What is the longest wavelength of radiation that can eject a photoelectron from silver? Is it in the visible range?

The work function of a material, such as silver, is a crucial concept in understanding the photoelectric effect. In simple terms, the work function is the minimum energy required to remove an electron from the surface of a metal.

When light or any electromagnetic radiation hits the surface of a metal, it can give energy to the electrons. If this energy is greater than or equal to the work function of the metal, electrons can be ejected, creating a phenomenon known as the photoelectric effect. For silver, the work function is typically given in electron volts (eV), a unit of energy commonly used in atomic and particle physics to denote small amounts of energy.

Research indicates that the work function for silver is around 4.73 eV. When converting this value to joules (the SI unit for energy) using the conversion factor of approximately 1.602 × 10^-19 J/eV, we can proceed to relate this energy to the frequency or wavelength of light capable of causing the effect, linking the work function directly to the nature of the incident light.

Planck's constant, denoted by the symbol \(h\), is a profound fundamental constant in quantum mechanics that relates the energy carried by a photon to the frequency of its associated electromagnetic wave. The constant has a value of 6.626 × 10^-34 joule seconds (J·s).

The photoelectric equation, derived from the principles outlined by Max Planck, equates the energy \(E\) of a photon with the product of Planck's constant and its frequency \(f\) as \(E = hf\). However, we often need to consider the wavelength \(\lambda\) of the light instead of the frequency, particularly when discussing the visible light spectrum.

This relationship between energy, wavelength, and frequency becomes pivotal when solving for the threshold wavelength capable of ejecting electrons from materials with a known work function. Planck's constant serves as the bridge between the microscopic quantum world and the macroscopic classical world, and its value is imperative to any calculations involving quantum energies.

The visible light spectrum is the segment of the electromagnetic spectrum that is visible to the human eye. It encompasses wavelengths approximately in the range of 400 to 700 nanometers (nm). Each wavelength within this range corresponds to a different color, starting from violet at the shortest wavelengths to red at the longest.

When relating this to the photoelectric effect, the wavelength of light used can determine if photoelectrons will be ejected from a metal surface. Silver's work function value corresponds with specific wavelengths of light capable of ejecting electrons.

If we calculate a threshold wavelength for silver and find it within the visible light spectrum, it means that light we can see with our unaided eye has the energy to cause the photoelectric effect in silver. This is important for practical applications involving light sensors and various photoelectric devices that rely on understanding which wavelengths of light are suitable for electron emission.