Ultraviolet light is incident normally on the surface of a...

Ultraviolet light is incident normally on the surface of a certain substance. The binding energy of the electrons in this substance is $3.44 \mathrm{eV}$. The incident light has an intensity of $0.055 \mathrm{~W} / \mathrm{m}^{2}$. The electrons are photoelectrically emitted with a maximum speed of $4.2 \times 10^{5} \mathrm{~m} / \mathrm{s}$. How many electrons are emitted from a square centimeter of the surface each second? Assume the absorption of every photon ejects an electron.

Key Concepts

Kinetic Energy of Electrons

The maximum kinetic energy of the emitted electrons is given by the difference between the energy of the incident photon and the work function. This kinetic energy can also be related to the speed of the electrons using classical mechanics, providing a way to verify that the energy balance predicted by the photoelectric effect is consistent with the observed electron velocities.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. In the context of the photoelectric effect, only photons with energies greater than this binding energy can liberate electrons, with any excess energy converting into the kinetic energy of the emitted electrons.

Intensity and Photon Flux

The intensity of the incident light represents the energy delivered per unit area per second. By dividing the intensity by the energy of a single photon, one can determine the photon flux—the number of photons striking a specific area each second. This is essential for calculating the number of electrons that could be emitted assuming each photon ejects one electron.

Photoelectric Effect

The photoelectric effect is the emission of electrons from a material when it is exposed to light of sufficient energy. This phenomenon is governed by the principle that the energy of the incident photons must exceed the work function (binding energy) of the material for electrons to be ejected.

Photon Energy

Photon energy is determined by the equation E = h?, where h is Planck’s constant and ? is the frequency of the light. This concept is central to understanding how much energy is available in each photon to overcome the electron's binding energy and provide any excess as kinetic energy.

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