Light with a wavelength of 425 nm fell on a potassium surface, and electrons were ejected at a

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Light with a wavelength of 425 nm fell on a potassium...

Light with a wavelength of $425 \mathrm{~nm}$ fell on a potassium surface, and electrons were ejected at a speed of $4.88 \times 10^{5} \mathrm{~m} / \mathrm{s}$. What energy was expended in removing an electron from the metal? Express the answer in joules (per electron) and in kilojoules per mole (of electrons).

Key Concepts

Photon Energy

Photon energy is determined by the relation E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the light. This concept quantifies how much energy a single photon carries, establishing a direct link between the electromagnetic spectrum and the energy imparted by light on matter.

Electron Kinetic Energy

Electron kinetic energy is the energy an electron possesses due to its motion, calculated by the formula KE = ½ mv², where m is the electron mass and v is its velocity. In the context of the photoelectric effect, it represents the surplus energy an electron gains after absorbing a photon and overcoming the energy threshold of the material.

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are ejected from a material when it is exposed to light of sufficient energy. It is governed by the conservation of energy principle, where the energy of the incident photon is used first to overcome the binding energy (work function) of the electron, and any remaining energy appears as the kinetic energy of the emitted electron.

Work Function

The work function is the minimum amount of energy required to remove an electron from the surface of a material. It is a characteristic property of each material and is a critical parameter in the photoelectric effect, as only photons with energy equal to or greater than the work function can result in electron emission.

Molar Energy Conversion

Molar energy conversion involves scaling the energy value from a single particle (such as one electron or one photon) to a mole of particles using Avogadro’s number. This conversion is essential in chemistry and physics for relating microscopic energy values to macroscopic amounts that are practical for laboratory measurements and industrial applications.

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