Light of wavelength 340 nm is incident on a metal surface and ejects electrons that have a maxim

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Light of wavelength 340 nm is incident on a metal surface...

Light of wavelength $340 \mathrm{nm}$ is incident on a metal surface and ejects electrons that have a maximum speed of $3.5 \times 10^{5} \mathrm{~m} / \mathrm{s}$. (a) What is the work function of the metal? (b) What is its stopping voltage?
(c) What is its threshold wavelength?

Key Concepts

Threshold Wavelength

The threshold wavelength is the longest wavelength (or lowest frequency) of incident light that can cause photoemission from a material. It corresponds to the condition where the photon's energy is exactly equal to the work function of the material, and no kinetic energy is left for the electron after overcoming the work function.

Kinetic Energy

In photoelectric experiments, the electrons emitted from the surface possess a maximum kinetic energy given by the difference between the energy of the incident photon and the work function of the material. This maximum kinetic energy can be computed using classical mechanics once the velocity of the emitted electron is known.

Stopping Voltage

The stopping voltage is defined as the minimum voltage needed to stop the most energetic photoelectrons from reaching a detector. It is directly related to the maximum kinetic energy of the electrons through the equation eV = Kmax, thereby providing an experimental method to measure the kinetic energy of the emitted electrons.

Photon Energy

Photon energy is given by the relation E = h?, where h is Planck's constant and ? is the frequency of the incident light. This concept is essential for understanding how the energy of incoming light is distributed between overcoming the work function of the metal and providing kinetic energy to the emitted electrons.

Photoelectric Effect

The photoelectric effect describes the phenomenon where electrons are emitted from a material, typically a metal, when it is exposed to electromagnetic radiation of sufficiently high frequency. This effect provides evidence for the quantization of light and helped establish quantum theory by showing that light can act as particles (photons) with energy proportional to its frequency.

Work Function

The work function is the minimum amount of energy required to eject an electron from the surface of a material. In the context of the photoelectric effect, it represents the energy threshold that the incident photon must exceed for the electron emission to occur.

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