The Photoelectric Effect and the Quantum Theory of Light

1. Hertz’s Experiment on the Photoelectric Effect

Hertz’s experiment demonstrated the photoelectric effect. In this experiment, a negatively charged zinc plate was attached to the rod of an electroscope. When a beam of light from an arc lamp (containing ultraviolet rays) was shone on the zinc plate, the deflection of the electroscope needle decreased. This indicates that electrons were emitted from the zinc plate. This phenomenon occurred with various metals, showing that it is a common occurrence.

2. The Photoelectric Effect

The photoelectric effect is the phenomenon where light ejects electrons from the surface of a metal.

Ultraviolet radiation can cause the photoelectric effect in zinc, while visible light cannot. This suggests that the energy of light plays a crucial role in the photoelectric effect.

3. The Law of Photoelectric Effect

For the photoelectric effect to occur, the incident light must have a wavelength less than or equal to the photoelectric work function (λ’) of the metal. Each metal has a specific photoelectric work function.

The law of photoelectric effect cannot be explained by the classical electromagnetic theory of light. This theory cannot explain why the wavelength of light affects whether the photoelectric effect occurs or not.

4. The Quantum Theory of Light

a. Planck’s Hypothesis

Planck proposed that the amount of energy absorbed or emitted by an atom at a time is a definite value equal to h.f, where:

• f is the frequency of the light absorbed or emitted

• h is Planck’s constant (h = 6.625.10^-34 J.s)

b. Energy Quanta

According to Planck, light energy is quantized and is called “energy quanta”: ε = h.f

c. Einstein’s Quantum Theory of Light

Einstein developed the quantum theory of light, also known as the photon theory:

• Light is made up of photons.

• Each monochromatic light of frequency f, the photons are all the same, each photon is a quantum of light with energy h.f.

• In a vacuum, photons travel at the speed of light c = 3.10^8 m/s, along light rays.

• Each time an atom or molecule emits or absorbs light, it emits or absorbs a photon.

• Photons only exist in a state of motion, there are no stationary photons.

5. Explaining the Law of Photoelectric Effect using the Quantum Theory of Light

Each photon is absorbed by an electron in the metal and transfers its energy to the electron. For an electron to be ejected from the metal, the energy of the incident photon (h.f) must be greater than or equal to the work function A of the metal.

The work function A is defined by the formula: A = h.c/λ’, where λ’ is the photoelectric work function.

This explains why light with a wavelength smaller than the photoelectric work function can cause the photoelectric effect.

6. Wave-particle Duality of Light

Light has a dual nature, meaning it exhibits both wave-like and particle-like properties.

Note: Regardless of its nature, light is still electromagnetic in nature.