It is generally argued that the photoelectric effect provides evidence for the particle nature of light as the photoelectrons are almost released instantaneously when the light hits the detector. This argument is based on the classical wave theory of light and the assumption that a light wave has an energy flux c^.E²/4π where E is the electric field amplitude of the wave and c the speed of light. Using this expression, the energy absorbed by an atom would indeed be so small that it would take about one second for sunlight to release any photoelectrons, contrary to what is observed and hence suggesting that the wave model of light could not explain the photoeffect. However, this conclusion is based on the flawed assumption that the above expression can be assigned to the 'energy flux' of the electromagnetic wave and in fact that such a physical quantity exists in the first place for electromagnetic waves. The point is that this expression is a result from classical electrostatics describing the potential energy of a capacitor (i.e. the work that is needed to charge the capacitor). However, even here it is wrong to interpret this as energy stored in the electric field, because kinetic and potential energies of the particles fully describe the system and there is no room for a separate field energy, neither in electrostatics nor in electrodynamics. Additionally of course, there is no explanation as to how this assumed electromagnetic wave 'energy' should be converted to the kinetic energy of the released photoelectrons .



In the following it is shown that a consistent semi-classical treatment of the interaction process between an atomic electron and an electromagnetic wave does indeed yield ionization times that may be short enough to explain the observations. On the other hand, it is shown that the particle model would in fact not enable any photoelectric effect at all as the collisional energy transfer would be much too small.

Wave Model

The interaction of light with atoms can generally be described as a forced oscillator (in the case of photoionization as a Pseudo-oscillator. If the oscillation is in phase with the driving field of the electromagnetic wave throughout, this is exactly equivalent to the acceleration of an electron by a constant electric field E (where E is the amplitude of the wave). The electron will therefore be accelerated to the velocity v within a time

T_c=v/a  =  v/(eE/m)   ,

where e is the elementary charge.



Since v is related to the energy ε by

v= √(2ε/m)   (m=electron mass)   ,

and ε has to be taken as identical to hν (h=Planck-constant, ν=wave-frequency), this yields

T_c= √(2hν^.m) /(eE) .

After evaluating the constants this gives the numerical expression

T_c= 7^.10^-18.√ν /E     [sec]     (in Gausssian cgs-units i.e. ν [Hz], E [statvolt/cm](=3^.10⁴V/m) ) .

For sunlight (assuming E=10^-2 statvolt/cm), this amounts to about 10^-8 sec, i.e. the almost instantaneous release of electrons in the photoeffect can well be explained within the wave theory of light if a proper interaction model is used (of course, the wave frequency ν has to be high enough here to enable photoionization in the first place)(note: the assumption E=10^-2 statvolt/cm should be merely considered to be exemplary here as the electric field strength E of the radiation field is in fact unknown; it has been derived here by equating the well known 'energy' flux of the sun with c^.E²/4π , which however, as pointed out in the first paragraph, is theoretically flawed and is ambiguous anyway due other physical parameters affecting the measured intensity as addressed on this page).

Particle Model

In contrast, the particle theory of light is completely inconsistent and would in fact not enable photoionization at all:



Assuming that a photon with energy ε has a mass

μ= ε/c²   ,

the energy transfer Δε to the electron with mass m is determined by the equation for momentum conservation

μc  =   mv  =  m^.√(2^.Δε/m)  ,

and therefore

Δε  =  μ²c²/2m  =  μ/2m ^.ε   .

With μ corresponding to ultraviolet radiation, this means that only about a fraction 10^-5 of the initial photon energy can be transferred to the electron. This amount is much too small for photoionization to occur (which would require a factor of the order of 1). The energy transferred to the atomic nucleus would be even 3-4 orders of magnitude smaller due to its higher mass.







A further proof for the incorrectness of the particle model for light is the experimental fact that photoelectrons are not primarily released in the direction of propagation of light (as one should expect it for particles) but perpendicular to this in the direction of the electric field vector











 

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