Why does the wave theory of light fail to explain the photoelectric effect?

Question

I don't understand!

Answer 1

Because waves are continuous and supply energy to the electrons in the metal. Eventually enough  energy should be supplied to liberate electrons from the metal. This should work at any intensity of light, you would just have to wait longer for the energy to build up at low intensities.  In practice below a certain frequency (threshold frequency) no electrons are ever  liberated.  The only way this can be explained is to assume the light is 'quantised' into packets carrying energy proportional to the frequency.

Answer 2

What is the theory of light? There is no such thing.

There are Maxwell equations though.

Only certain frequencies can liberate the electrons from atoms.

The energy of light is Known as Einstein's equation equal to Planck's constant times the frequency.

At low frequency there is not enough energy for the electrons to jump from one state to a higher state. At such low frequencies the kinetic energy of the atom is transfered as kinetic energy and the atom become agitated but does not emmit electrons.  

Energy of electron in atoms occupy certain energy bands.

There is Planck's constant associated with that.

So to liberate an electron you need specific energy corresponding to specific frequency.

Viola.

Effect on wave–particle question

The photoelectric effect helped propel the then-emerging concept of the dualistic nature of light, that light exhibits characteristics of waves and particles at different times. The effect was impossible to understand in terms of the classical wave description of light, as the energy of the emitted electrons did not depend on the intensity of the incident radiation. Classical theory predicted that the electrons could 'gather up' energy over a period of time, and then be emitted. For such a classical theory to work a pre-loaded state would need to persist in matter. The idea of the pre-loaded state was discussed in Millikan's book Electrons (+ & –) and in Compton and Allison's book X-Rays in Theory and Experiment.

The phenomena is called:

photoconductive effect (also known as photoconductivity or photoresistivitity),

the photovoltaic effect,

or the photoelectrochemical effect.

The photons of the light beam have a characteristic energy determined by the frequency of the light. In the photoemission process, if an electron absorbs the energy of one photon and has more energy than the work function, it is ejected from the material. If the photon energy is too low, the electron is unable to escape the surface of the material. Increasing the intensity of the light beam increases the number of photons in the light beam, and thus increases the number of electrons emitted without increasing the energy that each electron possesses. Thus the energy of the emitted electrons does not depend on the intensity of the incoming light, but only on the energy of the individual photons.

Electrons can absorb energy from photons when irradiated, but they follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or the energy is re-emitted. If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.

In analyzing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations are used:

Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

Albert Einstein's mathematical description in 1905 of how the photoelectric effect was caused by absorption of quanta of light (now called photons), was in the paper named "On a Heuristic Viewpoint Concerning the Production and Transformation of Light". This paper proposed the simple description of "light quanta," or photons, and showed how they explained such phenomena as the photoelectric effect. His simple explanation in terms of absorption of single quanta of light explained the features of the phenomenon and the characteristic frequency. Einstein's explanation of the photoelectric effect won him the Nobel Prize in Physics in 1921.

http://en.wikipedia.org/wiki/Condensed_m...

The photons of the light beam have a characteristic energy determined by the frequency of the light. In the photoemission process, if an electron absorbs the energy of one photon and has more energy than the work function, it is ejected from the material. If the photon energy is too low, the electron is unable to escape the surface of the material. Increasing the intensity of the light beam increases the number of photons in the light beam, and thus increases the number of electrons emitted without increasing the energy that each electron possesses. Thus the energy of the emitted electrons does not depend on the intensity of the incoming light, but only on the energy of the individual photons.

Electrons can absorb energy from photons when irradiated, but they follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or the energy is re-emitted. If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.

[edit] Experimental results of the photoelectric emission

   1. For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light.

   2. For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons can be emitted. This frequency is called the threshold frequency.

   3. Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident light but depends on the frequency of the incident light.

   4. The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 10-9 second.

In analyzing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations are used:

Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

Algebraically:

    hf = \phi + E_{k_{max}} \,

where

    * h is Planck's constant,

    * f is the frequency of the incident photon,

    * \phi = h f_0 \ is the work function (sometimes denoted W instead), the minimum energy required to remove a delocalised electron from the surface of any given metal,

    * E_{k_{max}} = \frac{1}{2} m v_m^2 is the maximum kinetic energy of ejected electrons,

    * f0 is the threshold frequency for the photoelectric effect to occur,

    * m is the rest mass of the ejected electron, and

    * vm is the speed of the ejected electron.

Since an emitted electron cannot have negative kinetic energy, the equation implies that if the photon's energy (hf) is less than the work function (φ), no electron will be emitted.

According to Einstein's special theory of relativity the relation between energy (E) and momentum (p) of a particle is E = \sqrt{(pc)^2 + (mc^2)^2}, where m is the rest mass of the particle and c is the velocity of light in a vacuum.

[edit] Three-step model

The photoelectric effect in crystalline material is often decomposed into three steps:[4]

   1. Inner photoelectric effect (see photodiode below). The hole left behind can give rise to auger effect, which is visible even when the electron does not leave the material. In molecular solids photons are excited in this step and may be visible as lines in the final electron energy. The inner photoeffect has to be dipole allowed. The transition rules for atoms translate via the tight-binding model onto the crystal. They are similar in geometry to plasma oscillations in that they have to be transversal.

   2. Ballistic transport of half of the electrons to the surface. Some electrons are scattered.

   3. Electrons escape from the material at the surface.

In the three-step model, an electron can take multiple paths through these three steps. All paths can interfere in the sense of the path integral formulation. For surface states and molecules the three-step model does still make some sense as even most atoms have multiple electrons which can scatter the one electron leaving.

Answer 3

If light were strictly a wave, the energy in the light would be represented by the amplitude of the light wave.  A more intense light source, even if it was light of a lower frequency, would have enough energy to knock electrons away from their molecular orbits, which is necessary to generate a photoelectric current.

What actuall occurs is that light below a certain threshold frequency does not generate any current, no matter how intense the light is.  Even though the total light energy hitting the photoelectric cell may be high, it cannot free electrons.

However, if the frequency is increased, even at low intensities, there will be a current.  That indicates that the energy from light is delivered in quanta (small units), which is consistent with a particle view of the light.  More intense light has more "units" of energy, but if the smallest unit (a photon) has too little oomph (low frequency means low energy per photon), then each collision is too weak to knock the electron.  A small number of higher frequency photons will not generate as many collisions, but each collision will set an electron free to jump over to the collector and make a current.