Happy New Year, 2019!
Through time,
van der Waals radius f_osc hf_osc
2 He helium 140 pm 6.351x1013Hz 0.263 eV
empirical radius f_osc hf_osc
2 He helium 120 pm 6.860x1013Hz 0.284 eV
A beam of \(hf_{osc}\) upon a \(He\) atom triggers resonance at \(f_{osc}\). The atom hollows out. Upon collapse, everything inside the hollow is send forward in time.
How to trigger a collapse? A push at \(f_{res}\), from the post "A Shield" and "A \(\Psi\) Gun" dated 31 May 2016.
More material to feed Sci-fi scripts...
Monday, December 31, 2018
Saturday, December 29, 2018
Hollow Metal
From the post "Shaking In The Infra Red" dated 24 Dec 2018, we have for the case of iron, \(Fe\),
metallic bond size of,
\(a_{\psi}=126\,pm\)
from which
\(f_{osc}=c\sqrt{\cfrac{2\pi}{(126*10^{-12})}}=6.6946e13\,Hz\)
If we were to deliver energy by the impact of electrons,
\(I_{osc}=q_e*f_{osc}=1.602176565\text{e-19}*6.6946e13=1.07259\text{e-5}\,A\approx10.7\,\mu A\)
What will happen? What is the nature of \(f_{osc}\) resonance?
And for aluminium \(Al\),
\(f_{osc}=c\sqrt{\cfrac{2\pi}{(143*10^{-12})}}=6.2841e13\,Hz\)
\(I_{osc}=q_e*f_{osc}=1.602176565\text{e-19}*6.2841e13=1.007\text{e-5}\,A\approx10.1\,\mu A\)
metallic bond size of,
\(a_{\psi}=126\,pm\)
from which
\(f_{osc}=c\sqrt{\cfrac{2\pi}{(126*10^{-12})}}=6.6946e13\,Hz\)
If we were to deliver energy by the impact of electrons,
\(I_{osc}=q_e*f_{osc}=1.602176565\text{e-19}*6.6946e13=1.07259\text{e-5}\,A\approx10.7\,\mu A\)
What will happen? What is the nature of \(f_{osc}\) resonance?
And for aluminium \(Al\),
\(f_{osc}=c\sqrt{\cfrac{2\pi}{(143*10^{-12})}}=6.2841e13\,Hz\)
\(I_{osc}=q_e*f_{osc}=1.602176565\text{e-19}*6.2841e13=1.007\text{e-5}\,A\approx10.1\,\mu A\)
Does the metal turn transparent when \(I_{osc}\) passes through it? It is difficult to image the metal turning red hot at such low current level. With a hole in the middle of each constituent atom, the metal may just be hollow.
Good night...
No Prize Getting Close
From the posts "X Ray, Inner Electron Cloud And Just As Shocking" dated 28 May 2016 and "X Ray, Inner Electron Cloud And Just As Shocking TWO" dated 15 Oct 2017, it was mistaken that for copper,
\(N=9\)
That is not true. The inner shell of the copper atom has \(N=10\) electrons surrounding a \(Ar\) nucleus. With \(E_{\beta}=1.39222\dot{A}\)
\(a_{\psi}=\cfrac{E_{\beta}}{N.2\pi}=\cfrac{1.39222\dot{A}}{10*2\pi}=0.02215\dot{A}\)
and,
\(f_{res}=0.061\cfrac{299792458}{0.02215*10^{-10}}=8.2532*10^{18}\)
And
\(I_{res}=q_e*f_{res}=1.602176565∗10^{-19}∗8.2532*10^{18}=1.322\,A\)
Compared to \(1.197\,A\), close enough, but no prize.
If \(N\) could be obtained by SPECULATING about the occupancy of the inner shell of copper, \(ave.E_{\alpha}\) will not be necessary to estimate \(N\). Only \(E_{\beta}\) is involved in the derivation of \(I_{res}\).
Can we be sure that \(N=10\) for copper? No...
\(N=9\)
That is not true. The inner shell of the copper atom has \(N=10\) electrons surrounding a \(Ar\) nucleus. With \(E_{\beta}=1.39222\dot{A}\)
\(a_{\psi}=\cfrac{E_{\beta}}{N.2\pi}=\cfrac{1.39222\dot{A}}{10*2\pi}=0.02215\dot{A}\)
and,
\(f_{res}=0.061\cfrac{299792458}{0.02215*10^{-10}}=8.2532*10^{18}\)
And
\(I_{res}=q_e*f_{res}=1.602176565∗10^{-19}∗8.2532*10^{18}=1.322\,A\)
Compared to \(1.197\,A\), close enough, but no prize.
If \(N\) could be obtained by SPECULATING about the occupancy of the inner shell of copper, \(ave.E_{\alpha}\) will not be necessary to estimate \(N\). Only \(E_{\beta}\) is involved in the derivation of \(I_{res}\).
Can we be sure that \(N=10\) for copper? No...
Tuesday, December 25, 2018
Talking Entanglement
This is wrong,
\(hf_{osc}\) does not return to the space dimension with the collapse of resonance. When \(\psi\) accelerate to light speed near the center of the particle, it is transported to the time dimension. Collision in the time dimension triggers an entanglement event. Such collisions in the time dimension is the cause of entanglement. This damps the oscillations in the particle as energy is lost. After the collision in time, \(hf_{osc}\) returns to the space dimension,
displaced from its location where it first disappeared (the center of of the oscillating particle).
If all these speculation is true, this is how entanglement can be trigger periodically using \(hf_{osc}\). A bombardment of \(hf_{osc}\) replenishes energy loss as impacted \(hf_{osc}\) returning from the time dimension is displaced outside of the oscillating particle. If \(hf_{osc}\) triggers an entanglement event in the time dimension immediately, ie collides with some other particle in the time dimension upon arrival, then entanglement is also periodic.
Loss through displaced \(hf_{osc}\) can be reduced by using a big oscillating particle.
But with whom does \(hf_{osc}\) collide? Another big oscillating particle created at the same time.
So we need, two simultaneous big particles and lots of \(hf_{osc}\). We may also differentiate \(hf_{osc\,c}\), impacting particles that attained light speed inside the big particle and \(hf_{osc\,t}\), particles that returned from the time dimension after triggering an entanglement event.
The frequency at which \(\psi\) is replenished is \(f_r\). When,
\(f_r\gt f_{osc}\)
the big oscillating particle increase in \(\psi\) and \(f_{osc}\) decreases via,
\(f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}\)
because \(a_{\psi}\) increases. When,
\(f_r\lt f_{osc}\)
oscillations may stop and start with every impact and loss of \(hf_{osc}\). When,
\(f_r=f_{osc}\)
and very passing of \(hf_{osc}\) through the center of the oscillating particle, transports one \(hf_{osc}\) (\(hf_{osc}\rightarrow h_{osc\,c}\)) to the time dimension (at a frequency of \(2f_{osc}\)), oscillation is sustain without the oscillating particle growing bigger when the return particle \(hf_{osc\,t}\) is displaced outside of the oscillating particle, ie lost.
We might have \(hf_{osc\,r}\) for returned particles that is retained inside the oscillating particle and \(hf_{osc\,l}\) for returned particles that is lost.
The simplest communication coding will be a burst of entanglements over a clocked period to signal "\(X\)" and none for "\(Y\)". And to add noise resilience, a coded "\(XXYY\)" for the binary "\(1\)" bit and "\(XYXY\)" for the binary "0" bit.
And lastly, \(a_{\psi}\) the size of the particle oscillating at \(f_{osc}\) as governed by,
\(f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}\)
It is possible to change \(f_{osc}\) by changing \(a_{\psi}\) through the bombardment with \(hf_{osc}\) at different \(f_r\); as such \(FM\).
The size of \(hf_{osc}\) is not fixed by \(f_{osc}\). So we have a new parameter \(a_{\psi\,hf}\), the size of \(hf_{osc}\), in addition to \(a_{\psi}\), the size of the oscillating particle. Adjusting \(a_{\psi\,hf}\) can change the fate of the returning \(hf_{osc\,t}\); loss or be retained inside the oscillating particle.
Good day.
Note: \(\psi\) is energy density not energy. \(hf_{osc}\) indicates a certain amount of energy; as \(\psi\) varies, the \(\psi\) ball that contains this amount of energy is of different size. ie \(a_{\psi\,hf}\) varies.
\(hf_{osc}\) does not return to the space dimension with the collapse of resonance. When \(\psi\) accelerate to light speed near the center of the particle, it is transported to the time dimension. Collision in the time dimension triggers an entanglement event. Such collisions in the time dimension is the cause of entanglement. This damps the oscillations in the particle as energy is lost. After the collision in time, \(hf_{osc}\) returns to the space dimension,
displaced from its location where it first disappeared (the center of of the oscillating particle).
If all these speculation is true, this is how entanglement can be trigger periodically using \(hf_{osc}\). A bombardment of \(hf_{osc}\) replenishes energy loss as impacted \(hf_{osc}\) returning from the time dimension is displaced outside of the oscillating particle. If \(hf_{osc}\) triggers an entanglement event in the time dimension immediately, ie collides with some other particle in the time dimension upon arrival, then entanglement is also periodic.
Loss through displaced \(hf_{osc}\) can be reduced by using a big oscillating particle.
But with whom does \(hf_{osc}\) collide? Another big oscillating particle created at the same time.
So we need, two simultaneous big particles and lots of \(hf_{osc}\). We may also differentiate \(hf_{osc\,c}\), impacting particles that attained light speed inside the big particle and \(hf_{osc\,t}\), particles that returned from the time dimension after triggering an entanglement event.
The frequency at which \(\psi\) is replenished is \(f_r\). When,
\(f_r\gt f_{osc}\)
the big oscillating particle increase in \(\psi\) and \(f_{osc}\) decreases via,
\(f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}\)
because \(a_{\psi}\) increases. When,
\(f_r\lt f_{osc}\)
oscillations may stop and start with every impact and loss of \(hf_{osc}\). When,
\(f_r=f_{osc}\)
and very passing of \(hf_{osc}\) through the center of the oscillating particle, transports one \(hf_{osc}\) (\(hf_{osc}\rightarrow h_{osc\,c}\)) to the time dimension (at a frequency of \(2f_{osc}\)), oscillation is sustain without the oscillating particle growing bigger when the return particle \(hf_{osc\,t}\) is displaced outside of the oscillating particle, ie lost.
We might have \(hf_{osc\,r}\) for returned particles that is retained inside the oscillating particle and \(hf_{osc\,l}\) for returned particles that is lost.
The simplest communication coding will be a burst of entanglements over a clocked period to signal "\(X\)" and none for "\(Y\)". And to add noise resilience, a coded "\(XXYY\)" for the binary "\(1\)" bit and "\(XYXY\)" for the binary "0" bit.
And lastly, \(a_{\psi}\) the size of the particle oscillating at \(f_{osc}\) as governed by,
\(f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}\)
It is possible to change \(f_{osc}\) by changing \(a_{\psi}\) through the bombardment with \(hf_{osc}\) at different \(f_r\); as such \(FM\).
The size of \(hf_{osc}\) is not fixed by \(f_{osc}\). So we have a new parameter \(a_{\psi\,hf}\), the size of \(hf_{osc}\), in addition to \(a_{\psi}\), the size of the oscillating particle. Adjusting \(a_{\psi\,hf}\) can change the fate of the returning \(hf_{osc\,t}\); loss or be retained inside the oscillating particle.
Good day.
Note: \(\psi\) is energy density not energy. \(hf_{osc}\) indicates a certain amount of energy; as \(\psi\) varies, the \(\psi\) ball that contains this amount of energy is of different size. ie \(a_{\psi\,hf}\) varies.
A Lower Speed Limit, Lower Energy, Einstein
From the post "Just When You Think \(c\) Is The Last Constant" dated 26 Jun 2015, when considering only one particle instead of \(77\) particles making up one big particle we obtain the value for light speed before adjusting for \(\mu_o\) and \(\varepsilon_{old}\),
\(c=1.42156133\)
if we adjust this value for \(\mu_o\) and \(\varepsilon_{old}\) by taking a short cut,
\(c=77.5871223\) adjusts to \(c_{ adj }=301763665\)
so,
\(c=1.42156133\) adjusts to
\(c_{ adj }=\cfrac{301763665}{77.5871223}*1.42156133=5528953.06\,ms^{-1}\)
This value was one of the early quoted values for light speed.
Does this mean a basic particle \(a_{\psi\,c}\) has a lower light speed limit? If \(a_{\psi\,c}\) does have a lower light speed, this will explain the missing matter in the universe. \(a_{\psi\,c}\) is the dark matter; it simply has not reach us yet for its slower speed. The missing energy is the result of holding out for \(c=299792458\,ms^{-1}\) where in fact it should be \(c=5528953.06\,ms^{-1}\), ie
\(E=mc^2=m*(5528953.06)^2\)
instead of to expect,
\(E=m*(299792458)^2\)
Good night and Merry Christmas...
Note:
\(c_{ adj }=c.\cfrac { 2ln(cosh(3.135009)) }{ 4\pi\times10^{-7} }\)
\(c=1.42156133\)
if we adjust this value for \(\mu_o\) and \(\varepsilon_{old}\) by taking a short cut,
\(c=77.5871223\) adjusts to \(c_{ adj }=301763665\)
so,
\(c=1.42156133\) adjusts to
\(c_{ adj }=\cfrac{301763665}{77.5871223}*1.42156133=5528953.06\,ms^{-1}\)
This value was one of the early quoted values for light speed.
Does this mean a basic particle \(a_{\psi\,c}\) has a lower light speed limit? If \(a_{\psi\,c}\) does have a lower light speed, this will explain the missing matter in the universe. \(a_{\psi\,c}\) is the dark matter; it simply has not reach us yet for its slower speed. The missing energy is the result of holding out for \(c=299792458\,ms^{-1}\) where in fact it should be \(c=5528953.06\,ms^{-1}\), ie
\(E=mc^2=m*(5528953.06)^2\)
instead of to expect,
\(E=m*(299792458)^2\)
Good night and Merry Christmas...
Note:
\(c_{ adj }=c.\cfrac { 2ln(cosh(3.135009)) }{ 4\pi\times10^{-7} }\)
Monday, December 24, 2018
More Red Hot
Here is a table of Van der Waals radii also from https://en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page)
For metals with obtainable data to be compared, measured threshold frequencies for photoelectric effect are about twenty \((\approx 20)\) times higher than the data here. This corresponds to an \(a_{\psi}\) about four hundred \((\approx 20^2)\) times smaller than the radii data presented here; where,
\(f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}\)
Good night
atomic number | symbol | name | van der Waals pm | f_osc (10^14 Hz) | hf_osc eV |
1 | H | hydrogen | 120 | 0.6860 | 0.284 |
2 | He | helium | 140 | 0.6351 | 0.263 |
3 | Li | lithium | 182 | 0.5570 | 0.230 |
4 | Be | beryllium | 153 | 0.6075 | 0.251 |
5 | B | boron | 192 | 0.5423 | 0.224 |
6 | C | carbon | 170 | 0.5763 | 0.238 |
7 | N | nitrogen | 155 | 0.6036 | 0.250 |
8 | O | oxygen | 152 | 0.6095 | 0.252 |
9 | F | fluorine | 147 | 0.6198 | 0.256 |
10 | Ne | neon | 154 | 0.6056 | 0.250 |
11 | Na | sodium | 227 | 0.4988 | 0.206 |
12 | Mg | magnesium | 173 | 0.5713 | 0.236 |
13 | Al | aluminium | 184 | 0.5540 | 0.229 |
14 | Si | silicon | 210 | 0.5186 | 0.214 |
15 | P | phosphorus | 180 | 0.5601 | 0.232 |
16 | S | sulfur | 180 | 0.5601 | 0.232 |
17 | Cl | chlorine | 175 | 0.5681 | 0.235 |
18 | Ar | argon | 188 | 0.5481 | 0.227 |
19 | K | potassium | 275 | 0.4532 | 0.187 |
20 | Ca | calcium | 231 | 0.4944 | 0.204 |
21 | Sc | scandium | 211 | 0.5173 | 0.214 |
22 | Ti | titanium | no data | no data | no data |
23 | V | vanadium | no data | no data | no data |
24 | Cr | chromium | no data | no data | no data |
25 | Mn | manganese | no data | no data | no data |
26 | Fe | iron | no data | no data | no data |
27 | Co | cobalt | no data | no data | no data |
28 | Ni | nickel | 163 | 0.5886 | 0.243 |
29 | Cu | copper | 140 | 0.6351 | 0.263 |
30 | Zn | zinc | 139 | 0.6374 | 0.264 |
31 | Ga | gallium | 187 | 0.5495 | 0.227 |
32 | Ge | germanium | 211 | 0.5173 | 0.214 |
33 | As | arsenic | 185 | 0.5525 | 0.228 |
34 | Se | selenium | 190 | 0.5452 | 0.225 |
35 | Br | bromine | 185 | 0.5525 | 0.228 |
36 | Kr | krypton | 202 | 0.5287 | 0.219 |
37 | Rb | rubidium | 303 | 0.4317 | 0.179 |
38 | Sr | strontium | 249 | 0.4762 | 0.197 |
39 | Y | yttrium | no data | no data | no data |
40 | Zr | zirconium | no data | no data | no data |
41 | Nb | niobium | no data | no data | no data |
42 | Mo | molybdenum | no data | no data | no data |
43 | Tc | technetium | no data | no data | no data |
44 | Ru | ruthenium | no data | no data | no data |
45 | Rh | rhodium | no data | no data | no data |
46 | Pd | palladium | 163 | 0.5886 | 0.243 |
47 | Ag | silver | 172 | 0.5730 | 0.237 |
48 | Cd | cadmium | 158 | 0.5978 | 0.247 |
49 | In | indium | 193 | 0.5409 | 0.224 |
50 | Sn | tin | 217 | 0.5101 | 0.211 |
51 | Sb | antimony | 206 | 0.5236 | 0.217 |
52 | Te | tellurium | 206 | 0.5236 | 0.217 |
53 | I | iodine | 198 | 0.5340 | 0.221 |
54 | Xe | xenon | 216 | 0.5113 | 0.211 |
55 | Cs | caesium | 343 | 0.4058 | 0.168 |
56 | Ba | barium | 268 | 0.4590 | 0.190 |
57 | La | lanthanum | no data | no data | no data |
58 | Ce | cerium | no data | no data | no data |
59 | Pr | praseodymium | no data | no data | no data |
60 | Nd | neodymium | no data | no data | no data |
61 | Pm | promethium | no data | no data | no data |
62 | Sm | samarium | no data | no data | no data |
63 | Eu | europium | no data | no data | no data |
64 | Gd | gadolinium | no data | no data | no data |
65 | Tb | terbium | no data | no data | no data |
66 | Dy | dysprosium | no data | no data | no data |
67 | Ho | holmium | no data | no data | no data |
68 | Er | erbium | no data | no data | no data |
69 | Tm | thulium | no data | no data | no data |
70 | Yb | ytterbium | no data | no data | no data |
71 | Lu | lutetium | no data | no data | no data |
72 | Hf | hafnium | no data | no data | no data |
73 | Ta | tantalum | no data | no data | no data |
74 | W | tungsten | no data | no data | no data |
75 | Re | rhenium | no data | no data | no data |
76 | Os | osmium | no data | no data | no data |
77 | Ir | iridium | no data | no data | no data |
78 | Pt | platinum | 175 | 0.5681 | 0.235 |
79 | Au | gold | 166 | 0.5833 | 0.241 |
80 | Hg | mercury | 155 | 0.6036 | 0.250 |
81 | Tl | thallium | 196 | 0.5368 | 0.222 |
82 | Pb | lead | 202 | 0.5287 | 0.219 |
83 | Bi | bismuth | 207 | 0.5223 | 0.216 |
84 | Po | polonium | 197 | 0.5354 | 0.221 |
85 | At | astatine | 202 | 0.5287 | 0.219 |
86 | Rn | radon | 220 | 0.5066 | 0.210 |
87 | Fr | francium | 348 | 0.4028 | 0.167 |
88 | Ra | radium | 283 | 0.4467 | 0.185 |
89 | Ac | actinium | no data | no data | no data |
90 | Th | thorium | no data | no data | no data |
91 | Pa | protactinium | no data | no data | no data |
92 | U | uranium | 186 | 0.5510 | 0.228 |
93 | Np | neptunium | no data | no data | no data |
94 | Pu | plutonium | no data | no data | no data |
95 | Am | americium | no data | no data | no data |
96 | Cm | curium | no data | no data | no data |
97 | Bk | berkelium | no data | no data | no data |
98 | Cf | californium | no data | no data | no data |
99 | Es | einsteinium | no data | no data | no data |
100 | Fm | fermium | no data | no data | no data |
101 | Md | mendelevium | no data | no data | no data |
102 | No | nobelium | no data | no data | no data |
103 | Lr | lawrencium | no data | no data | no data |
104 | Rf | rutherfordium | no data | no data | no data |
105 | Db | dubnium | no data | no data | no data |
106 | Sg | seaborgium | no data | no data | no data |
107 | Bh | bohrium | no data | no data | no data |
108 | Hs | hassium | no data | no data | no data |
109 | Mt | meitnerium | no data | no data | no data |
110 | Ds | darmstadtium | no data | no data | no data |
111 | Rg | roentgenium | no data | no data | no data |
112 | Cn | copernicium | no data | no data | no data |
113 | Nh | nihonium | no data | no data | no data |
114 | Fl | flerovium | no data | no data | no data |
115 | Mc | moscovium | no data | no data | no data |
116 | Lv | livermorium | no data | no data | no data |
117 | Ts | tennessine | no data | no data | no data |
118 | Og | oganesson | no data | no data | no data |
For metals with obtainable data to be compared, measured threshold frequencies for photoelectric effect are about twenty \((\approx 20)\) times higher than the data here. This corresponds to an \(a_{\psi}\) about four hundred \((\approx 20^2)\) times smaller than the radii data presented here; where,
\(f_{osc}=c\sqrt{\cfrac{2\pi}{a_{\psi}}}\)
Good night
Here, Ball Ball
Can this be so? It is still just one \(\psi\) particle,
where the little insert graph denoted oscillation through the center of the \(psi\) particle/cloud. A larger graph can be found in the post "\(T^4\) Strikes Again" dated 18 Jul 2015 where the first expression for \(f_{osc}\) is derived. The expression used in the previous two posts to tabulate the elemental data is from "Another Resonance Hollow" dated 16 Dec 2018.
\(f_{osc}\) plays the role as resonance frequency of the big particle and the frequency of \(\psi\) around the smaller impact particle, \(hf_{osc}\); both big and small particles are \(\psi\) balls.
If this is so, setting a \(\psi\) particle to oscillating at \(f_o\) can be achieved by colliding it with another of energy \(hf_o\).
\(f_{osc}\) depends on \(a_{\psi}\) directly and the Kelvin temperature is not involved until we consider the change in \(a_{\psi}\) due to temperature. At higher temperature, \(a_{\psi}\) might reduce due to collisions. Here, temperature is as defined in the Kinetic Theory of Gases. This temperature is not explicitly involved in the derivation of \(\psi\).
Even if this is so, how can Fermi levels be measured as a voltage difference using a voltmeter. Why would \(hf_{osc}\) captured by a particle, set into resonance (lasting for ever), as such an energy depletion, shows up as a voltage difference?
Does energy drain = voltage drop? Still, \(f\) as both \(f_{osc}\) and \(hf_{osc}\) is important when two particles collide.
Note: The logic leading to this post was, find \(f_{osc}\), find \(hf_{osc}\), looks like Fermi levels...
This view resolve the need to state zero absolute temperature, that differentiate between Fermi energy and Fermi levels and rising energy states with rising temperature. But, given a particle none is in orbit other than \(\psi\).
where the little insert graph denoted oscillation through the center of the \(psi\) particle/cloud. A larger graph can be found in the post "\(T^4\) Strikes Again" dated 18 Jul 2015 where the first expression for \(f_{osc}\) is derived. The expression used in the previous two posts to tabulate the elemental data is from "Another Resonance Hollow" dated 16 Dec 2018.
\(f_{osc}\) plays the role as resonance frequency of the big particle and the frequency of \(\psi\) around the smaller impact particle, \(hf_{osc}\); both big and small particles are \(\psi\) balls.
If this is so, setting a \(\psi\) particle to oscillating at \(f_o\) can be achieved by colliding it with another of energy \(hf_o\).
\(f_{osc}\) depends on \(a_{\psi}\) directly and the Kelvin temperature is not involved until we consider the change in \(a_{\psi}\) due to temperature. At higher temperature, \(a_{\psi}\) might reduce due to collisions. Here, temperature is as defined in the Kinetic Theory of Gases. This temperature is not explicitly involved in the derivation of \(\psi\).
Even if this is so, how can Fermi levels be measured as a voltage difference using a voltmeter. Why would \(hf_{osc}\) captured by a particle, set into resonance (lasting for ever), as such an energy depletion, shows up as a voltage difference?
Does energy drain = voltage drop? Still, \(f\) as both \(f_{osc}\) and \(hf_{osc}\) is important when two particles collide.
Note: The logic leading to this post was, find \(f_{osc}\), find \(hf_{osc}\), looks like Fermi levels...
This view resolve the need to state zero absolute temperature, that differentiate between Fermi energy and Fermi levels and rising energy states with rising temperature. But, given a particle none is in orbit other than \(\psi\).
Shaking In The Infra Red Crystals
Cont'd from the previous post "Shaking In The Infra Red" dated 24 Dec 2018.
We have covalent radii of the elements of the periodic table, commonly found in crystals.
What about Fermi levels?
Note: The data are derived from https://en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page)
We have covalent radii of the elements of the periodic table, commonly found in crystals.
atomic no. | symbol | name | Covalent (single bond) pm | f_osc (10^14)Hz | _hf eV | Covalent (triple bond) pm | f_osc (10^14)Hz | _hf eV |
1 | H | hydrogen | 38 | 1.2190 | 0.504 | no data | no data | no data |
2 | He | helium | 32 | 1.3284 | 0.549 | no data | no data | no data |
3 | Li | lithium | 134 | 0.6492 | 0.268 | no data | no data | no data |
4 | Be | beryllium | 90 | 0.7921 | 0.328 | 85 | 0.8151 | 0.337 |
5 | B | boron | 82 | 0.8299 | 0.343 | 73 | 0.8795 | 0.364 |
6 | C | carbon | 77 | 0.8564 | 0.354 | 60 | 0.9701 | 0.401 |
7 | N | nitrogen | 75 | 0.8677 | 0.359 | 54 | 1.0226 | 0.423 |
8 | O | oxygen | 73 | 0.8795 | 0.364 | 53 | 1.0322 | 0.427 |
9 | F | fluorine | 71 | 0.8918 | 0.369 | 53 | 1.0322 | 0.427 |
10 | Ne | neon | 69 | 0.9047 | 0.374 | no data | no data | no data |
11 | Na | sodium | 154 | 0.6056 | 0.250 | no data | no data | no data |
12 | Mg | magnesium | 130 | 0.6591 | 0.273 | 127 | 0.6668 | 0.276 |
13 | Al | aluminium | 118 | 0.6918 | 0.286 | 111 | 0.7133 | 0.295 |
14 | Si | silicon | 111 | 0.7133 | 0.295 | 102 | 0.7441 | 0.308 |
15 | P | phosphorus | 106 | 0.7299 | 0.302 | 94 | 0.7751 | 0.321 |
16 | S | sulfur | 102 | 0.7441 | 0.308 | 95 | 0.7710 | 0.319 |
17 | Cl | chlorine | 99 | 0.7553 | 0.312 | 93 | 0.7792 | 0.322 |
18 | Ar | argon | 97 | 0.7630 | 0.316 | 96 | 0.7670 | 0.317 |
19 | K | potassium | 196 | 0.5368 | 0.222 | no data | no data | no data |
20 | Ca | calcium | 174 | 0.5697 | 0.236 | 133 | 0.6516 | 0.269 |
21 | Sc | scandium | 144 | 0.6262 | 0.259 | 114 | 0.7038 | 0.291 |
22 | Ti | titanium | 136 | 0.6444 | 0.266 | 108 | 0.7231 | 0.299 |
23 | V | vanadium | 125 | 0.6721 | 0.278 | 106 | 0.7299 | 0.302 |
24 | Cr | chromium | 127 | 0.6668 | 0.276 | 103 | 0.7404 | 0.306 |
25 | Mn | manganese | 139 | 0.6374 | 0.264 | 103 | 0.7404 | 0.306 |
26 | Fe | iron | 125 | 0.6721 | 0.278 | 102 | 0.7441 | 0.308 |
27 | Co | cobalt | 126 | 0.6695 | 0.277 | 96 | 0.7670 | 0.317 |
28 | Ni | nickel | 121 | 0.6832 | 0.283 | 101 | 0.7477 | 0.309 |
29 | Cu | copper | 138 | 0.6397 | 0.265 | 120 | 0.6860 | 0.284 |
30 | Zn | zinc | 131 | 0.6566 | 0.272 | no data | no data | no data |
31 | Ga | gallium | 126 | 0.6695 | 0.277 | 121 | 0.6832 | 0.283 |
32 | Ge | germanium | 122 | 0.6803 | 0.281 | 114 | 0.7038 | 0.291 |
33 | As | arsenic | 119 | 0.6889 | 0.285 | 106 | 0.7299 | 0.302 |
34 | Se | selenium | 116 | 0.6977 | 0.289 | 107 | 0.7265 | 0.300 |
35 | Br | bromine | 114 | 0.7038 | 0.291 | 110 | 0.7165 | 0.296 |
36 | Kr | krypton | 110 | 0.7165 | 0.296 | 108 | 0.7231 | 0.299 |
37 | Rb | rubidium | 211 | 0.5173 | 0.214 | no data | no data | no data |
38 | Sr | strontium | 192 | 0.5423 | 0.224 | 139 | 0.6374 | 0.264 |
39 | Y | yttrium | 162 | 0.5904 | 0.244 | 124 | 0.6748 | 0.279 |
40 | Zr | zirconium | 148 | 0.6177 | 0.255 | 121 | 0.6832 | 0.283 |
41 | Nb | niobium | 137 | 0.6420 | 0.266 | 116 | 0.6977 | 0.289 |
42 | Mo | molybdenum | 145 | 0.6241 | 0.258 | 113 | 0.7069 | 0.292 |
43 | Tc | technetium | 156 | 0.6017 | 0.249 | 110 | 0.7165 | 0.296 |
44 | Ru | ruthenium | 126 | 0.6695 | 0.277 | 103 | 0.7404 | 0.306 |
45 | Rh | rhodium | 135 | 0.6468 | 0.267 | 106 | 0.7299 | 0.302 |
46 | Pd | palladium | 131 | 0.6566 | 0.272 | 112 | 0.7101 | 0.294 |
47 | Ag | silver | 153 | 0.6075 | 0.251 | 137 | 0.6420 | 0.266 |
48 | Cd | cadmium | 148 | 0.6177 | 0.255 | no data | no data | no data |
49 | In | indium | 144 | 0.6262 | 0.259 | 146 | 0.6219 | 0.257 |
50 | Sn | tin | 141 | 0.6329 | 0.262 | 132 | 0.6541 | 0.271 |
51 | Sb | antimony | 138 | 0.6397 | 0.265 | 127 | 0.6668 | 0.276 |
52 | Te | tellurium | 135 | 0.6468 | 0.267 | 121 | 0.6832 | 0.283 |
53 | I | iodine | 133 | 0.6516 | 0.269 | 125 | 0.6721 | 0.278 |
54 | Xe | xenon | 130 | 0.6591 | 0.273 | 122 | 0.6803 | 0.281 |
55 | Cs | caesium | 225 | 0.5010 | 0.207 | no data | no data | no data |
56 | Ba | barium | 198 | 0.5340 | 0.221 | 149 | 0.6156 | 0.255 |
57 | La | lanthanum | 169 | 0.5781 | 0.239 | 139 | 0.6374 | 0.264 |
58 | Ce | cerium | no data | no data | no data | 131 | 0.6566 | 0.272 |
59 | Pr | praseodymium | no data | no data | no data | 128 | 0.6642 | 0.275 |
60 | Nd | neodymium | no data | no data | no data | no data | no data | no data |
61 | Pm | promethium | no data | no data | no data | no data | no data | no data |
62 | Sm | samarium | no data | no data | no data | no data | no data | no data |
63 | Eu | europium | no data | no data | no data | no data | no data | no data |
64 | Gd | gadolinium | no data | no data | no data | 132 | 0.6541 | 0.271 |
65 | Tb | terbium | no data | no data | no data | no data | no data | no data |
66 | Dy | dysprosium | no data | no data | no data | no data | no data | no data |
67 | Ho | holmium | no data | no data | no data | no data | no data | no data |
68 | Er | erbium | no data | no data | no data | no data | no data | no data |
69 | Tm | thulium | no data | no data | no data | no data | no data | no data |
70 | Yb | ytterbium | no data | no data | no data | no data | no data | no data |
71 | Lu | lutetium | 160 | 0.5941 | 0.246 | 131 | 0.6566 | 0.272 |
72 | Hf | hafnium | 150 | 0.6136 | 0.254 | 122 | 0.6803 | 0.281 |
73 | Ta | tantalum | 138 | 0.6397 | 0.265 | 119 | 0.6889 | 0.285 |
74 | W | tungsten | 146 | 0.6219 | 0.257 | 115 | 0.7007 | 0.290 |
75 | Re | rhenium | 159 | 0.5960 | 0.246 | 110 | 0.7165 | 0.296 |
76 | Os | osmium | 128 | 0.6642 | 0.275 | 109 | 0.7198 | 0.298 |
77 | Ir | iridium | 137 | 0.6420 | 0.266 | 107 | 0.7265 | 0.300 |
78 | Pt | platinum | 128 | 0.6642 | 0.275 | 110 | 0.7165 | 0.296 |
79 | Au | gold | 144 | 0.6262 | 0.259 | 123 | 0.6776 | 0.280 |
80 | Hg | mercury | 149 | 0.6156 | 0.255 | no data | no data | no data |
81 | Tl | thallium | 148 | 0.6177 | 0.255 | 150 | 0.6136 | 0.254 |
82 | Pb | lead | 147 | 0.6198 | 0.256 | 137 | 0.6420 | 0.266 |
83 | Bi | bismuth | 146 | 0.6219 | 0.257 | 135 | 0.6468 | 0.267 |
84 | Po | polonium | no data | no data | no data | 129 | 0.6616 | 0.274 |
85 | At | astatine | no data | no data | no data | 138 | 0.6397 | 0.265 |
86 | Rn | radon | 145 | 0.6241 | 0.258 | 133 | 0.6516 | 0.269 |
87 | Fr | francium | no data | no data | no data | no data | no data | no data |
88 | Ra | radium | no data | no data | no data | 159 | 0.5960 | 0.246 |
89 | Ac | actinium | no data | no data | no data | 140 | 0.6351 | 0.263 |
90 | Th | thorium | no data | no data | no data | 136 | 0.6444 | 0.266 |
91 | Pa | protactinium | no data | no data | no data | 129 | 0.6616 | 0.274 |
92 | U | uranium | no data | no data | no data | 118 | 0.6918 | 0.286 |
93 | Np | neptunium | no data | no data | no data | 116 | 0.6977 | 0.289 |
94 | Pu | plutonium | no data | no data | no data | no data | no data | no data |
95 | Am | americium | no data | no data | no data | no data | no data | no data |
96 | Cm | curium | no data | no data | no data | no data | no data | no data |
97 | Bk | berkelium | no data | no data | no data | no data | no data | no data |
98 | Cf | californium | no data | no data | no data | no data | no data | no data |
99 | Es | einsteinium | no data | no data | no data | no data | no data | no data |
100 | Fm | fermium | no data | no data | no data | no data | no data | no data |
101 | Md | mendelevium | no data | no data | no data | no data | no data | no data |
102 | No | nobelium | no data | no data | no data | no data | no data | no data |
103 | Lr | lawrencium | no data | no data | no data | no data | no data | no data |
104 | Rf | rutherfordium | no data | no data | no data | 131 | 0.6566 | 0.272 |
105 | Db | dubnium | no data | no data | no data | 126 | 0.6695 | 0.277 |
106 | Sg | seaborgium | no data | no data | no data | 121 | 0.6832 | 0.283 |
107 | Bh | bohrium | no data | no data | no data | 119 | 0.6889 | 0.285 |
108 | Hs | hassium | no data | no data | no data | 118 | 0.6918 | 0.286 |
109 | Mt | meitnerium | no data | no data | no data | 113 | 0.7069 | 0.292 |
110 | Ds | darmstadtium | no data | no data | no data | 112 | 0.7101 | 0.294 |
111 | Rg | roentgenium | no data | no data | no data | 118 | 0.6918 | 0.286 |
112 | Cn | copernicium | no data | no data | no data | 130 | 0.6591 | 0.273 |
113 | Nh | nihonium | no data | no data | no data | no data | no data | no data |
114 | Fl | flerovium | no data | no data | no data | no data | no data | no data |
115 | Mc | moscovium | no data | no data | no data | no data | no data | no data |
116 | Lv | livermorium | no data | no data | no data | no data | no data | no data |
117 | Ts | tennessine | no data | no data | no data | no data | no data | no data |
118 | Og | oganesson | no data | no data | no data | no data | no data | no data |
What about Fermi levels?
Note: The data are derived from https://en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page)