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When someone, who is not a physicist, attempts to understand the relationship of matter to energy, one of the difficulties which encounters it is, what units should be used to give the correct result. Also, the concept of energy not immediately reveals clearly in our minds, what phenomenon summarizes exactly. But the original ambiguity, indeed should not prevent the proper use of the term and the use of mathematical relationships. We have the ability to we use a concept properly, which it is hard to define in the start or because it is general and not clearly defined. This ability, we have with many words and concepts and not only with the energy. A provocative example and with great history is the concept of "truth" or "existence".

An example of calculation of energy (E) and rest mass (M) of the electron, with the most famous equation: E = Μοc2 If at this simple formula we put the mass in kilograms (kg) and the speed of light (c2) in meters per second at the square (m2/s2), then the result will be the energy in Joule units. If a quantity of mass multiplied with speed of light at square thus result an equivalent quantity of energy E=mc2. If the quantity of energy is divided by speed of light at square thus result an equivalent mass m=E/c2

Remind: 1 Joule is equal to 1kgr m2/s2. The 1eV =1,602176462x10-19 Joule and 1Joule = 0,62415097445 x 1019 eV (or 1,6x10-12 erg). Δηλαδή, σύμφωνα με τις μονάδες της φυσικής, 1Joule είναι η δύναμη 1Newton x μετατόπιση 1m. Το 1 Newton ορίζεται ως η δύναμη που πρέπει να εφαρμοστεί σε ένα σώμα μάζας ενός κιλού (1 kg) για να επιταχυνθεί κατά ένα μέτρο ανά δευτερόλεπτο εις το τετράγωνο (1 m/s2).



Eο=Μο c2 → Eee c2

Ee= (9,109389 x10-31 kg) x (8,987551 x1016 m2/s2) = 81,87110 x10-15 J

In eV: 8,187110 x10-14 J x 6,2415097445 x 1018 eV = 510,9993 x103 eV/s (= 0,5109993 MeV/s)


1eV =1,602176462 x10-19 = 1,6021764 x10-12 erg → 1Joule = 6,2415097445 x1018 eV



Mο =Eο/c2 → Me= 81,8711 x 10-15 J / 8,987551 x1016 m2/s2 = 9,109389 x 10-31 kg

Me= (510,9993 x103 eV/s) x (1,6021764 x 10-19 J) / 8,987551 x1016 m2/s2


HOW MANY TIMES "FIT" THE CONSTANT h IN THE ENERGY of an electron. THIS CALCULATION GIVES FREQUENCY (f) That is, how many times the energy of the numerator is greater than the constant h in the denominator (in time 1sec).

f= E/h

fe= Ee / h = 81,8711 x 10-15 J / 6,626069 x10-34 Js = 1,2355909 x 1020 Hz

In units eV: Ee / h = 510,9993 x103 eV/s / 4,1356676 x 10-15 eV sec = 1,2355908 x 1020 Hz



h=E/f =Μc2/f Μe = h fe/c2 = 6,626069 x10-34 J s x 1,2355908 x1020 Hz / 8,987551 x1016 m2/s2 = 8,187110 x 10-14 J / 8,987551 x1016 m2/s2 = 9,109389 x10-31 kg

* In physics, the formula c=fλ for calculation of the frequency and wavelength applies only for electromagnetic waves and photons, which are considered massless.


EQUIVALENT LENGTH "WAVE" of electron λe which called Compton's length.

Since frequency units we can find a length (corresponding) wavelength or a radius (r=c/ω), according to the known relation: λ=c / f → λe = c / fe

λe=2,997924 5 x108 m/s / 1,2355908 x1020 Hz =0,2426308 x10-11m (=2,426308x10-12 m)

The same result is found with formula: λ=h/Μc (Compton's length)

λe = (6,626069 x10-34 Js) / Me c →

λe = (6,626069 x10-34 Js) / (27,30926 x10-23) = 0,24263085 x10-11 m

1m =109 nm | 1nm =10-9 m

0,24263085 x10-11 (x109 nm) = 0,24263085 x10-3 nm

The visible light wavelength: 400 nm to 700 nm (or 4000 - 7000 ≈ 4 x10-7 - 7 x10-7 m). A comparison Compton electron length to the wavelength of visible light:10-7 m/10-12 m. For the electron is about 105 times less.

The length measuring unit Angstrom:

= 0,1nm = 1 10-10 m and micron = 1 10−6 m



λ=h/Μc →Μ=h/cλ =

6,626069 x10-34 / (2,997924 x108 ) (0,2426308 x10-11 )→

Me= 6,626069 x10-34 / 0,7273886 x10-3 = 9,1094 x10-31 kg



6,6260693 x10-34 J sec x 0,62415097445 x 1019 eV = 4,1356676 x 10-15 eV sec (ή eV/Hz)



If per Hz (or for sec) correspond 4,1356676 x 10-15 eV then for 1 eV :

1Hz 1eV / 4,1356676 x10-15 eV = 2,41798929 x1014 Hz (times the quantity h).

 1 eV = 2,41798929 x1014 Hz (times the quantity h)


1eV correspond at frequency n=241,8 THz (where 1THz =1012 Hz)

h =4,1356 x10-15 eV/Hz = 1eV/241,8 THz

1012 Hz=1THz και 1Hz=10-12 THz


Frequency fe of electron in THz: 1,2355908 x 1020 Hz x 10-12 THz = 123559,08 x103 THz

Equivalent mass of energy 1eV

1Joule = 0,62415097445 x 1019 eV 150,919037 x 1031 Hz

1eV = 1,602176462x10-19 J 241,798929 x 1012 Hz  (or 241,798929 THz)

m=E/c2 → 1ev x (1,602176 x 10-19 J) /c2 = 0,178266131 x10-35 kg

The minimal quantity h multiplied by a frequency f is equivalent with a quantity of energy (energy that are bring the electromagnetic waves with the " null " mass of the photons). So as, the mass on the square in speed of the light amounts also with energy, that is to say:


h f = Μ c2 = E  →  Μ = h f / c2  = h /cλ = h / f λ2  or  Μ = Mmin f



With mass M we can find a frequency f and reversely. When we multiply the Planck's constant h  by a minimal frequency 1Hz then results a minimal quantity of energy Emin = h 1Hz. The minimal quantity h on each other frequency f gives us multiples quantity of energy Ε=hf. When on the contrary, we divide the quantity of energy with a certain frequency, then results the minimal quantity of energy h=E/f .

Because the reverse of the frequency is the (periodic) time t = 1/f is also in effect t = h/E.

(!) We do not forget, that in the microscopic dimensions, a mass M does not exist in (stable) situation of rest and we use the measurement in kg for reasons of comprehension and simplification. In the physics, it is known and we should take in our consideration, the type c= f λ is valid for the calculation of frequency and length for the electromagnetic waves only and for the photons, that are considered without mass. However, this aspect does not prevent to we speak with term of frequency, when we observe phenomena of repetition and similar quantities that change multiple or sub-multiple.


We observe, the first useful mathematic relations for the description of structure of the matter and shaping of the mass. A minimal quantity of energy Emin = h 1Hz is connected with a minimal frequency fmin and the largest length λmax=c/fmin. As long as the frequency f increases, also increases the quantity of energy h f and it minimizes the length λ (since c/f and λ=h/M c). In increased frequency and quantity of energy amounts more mass (h fmax / c2 = Mmax). In more much quantity of mass corresponds more quantity of energy and the mass is connected with higher frequency and smaller length. Thus in the theoretical mass of unification (Mplanck =√(h c/G) we find a maximum high frequency fmax, a most quantity of energy Emax and a minimal length λmin.

Without well knowledge of physics we observe:

Emax / c2 = h fmax / c2 = h / c λmin = Mmax



Η ελάχιστη ποσότητα ενέργειας που εκφράζεται μέσω της σταθεράς h (x1Hz) μπορεί να θεωρηθεί σαν το γινόμενο μίας μικρότερης μάζας επί c2 (δηλαδή Mmin c2). Συνεπώς, εάν η ελάχιστη ποσότητα της ενέργειας που εκφράζει η σταθερά h διαιρεθεί με την ταχύτητα του φωτός εις στο τετράγωνο c2 προκύπτει μία ελάχιστη ποσότητα μάζας h/c2 =Mmin sec. (Αν το μαθηματικό αποτέλεσμα θέλουμε να είναι καθαρά μάζα σε μονάδα kg μπορούμε τότε να πολλαπλασιάσουμε το h στον αριθμητή με τη μονάδα μίας ελάχιστης συχνότητας f =1Hz)

Δηλαδή αν στη θέση της ενέργειας E το h*1Hz τότε :

h 1Hz/c2 =Mmin→6,6260693 x10-34 J / 8,9875513 x 1016 m2/sec2 =0,737249 x10-50 kg

► Όπως από την ελάχιστη ποσότητα h προκύπτουν πολλαπλάσιες ποσότητες ενέργειας (E=hf), ισοδύναμα από την ελάχιστη ποσότητα Mmin προκύπτουν πολλαπλάσιες ποσότητες μάζας (M=Mmin f). Κατά συνέπεια, όταν διαιρούμε μία ποσότητα μάζας m με την ελάχιστη ποσότητα Mmin προκύπτει μία συχνότητα της μάζας, όπως αντίστοιχα όταν διαιρούμε μία ποσότητα ενέργειας E με την ελάχιστη ποσότητα h προκύπτει μία συχνότητα για την ποσότητα της ενέργειας

f =Μ / Mmin  ή  Μ / (h/c2 )  και  f =E/h = Μc2 / h


Π.χ. f =Μe/Mmin9,1093897 x10-31 kg / 0,73724967 x10-50kg =12,355908 x1019 Hz Βρίσκουμε το ίδιο αποτέλεσμα όπως με τον τύπο f = E/h

Το h πολλαπλασιασμένο με τη συχνότητα f μας δίνει το ίδιο αποτέλεσμα όσο το m πολλαπλασιασμένο με το c2 , δηλαδή την ίδια ποσότητα ενέργειας:


Μ c2 = h f = E    Μ = h f / c2 Μ = h /cλ  or  Μ = Mmin f




* Το σύμβολο "→" στους τύπους χρησιμοποιείται για το "συνεπάγεται".



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