Monochromatic ultraviolet light with intensity 550 W / m^2...

Monochromatic ultraviolet light with intensity $550 \mathrm{~W} / \mathrm{m}^{2}$ is incident normally on the surface of a metal that has a work function of $3.44 \mathrm{eV}$. Photoelectrons are emitted with a maximum speed of $420 \mathrm{~km} / \mathrm{s}$. (a) Find the maximum possible rate of photoelectron emission from $1.00 \mathrm{~cm}^{2}$ of the surface by imagining that every photon produces one photoelectron. (b) Find the electric current density these electrons constitute. (c) How do you suppose the actual current compares with this maximum possible current?

Key Concepts

Photoelectric Effect

The photoelectric effect describes the process by which electrons are emitted from a material when it is exposed to light of sufficient energy. It demonstrates that light can behave as discrete packets of energy (photons), with each photon having the potential to eject an electron if its energy exceeds the material’s work function.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It represents the binding energy that must be overcome for an electron to escape the metal, setting the threshold frequency (or energy) of the incident light needed to initiate the photoelectric effect.

Light Intensity

Light intensity is defined as the power of electromagnetic radiation per unit area, usually measured in watts per square meter (W/m²). In the context of the photoelectric effect, intensity is key to determining the rate at which photons strike a surface and, assuming each photon liberates one electron, the potential rate of electron emission.

Photon Energy and Frequency

Photon energy is given by Planck’s relation, E = h?, where h is Planck’s constant and ? is the frequency of the light. This energy must be compared with the work function in order to determine if the incident light has sufficient energy to eject electrons, and it is also used to calculate the number of incident photons given the light intensity.

Photoelectron Emission Rate and Electric Current Density

The photoelectron emission rate is the number of electrons ejected per unit time from the material’s surface. When every incident photon is assumed to produce an emitted electron, this rate directly relates to the intensity and photon energy. The electric current density is then determined by multiplying the emission rate by the elementary charge and dividing by the area, providing a measure of the electrical current per unit area.

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