The calculus of the photon’s mass

Calculus of the cólor mass

According to Newton, the kinetic energy of a particle is . In the other hand, according to Planck’s formula, the energy of electromagnetic wave is quantified in , being f the wave’s frequency and h the constant of Planck. If we equalize both relations, we can calculate the cólor mass, verifying that the velocity v of cólor for this frequency is v = c. Thus, we will write::

; ( 8 )

Then,

( 9 )

which are defined as:

h = 6,6260 x 10^-34 J.s;
f = 5,8928 x 10¹⁴ Hz;
c = 3 x 10⁸ m/s.

Finally, we have obtained:

m =( 2 x 6,62 x 10^-34 x 5,8928 x 10¹⁴ ) / ( 3 x 10⁸)2 = 8,6768 x 10^-36kg

The mass that we have already obtained is a color mass. Thus, as a photon is constituted by two cólores, so, its mass is 2m = 1,7353 x 10^-35kg.

Attesting the consistence between the calculus of the cólor’s energy by Logical Deductions, with E = ½ mc2, and the calculus given by Science, using the Planck’s formula (E = hf)

Using the m value for the cólor´s mass, which we have already obtained, and the value of the Planck’s constant h, we have:
1) to Violet
1 a) by science:

the highest frequency of violet f₁ =7,5000 x 10¹⁴Hz;

Energy E = hf₁;

E = 6,6260 x 10^-19 J.s x 7,5000 x 10¹⁴Hz =
= 4,9695 x 10^-19 J. (1 . a)

1 b) By “Logical Deductions” :

The energy is E = ½ mv’2, where v’ = c + v, being v as the cólor´s tangential velocity of the photon, which is v = 0,818181 x 10⁸ m/s. Then,

E = ½ (8,6769 x 10^-36) x (3 x 10⁸ + 0,818181 x 10⁸)²
= 6,3248 x 10^-19J (1 . b)

2) To the red
2 a) By science:

the lowest frequency of red f₂ = 4,2857 x 10¹⁴ Hz

Energy E = hf₂;

E = 6,6260 x 10^-34 J.s x 4,2857 x 10¹⁴ Hz
= 2,8397 x 10^-19 J (2 . a)

2 b) By “Logical Deductions”:

The energy is E = ½ m(v´)², where v´ = c + v, being v as the cólor´s tangential velocity in the photon, which is v = 0,818181 x 10⁸ m/s. Thus,
E = ½ (8,6769 x 10^-36) x (3 x 10⁸ + 0,818181 x 10⁸)² =
= 2,0652 x 10^-19 J (2 . b)

Conclusion:

The consistence of the values obtained for the cólor´s energy by both Planck’s energy and “Logical Deductions” formulas, based on Newton’s theory, is proved through the results that present the same magnitude order to the Violet energy (1 . a e 1 . b) and to red( 2 . a e 2 . b) as well, which values also give consistence to those one calculated for the cólor mass.The few differences obtained between (1 . a) (1 . b), (2 . a) and (2 . b) were expected, because the “limit” values of the wavelength of visible light are not defined very well, creating an inaccuracy in our results, which its few error margin is already expected.