Question

Explain the photoelectric effect.

Short answer

The photoelectric effect is a phenomenon where electrons are emitted from a material when exposed to electromagnetic radiation (light) with energy greater than the material's work function ($\mathrm{\Phi }$). The ejected electrons' kinetic energy depends on the difference between the photon's energy ($h\nu$) and the work function. The number of emitted electrons is directly proportional to the light intensity.

Step-by-step solution

1. Introduction to the Photoelectric Effect

The photoelectric effect is the process in which electrons are ejected from a material when it is exposed to electromagnetic radiation (light). It was first observed by Heinrich Hertz in 1887. Later, in 1905, Albert Einstein provided a theoretical explanation of the effect, which ultimately led him to win the Nobel Prize in Physics in 1921.

2. The Work Function and the Threshold Frequency

In order for the photoelectric effect to occur, the energy of the incoming photons must be greater than the work function ($\mathrm{\Phi }$) of the material, which is the minimum energy required to release an electron from the surface of the material. The threshold frequency (${\nu }_0$) is the minimum frequency of the electromagnetic radiation required to eject an electron. It is related to the work function by the equation $\mathrm{\Phi }=h{\nu }_0$, where $h$ is Planck's constant.

3. Energy and Frequency Relationship

According to the quantum theory of electromagnetic radiation, the energy of a photon (E) is directly proportional to its frequency ($\nu$). The relationship is given by the equation $E=h\nu$, where again, h is Planck's constant. For the photoelectric effect to occur, the energy of the incoming photon must be greater than the work function, i.e., $E>\Phi$.

4. Conservation of Energy

When a photon with energy $E=h\nu$ is incident on the material, part of its energy is used to overcome the material's work function ($\Phi$), and the rest is given to the ejected electron as its kinetic energy ($K.E.$). This conservation of energy can be represented by the following equation: $E=\Phi +K.E.$, or $h\nu =\Phi +K.E.$.

5. Characteristics of the Emitted Electrons

The kinetic energy of the emitted electrons depends on the difference between the energy of the incident photon and the work function. This means that electrons are more likely to be ejected when the incident photon has a higher frequency (and thus higher energy). Moreover, the number of emitted electrons is directly proportional to the intensity of the incident light. In summary, the photoelectric effect occurs when a material is exposed to electromagnetic radiation, and electrons are ejected as a result. The energy of the incoming photons must be greater than the material's work function for the emission of electrons, and this emitted electron's kinetic energy depends on the difference between the photon's energy and the work function.