# How Does the Photoelectric Effect Transition from Wave to Particle Theory?

• i_island0
In summary, in the photoelectric effect, the intensity of light reaching a metal plate is related to the power of the light source and the area of the metal plate. The power received is also related to the area of the metal plate. When photons strike the metal plate, their energy is transferred to the electrons in the metal.
i_island0
This is regarding photoelectric effect.

Suppose a power source (having power P) is at distance r from the metal plate and photons are assumed to strike the plate normally.
Intensity of light reaching the plate is: I = P/4.PI.r^2
If plate area is A, we say power received is: P(R) = I.A = nhv/t ----(1)

Now, my question is how suddenly we merged wave theory and quantum theory in equation (1).

Because treating light like a single wave with an intensity is just a macroscopic representation of a _very_ large number of photons randomly distributed around the source according to their wave functions.

peter0302 said:
Because treating light like a single wave with an intensity is just a macroscopic representation of a _very_ large number of photons randomly distributed around the source according to their wave functions.

can u explain in more detail please

i never read anywhere that wave distribution represents photons

The probabilistic distribution of the photons (which are particles) around a point light source is going to represent a wave eminating from a source. Photons are governed by wave functions and the Schrodinger Equation just like all particles. Therefore, like a wave, intensity will decrease with the square of the distance.

i_island0 said:
This is regarding photoelectric effect.

Suppose a power source (having power P) is at distance r from the metal plate and photons are assumed to strike the plate normally.
Intensity of light reaching the plate is: I = P/4.PI.r^2
If plate area is A, we say power received is: P(R) = I.A = nhv/t ----(1)

Now, my question is how suddenly we merged wave theory and quantum theory in equation (1).

'Quantum theory' is in hv----the energy of a photon is proportional to the frequency. That is completely in conflict with classical eletromagnetism, or electrodynamics, where the energy of the electromagnetic wave does not depend on frequency.

That's right, but the question, I thought, was how could a wave concept like intensity be reconciled with the particle concept, and the answer is because a gazillion photons distributed randomly from a point-source look like a wave with intensity proportional to the number of photons divided by r^2.

joyer2 said:
'Quantum theory' is in hv----the energy of a photon is proportional to the frequency. That is completely in conflict with classical eletromagnetism, or electrodynamics, where the energy of the electromagnetic wave does not depend on frequency.

But look at the experimental results of the photo-electric effect :

1) The kinetic energy of the electrons is proportional to he frequency of the EM radiation
2) The kinetic energy of the electrons is independent of the total energy of the EM radiation (ie the intensity).

marlon

marlon said:
But look at the experimental results of the photo-electric effect :

1) The kinetic energy of the electrons is proportional to he frequency of the EM radiation
2) The kinetic energy of the electrons is independent of the total energy of the EM radiation (ie the intensity).

marlon

1) tells you the light is quantized---Ek~hv, the kinetic energy of an electron is transferred from one 'light particle'.
2) tells you the light is quantized---the number of photoelectrons N_pe is proportional to the intensity which is the number of photons N_p, i.e, N_pe = N_p, one photon knocks one electron out.

What exactly is the question here?

i_island0 said:
i never read anywhere that wave distribution represents photons

At what level are you studying? In the USA, most university physics students see this in their second-year "introductory modern physics" course and textbook.

I am a mentor myself. Hopefully will become a good one soon.

joyer2 said:
1) tells you the light is quantized---Ek~hv, the kinetic energy of an electron is transferred from one 'light particle'.
2) tells you the light is quantized---the number of photoelectrons N_pe is proportional to the intensity which is the number of photons N_p, i.e, N_pe = N_p, one photon knocks one electron out.

OOPS, my post was adressed to I_Island, i should have quoted him.

LOL,

I_Island, the above two questions illustrate how the transistion from "wave to particle" is made and explained.

marlon

Quote:
Originally Posted by joyer2 View Post
1) tells you the light is quantized---Ek~hv, the kinetic energy of an electron is transferred from one 'light particle'.
2) tells you the light is quantized---the number of photoelectrons N_pe is proportional to the intensity which is the number of photons N_p, i.e, N_pe = N_p, one photon knocks one electron out.
OOPS, my post was adressed to I_Island, i should have quoted him.

LOL,

I_Island, the above two questions illustrate how the transistion from "wave to particle" is made and explained.

marlon
Does one photon have energy=hv so n photons have energy nhv?
Isn't this another way of explaining the discrete energy levels Planck used to explain the BB radiation. I take it this means that a particle can only act on one other particle and that one photon can't influence two electrons.

This would mean that if we increase n the quantity of photons and intensity then it won't result in an increase in the photoelectrons emitted as long as there are enough photons n to satisfy all the electrons availiable for release?

Im not sure I like the idea of having duality :(

Alex

## 1. What is the wave-particle duality?

The wave-particle duality is a fundamental concept in quantum mechanics that describes how particles can exhibit both wave-like and particle-like behavior. It suggests that all particles, such as electrons and photons, have both wave-like and particle-like properties.

## 2. How can a particle behave like a wave?

Particles can behave like waves due to their quantum nature. In quantum mechanics, particles are described by wave functions that determine their probability of being in a certain location. This wave-like behavior is observed in experiments such as the double-slit experiment, where particles exhibit interference patterns similar to waves.

## 3. Can a wave be treated as a particle?

Yes, waves can also exhibit particle-like behavior in certain situations. This is known as wave-particle duality. In experiments such as the photoelectric effect, light behaves like a stream of particles (photons) rather than a continuous wave.

## 4. Why is it confusing to think of particles as waves?

The concept of particles behaving like waves goes against our classical understanding of physics. It can be difficult to reconcile the idea of a tiny, solid particle also having wave-like properties. This can lead to confusion and difficulty in understanding the behavior of particles at the quantum level.

## 5. How is the wave-particle duality relevant in modern technology?

The wave-particle duality is essential in understanding and developing many modern technologies, such as transistors and lasers. It also plays a crucial role in fields such as quantum computing and cryptography, where the behavior of particles at the quantum level is utilized for various applications.

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