Light of 300 nm wavelength strikes a metal plate, and...

Light of $300 \mathrm{nm}$ wavelength strikes a metal plate, and photoclectrons are produced moving as $f$ ast as $0.002 c$.
(a) What is the work function of the metal?
(b) What is the threshold wavelength for this metal?

Key Concepts

Photoelectric Effect

The photoelectric effect is the phenomenon in which electrons are emitted from a material (typically a metal) when it absorbs electromagnetic radiation. This effect was key to the development of quantum mechanics, as it provided evidence that light has particle-like properties, with each photon carrying a discrete amount of energy that can eject an electron if the energy exceeds a certain threshold.

Photon Energy

Photon energy 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 incoming light. This energy must be sufficient to overcome the work function of the material for electrons to be emitted, and any excess energy is converted into the kinetic energy of the emitted electrons.

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, the work function represents the energy barrier that must be overcome by an incident photon for electron liberation. It is a material-specific constant and is calculated by subtracting the maximum kinetic energy of the ejected electrons from the energy of the incident photons.

Threshold Wavelength

The threshold wavelength is the maximum wavelength (or equivalently, the minimum photon energy) at which electrons can be emitted from a material. It corresponds to the scenario where the photon energy exactly equals the work function, resulting in zero kinetic energy for the emitted electrons. This threshold sets a limit for the photoelectric effect – if the wavelength is longer than the threshold value (energy lower than the work function), no electrons will be emitted.

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