with photons at bigger size than $a_{hole}$ will cause the metal to appear very bright and without the emission of charged particles.  All illuminating photons is rejected by the hole opened by $f_{osc}$.

Photons of size smaller, $a_{\psi}\lt a_{\psi\,hole}$ falls into the hole.  When do such photons return after falling into the hole?  What dictates the size of the hole?  Hole of different sizes could explain the seemingly different processes that occurs simultaneously during photoelectric emission where two $K_{max}$ values were noted.  The post related to this is "More Fodo Effects" dated 04 Jun 2014; two related diagrams are shown below,

Impurities could explain the two $K_{max}s$.

$f_{hole}$ is the threshold frequency.  Given $f_{\psi}$, $a_{\psi}$ can be derived given,

$2\pi a_{\psi}=n\lambda=n\cfrac{c}{f_{\psi}}$

$f_{\psi}=\cfrac{c}{2\pi a_{\psi}}$,  with  $n=1$

but an impacting photon interact through,

$f_{\psi}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}$

when $f_{\psi}\gt f_{hole}$,  $a_{\psi}\lt a_{\psi\,hole}$ and the photon goes through the hole, and its energy is split via,

$K_{max}=hf-\Phi$

$\Phi=hf_{hole}$ and $K_{max}$ is the maximum kinetic energy of a emitted particle.

$f_{osc}$ that triggers $f_{hole}$ is lower than $f_{hole}$.  $f_{hole}$ alone does not cause photoelectric emission.  $f_{osc}$, a frequency below the threshold, has first to create the hole, via a mode of oscillation with resonance at,

$f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}$

where $a_{\psi}$ is the size of the $\psi$ ball.

This hole is in effect, a region of negative energy that minus off energy of subsequent impacting photons of higher frequencies.  Photons of lower frequencies are too big to fit into the hole.  And only the resonance frequency, $f_{osc}$ opens the hole in the metal.

Besides being convoluted, this explanation does not hold $a_{\psi\,hole}$ at all, apart from the exertion that $f_{osc}$ caused it.  It however, allows for many size holes that can account for more than one $K_{max}$ and allows $f_{osc}$ to be different from the threshold frequency.  But charges are still created within the metal at $f_{osc}$ and, higher frequency photons interacting with the holes created can be outside the metal, ie emitted, when they return from the time dimension.

How does $f_{osc}$ create charges?  $f_{osc}$ set the $\psi$ cloud of the atom into resonance and the atom loses its orbiting valence electrons.  And, how a photon of higher energy $f_{\psi}\gt f_{hole}$ ejects a particle of kinetic energy $K_{max}$ after filling in the hole?  The hole requires $E=hf_{hole}$, what remains of the impacting photons with higher energy after making good for the hole is like a torus photon (posts "What Donuts? Dipoles?" and "Torus Photons" dated 29 Dec 2017).

$K_{max}=hf_{\psi}-hf_{hole}$

When the torus photon collapses however, the resulting particle may not have a full unit charge.  It may be a partial charge of size smaller than $a_{\psi\,c}$.

Is $f_{osc}$ valid?

Note:  The previous version of this post has mistaken $f_{osc}\gt f_{o}$  or $f_{hole}$ that was wrong.

Pulling Crystals

This was what I thought of pulling silicon crystal,

and the artifacts that it creates.  This is what I thought that would reduce such ringing artifacts,

$\theta$  for diamond cubic crystals will be,

$OA=OC=\cfrac{3}{4}\sqrt{\cfrac{2}{3}}a$

$OH=\cfrac{1}{4}\sqrt{\cfrac{2}{3}}a$

$\theta=arcsin(\cfrac{OH}{OC})=arcsin(\cfrac{1}{3})=19.47^o$.

where $C$ is at the first layer and is bonded to the next layer of silicon is at $O$.  The next pull does not form up the bond along $OA$, but it is at $19.47^o$ from $O$.  Bonds similar to $CO$ form up else where in the crystal.  After four steps, because $OH=\cfrac{1}{4}AH$, the atom needed at $A$ falls into place.  At each step, a sheet of atoms is shifted into place.

Good night...

Townsend Discharge In Solids

Cont'd from the post "Hollow Metal" dated 29 Dec 2018, if the matter is a gas,  $I_{osc}=q_e*f_{osc}$ might be Townsend discharge, where $q_e=1.602176565\text{e-19}\,C$

A table of $I_{osc}$ for covalent bond is given below.

atomic no.	symbol	name	Covalent  (single bond) pm	f_osc (10^14)Hz	_hf eV	q_e*f_osc A
1	H	hydrogen	38	1.2190	0.504	1.953E-05
2	He	helium	32	1.3284	0.549	2.128E-05
3	Li	lithium	134	0.6492	0.268	1.040E-05
4	Be	beryllium	90	0.7921	0.328	1.269E-05
5	B	boron	82	0.8299	0.343	1.330E-05
6	C	carbon	77	0.8564	0.354	1.372E-05
7	N	nitrogen	75	0.8677	0.359	1.390E-05
8	O	oxygen	73	0.8795	0.364	1.409E-05
9	F	fluorine	71	0.8918	0.369	1.429E-05
10	Ne	neon	69	0.9047	0.374	1.449E-05
11	Na	sodium	154	0.6056	0.250	9.702E-06
12	Mg	magnesium	130	0.6591	0.273	1.056E-05
13	Al	aluminium	118	0.6918	0.286	1.108E-05
14	Si	silicon	111	0.7133	0.295	1.143E-05
15	P	phosphorus	106	0.7299	0.302	1.169E-05
16	S	sulfur	102	0.7441	0.308	1.192E-05
17	Cl	chlorine	99	0.7553	0.312	1.210E-05
18	Ar	argon	97	0.7630	0.316	1.222E-05
19	K	potassium	196	0.5368	0.222	8.600E-06
20	Ca	calcium	174	0.5697	0.236	9.127E-06
21	Sc	scandium	144	0.6262	0.259	1.003E-05
22	Ti	titanium	136	0.6444	0.266	1.032E-05
23	V	vanadium	125	0.6721	0.278	1.077E-05
24	Cr	chromium	127	0.6668	0.276	1.068E-05
25	Mn	manganese	139	0.6374	0.264	1.021E-05
26	Fe	iron	125	0.6721	0.278	1.077E-05
27	Co	cobalt	126	0.6695	0.277	1.073E-05
28	Ni	nickel	121	0.6832	0.283	1.095E-05
29	Cu	copper	138	0.6397	0.265	1.025E-05
30	Zn	zinc	131	0.6566	0.272	1.052E-05
31	Ga	gallium	126	0.6695	0.277	1.073E-05
32	Ge	germanium	122	0.6803	0.281	1.090E-05
33	As	arsenic	119	0.6889	0.285	1.104E-05
34	Se	selenium	116	0.6977	0.289	1.118E-05
35	Br	bromine	114	0.7038	0.291	1.128E-05
36	Kr	krypton	110	0.7165	0.296	1.148E-05
37	Rb	rubidium	211	0.5173	0.214	8.289E-06
38	Sr	strontium	192	0.5423	0.224	8.689E-06
39	Y	yttrium	162	0.5904	0.244	9.459E-06
40	Zr	zirconium	148	0.6177	0.255	9.897E-06
41	Nb	niobium	137	0.6420	0.266	1.029E-05
42	Mo	molybdenum	145	0.6241	0.258	9.999E-06
43	Tc	technetium	156	0.6017	0.249	9.640E-06
44	Ru	ruthenium	126	0.6695	0.277	1.073E-05
45	Rh	rhodium	135	0.6468	0.267	1.036E-05
46	Pd	palladium	131	0.6566	0.272	1.052E-05
47	Ag	silver	153	0.6075	0.251	9.734E-06
48	Cd	cadmium	148	0.6177	0.255	9.897E-06
49	In	indium	144	0.6262	0.259	1.003E-05
50	Sn	tin	141	0.6329	0.262	1.014E-05
51	Sb	antimony	138	0.6397	0.265	1.025E-05
52	Te	tellurium	135	0.6468	0.267	1.036E-05
53	I	iodine	133	0.6516	0.269	1.044E-05
54	Xe	xenon	130	0.6591	0.273	1.056E-05
55	Cs	caesium	225	0.5010	0.207	8.027E-06
56	Ba	barium	198	0.5340	0.221	8.556E-06
57	La	lanthanum	169	0.5781	0.239	9.261E-06
58	Ce	cerium	no data	no data	no data	no data
59	Pr	praseodymium	no data	no data	no data	no data
60	Nd	neodymium	no data	no data	no data	no data
61	Pm	promethium	no data	no data	no data	no data
62	Sm	samarium	no data	no data	no data	no data
63	Eu	europium	no data	no data	no data	no data
64	Gd	gadolinium	no data	no data	no data	no data
65	Tb	terbium	no data	no data	no data	no data
66	Dy	dysprosium	no data	no data	no data	no data
67	Ho	holmium	no data	no data	no data	no data
68	Er	erbium	no data	no data	no data	no data
69	Tm	thulium	no data	no data	no data	no data
70	Yb	ytterbium	no data	no data	no data	no data
71	Lu	lutetium	160	0.5941	0.246	9.518E-06
72	Hf	hafnium	150	0.6136	0.254	9.830E-06
73	Ta	tantalum	138	0.6397	0.265	1.025E-05
74	W	tungsten	146	0.6219	0.257	9.964E-06
75	Re	rhenium	159	0.5960	0.246	9.548E-06
76	Os	osmium	128	0.6642	0.275	1.064E-05
77	Ir	iridium	137	0.6420	0.266	1.029E-05
78	Pt	platinum	128	0.6642	0.275	1.064E-05
79	Au	gold	144	0.6262	0.259	1.003E-05
80	Hg	mercury	149	0.6156	0.255	9.863E-06
81	Tl	thallium	148	0.6177	0.255	9.897E-06
82	Pb	lead	147	0.6198	0.256	9.930E-06
83	Bi	bismuth	146	0.6219	0.257	9.964E-06
84	Po	polonium	no data	no data	no data	no data
85	At	astatine	no data	no data	no data	no data
86	Rn	radon	145	0.6241	0.258	9.999E-06
87	Fr	francium	no data	no data	no data	no data
88	Ra	radium	no data	no data	no data	no data
89	Ac	actinium	no data	no data	no data	no data
90	Th	thorium	no data	no data	no data	no data
91	Pa	protactinium	no data	no data	no data	no data
92	U	uranium	no data	no data	no data	no data
93	Np	neptunium	no data	no data	no data	no data
94	Pu	plutonium	no data	no data	no data	no data
95	Am	americium	no data	no data	no data	no data
96	Cm	curium	no data	no data	no data	no data
97	Bk	berkelium	no data	no data	no data	no data
98	Cf	californium	no data	no data	no data	no data
99	Es	einsteinium	no data	no data	no data	no data
100	Fm	fermium	no data	no data	no data	no data
101	Md	mendelevium	no data	no data	no data	no data
102	No	nobelium	no data	no data	no data	no data
103	Lr	lawrencium	no data	no data	no data	no data
104	Rf	rutherfordium	no data	no data	no data	no data
105	Db	dubnium	no data	no data	no data	no data
106	Sg	seaborgium	no data	no data	no data	no data
107	Bh	bohrium	no data	no data	no data	no data
108	Hs	hassium	no data	no data	no data	no data
109	Mt	meitnerium	no data	no data	no data	no data
110	Ds	darmstadtium	no data	no data	no data	no data
111	Rg	roentgenium	no data	no data	no data	no data
112	Cn	copernicium	no data	no data	no data	no data
113	Nh	nihonium	no data	no data	no data	no data
114	Fl	flerovium	no data	no data	no data	no data
115	Mc	moscovium	no data	no data	no data	no data
116	Lv	livermorium	no data	no data	no data	no data
117	Ts	tennessine	no data	no data	no data	no data
118	Og	oganesson	no data	no data	no data	no data

Apart from the fact that $I_{osc}\approx10^{-6}\,\text{to}\,10^{-5}$, there is no reason to believe that $I_{osc}$ triggers Townsend discharge.

However, if $I_{osc}$ does trigger a discharge, then the negative charges produced during resonance will reduce the measured voltage and increase the current.  The changes in current and voltage are continued only if the resonance is sustained.  This means, the current remains at $I_{osc}$.  Superimposed on this is the effect of created charges that reduces the voltage and increases the current.  The applied voltage is also constant.  Townsend discharge then does not occur unless $I_{osc}$ is achieved first with a specific applied voltage ($V_{osc}$) and maintained at this specific voltage.  As long as there are free charges inside the tube, the tube is conductive.  If this is the case, a discharge tube when subjected to a higher voltage that produces a higher current, $I\gt I_{osc}$, will not glow or arc as there are no free charges in the tube.  This would refute the ionization-avalanche mechanism as the explanation for discharge because this mechanism should also occur at higher voltage.  Does $V_{osc}$ exist for sustained discharge? And that all discharge must pass through $V_{osc}$?

Does this happen in a metal like $Cu$ where a current $I_{osc}=1.025\text{e-05}\,A$ creates more charge carriers?

Maybe...

Note:  no data means no data but its does not mean no information, not including them will be wrong.