The work function for potassium is 2.24 eV. If potassium...

The work function for potassium is 2.24 eV. If potassium metal is illuminated with light of wavelength $350 \mathrm{nm},$ find $(\mathrm{a})$ the maximum kinetic energy of the photoclectrons and (b) the cutoff wavelength.

Key Concepts

Maximum Kinetic Energy of Photoelectrons

In the context of the photoelectric effect, the maximum kinetic energy of the emitted electrons is found by subtracting the work function from the energy of the incident photon. This energy difference, expressed by the equation K_max = E_photon - ?, accounts for the excess energy converted into the kinetic energy of the photoelectrons after overcoming the material's work function.

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are ejected from a material's surface when it is exposed to light or other forms of electromagnetic radiation. This effect was fundamental in the development of quantum mechanics as it demonstrated that light can act as discrete particles called photons, with energy quantized in packets.

Work Function

The work function is the minimum amount of energy that must be supplied to an electron to remove it from the surface of a material. It is a characteristic property of the material and is usually expressed in electron-volts (eV), representing the energy barrier that electrons need to overcome to escape from the material.

Photon Energy

Photon energy refers to the energy carried by individual photons and is determined by the equation E = hc/?, where h is Planck's constant, c is the speed of light, and ? is the wavelength of the photon. This concept is pivotal in understanding how light of different wavelengths can interact with matter.

Cutoff Wavelength

The cutoff wavelength is the longest wavelength (or lowest frequency) of light that can produce photoemission from a material. At this wavelength, the energy of the photon is exactly equal to the work function of the material. Any light with a longer wavelength would not have enough energy to overcome the work function, hence no electrons would be emitted.

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