The work function of a surface is 5.0 ×10^-19 J. If light of wavelength of 300 nm is incident o

step 1 In this question, we have a surface, we are told that the work function is 5 .0 times 10 to the

The work function of a surface is 5.0 ×10^-19 J. If light...

The work function of a surface is $5.0 \times 10^{-19} \mathrm{~J}$. If light of wavelength of $300 \mathrm{nm}$ is incident on the surface, what is the maximum kinetic energy of the photoelectrons ejected from the surface?

Key Concepts

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are emitted from a material's surface when electromagnetic radiation, such as light, of sufficient energy strikes it. This effect provided crucial evidence for the quantum nature of light and led to the development of quantum mechanics.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a property of the material and represents the barrier that must be overcome for photoemission to occur. In the context of the photoelectric effect, if the incoming photon does not have enough energy to overcome the work function, no electrons will be emitted.

Photon Energy Calculation

Photon energy is calculated using the relation E = hc/?, where h is Planck's constant, c is the speed of light, and ? is the wavelength of the incident light. This equation quantifies the energy carried by each photon, which is key in determining whether the photon can eject an electron from the material’s surface.

Maximum Kinetic Energy

The maximum kinetic energy of the emitted electrons is given by the difference between the energy of the incident photon and the work function of the material. This concept is derived from the conservation of energy principle in the photoelectric effect, where any extra energy beyond what is needed to overcome the work function is converted into the kinetic energy of the photoelectron.

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