Planck's Constant was first recognized by its originator Max Planck in 1900, who initially considered it to be the proportionality constant between the minimal increment of energy, e, of a hypothetical electrically charged oscillator in a cavity that contained black body radiation, and the frequency, [tex]\omega[/tex], of its associated electromagnetic wave. In 1905 Einstein further implemented this relationship by linking it to the energy of the of the electromagnetic wave. The value e, the minimal energy increment of a hypothetical oscillator, was theoretically associated by Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called the photon.

The point under consideration is whether, when such an anomalous definition of the photon is given, namely that it is a wave that behaved in some respects as an electrically neutral particle, were all the permutations and manipulations of the relationship that was Planck's constant justified ?

Where:

e = Energy of a particle,

m = mass of particle

c = Speed of light

h = Planck's constant

[tex]\omega[/tex] = Frequency of light

Einstein's equation : [tex] e = mc^2[/tex]

Planck's equation : [tex] e = h\omega[/tex]

Equating both we get : [tex] mc^2 = h \lambda[/tex]

we know that : [tex]v = \frac {c}{\lambda}[/tex]

[tex]mc^2 = h\frac{c}{\lambda}[/tex]

[tex]mc=\frac{h}{ \lambda}[/tex]

or : [tex] h = {\lambda}{mc}[/tex]

for macroscopic particles v can replace c:

Thus the equation becomes [tex]h = {\lambda}{mv}[/tex]

Now , mv = p ( momentum of particle) and therefore,

De Broglie relation: [tex]h = {\lambda}{p}[/tex]

Notice that these 'equations' only hold good IF the premise of wave/particle duality in the sense of classical wave and a classical particle hold good. If the premise fails then so does the theory and the equation becomes unproductive, since it points to a non-existent relationship.

For instance would it be possible, or even worthwhile, to apply the De Broglie relation to a hyper sonic sound wave such as used in lithotripsy ? These hypersonic sound waves, are definitely waves but they behave like particles in the sense that they possess the ability to break and even shatter stones. Suppose that frequency of the sound is 2 Hz and that the speed of sound is 343m/s

Then the wave-length would be 343/2 = 171.5 m.

so according to De Broglie: [tex] mv = \frac{h}{\lambda}[/tex] = [tex]mv =\frac{6.33 \times 10^{-34}}{171.5}[/tex] =[tex]3.8 \times10^{-36}[/tex]

Dividing by v we find that mass of the sound wave = [tex]1.1\times10^{-38}[/tex] Kg. approx.

Does it make sense, only if it is absolutely essential and you want it to.

What is needed and what unfortunately was never considered, everything being in a state of chaos and excitement was a new type of wave on the lines of the hypersonic waves used in lithotripsy, which incidentally was first introduced only in 1980, decades after all of these conventions including the de Broglie relation were firmly established. What was needed was a new idea, and a new wave, classical waves would never fit the various paradigm that planck's discovery denoted. The inability to come up with a new wave concept has resulted in the acceptance of the De Broglie relation with all its ambiguities and improbabilities.