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The solution to Newton's G1 The theory controlling planetary spin2 Pressure at the centre of the Earth3 Proof of the non-exitence of Dark Matter4 The atom as Newton describes it5
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Rydberg Atom {© 21/10/2017}

This page contains a summary of the formulas and values associated with an atom and its component parts.

The levels of accuracy on this page have been set to assist CalQlata in its effort to establish an accurate value for Newton's gravitational constant (G).
To this end, a great deal of effort has been made by Calqlata to confirm all constants used in these calculations using original formulas and indisputable data where possible.

Constants & Formulas

The constants used on this page can be found in our Constants page.
The symbols used on this page are identified as follows:
n = the electron shell number (1, 2, 3, 4, 5 etc.) counting out from the innermost shell (1s)
Z = atomic number
c = speed of light in a vacuum
v = velocity of electron
λ = the wavelength of an electron
ƒ = the frequency of an electron
t = the orbittal period of an electron
e = elementary charge unit
h = Planck's constant
ħ = Dirac's constant
h = Newton's motion constant
p = momentum of the electron
Rᵧ = Rydberg energy
R = Rydberg constant
R = the orbittal radius of an electron
PE = potential energy
KE = kinetic energy
E = total energy
m₁ = proton mass
m₂ & mₑ = electron mass

Formulas and Properties

The following tables contain the formulas and properties of a ground-state electron in a given shell (n) orbitting a single proton (Z=1)
To calculate the properties of a ground-state electron orbitting more than one proton, you must change 'Z' in the respective formulas to the correct number of protons where appropriate.

ShellKE = Rᵧ.(Z/n)²
= mₑ.R.(2.π/t)²
= mₑ.h² / R³
PE = -2.KE
= -h.ƒ
= -mₑ.v²
E = KE+PE
= -KE
(J)(J)(J)
12.17987197684936E-18-4.35974395369872E-18-2.17987197684936E-18
25.44967994212340E-19-1.08993598842468E-18-5.44967994212340E-19
32.42207997427707E-19-4.84415994855413E-19-2.42207997427707E-19
41.36241998553085E-19-2.72483997106170E-19-1.36241998553085E-19
58.71948790739744E-20-1.74389758147949E-19-8.71948790739744E-20
66.05519993569267E-20-1.21103998713853E-19-6.05519993569267E-20
74.44871832010073E-20-8.89743664020147E-20-4.44871832010073E-20
Kinetic, Potential and Total Energies in an Atom with one Proton and One Electron

 

Shellv = 2.KE / mₑ
= 2.π.R / t
= √[k.Q₁.Q₂ / mₑ.R]
R = aₒ.n² / Zt = v.R
= n.h / 2.Rᵧ
= n³ / 2.Z².c.R
= n³ . [π.aₒ]¹˙⁵ . [16.ε₀.mₑ]² / e
= n.λ / v
(m/s)(m)(s)
12187690.350535515.2917721067E-111.51983047973957E-16
21093845.175267752.11670884268E-101.21586438379166E-15
3729230.116845174.76259489603E-104.10354229529685E-15
4546922.5876338778.46683537072E-109.72691507033327E-15
5437538.0701071021.322943026675E-091.89978809967447E-14
6364615.0584225851.905037958412E-093.28283383623748E-14
7312527.1929336442.592968332283E-095.21301854550674E-14
Orbital Velocities, Radii and Periods

 

Shellh = R.vp = mₑ.v
(m²/s)(kg.m/s)
11.15767587750606E-041.99285239459576E-24
22.31535175501211E-049.96426197297878E-25
33.47302763251817E-046.64284131531919E-25
44.63070351002422E-044.98213098648939E-25
55.78837938753028E-043.98570478919151E-25
66.94605526503633E-043.32142065765959E-25
78.10373114254239E-042.84693199227965E-25
Newton’s Motion Constants and Momenta

 

Shellλ = 2πR / n
= p / h
ƒ = v / λ
(m)(Hz)
13.32491847497602E-106.57968117714912E+15
26.64983694995204E-101.64492029428728E+15
39.97475542492806E-107.31075686349903E+14
41.32996738999041E-094.11230073571820E+14
51.66245923748801E-092.63187247085965E+14
61.99495108498561E-091.82768921587476E+14
72.32744293248321E-091.34279207696921E+14
Electron Wavelengths and Frequencies

 

ShellFg = G.m₁.m₂ / R²
= G.m₁.m₂ / R³.(2.π/t)²
Fₑ = k.Q₁.Q₂ / R².εφ = Fg/Fₑ
= G.m₁ / R.(2.π.R/t)²
= G.m₁ / R.v²
= G.m₁.R / h²
(N)(N)
18.23872204961127E-083.63115175461573E-474.40742111792333E-40
25.14920128100705E-092.26946984663483E-484.40742111792333E-40
31.01712617896435E-094.48290340076016E-494.40742111792333E-40
43.21825080062940E-101.41841865414677E-494.40742111792333E-40
51.31819552793780E-105.80984280738517E-504.40742111792333E-40
66.35703861852722E-112.8018146254751E-504.40742111792333E-40
73.43137111603968E-111.51234975202654E-504.40742111792333E-40
Gravitational and Electrostatic Electron Holding Forces and their ratio (φ)

 

ShellKEn-1/KEn - 1 = [n/(n-1)]² - 1KE₁/KEn - 1 = n² - 1
1
233
31.258
40.77777777815
50.562524
60.4435
70.36111111148
Kinetic Energy Jump Factors Between Shell Numbers (n)
n=1 to n: KEn = KE₁ / n²
n-1 to n: KEn = KEn-1 . [(n-1)/n]²

Coupling Force

There are two principal forces holding an electron to its nucleus; Gravitational and Electrostatic
The gravitational force was defined by Newton's formula:
Fg = G.m₁.m₂ ÷ R² N
The electrostatic force was defined by Coulomb's formula:
Fₑ = k.Q₁.Q₂ ÷ R².ε N
where; ε = εₐ/εₒ = 1 inside an atom
The ratio of these forces is defined Thus:
φ = Fg/Fₑ = 4.40742111792333E-40 (see above Table)
which is a constant

Applying φ to a ground-state electron and a proton we get:
ψ = φ.m₁/m₂ = 2.40035855253320E-43
which is the force coupling factor between both masses
This is not a constant as it varies with the masses concerned.

Further Reading

You will find further reading on this subject in reference publications(55, 60, 61 & 62)

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