Light with a wavelength of 405 nm fell on a strontium surface, and electrons were ejected. If t

step 1 length 409 nanometers and this falls onto strontium material and so what we find is that electro

Light with a wavelength of 405 nm fell on a strontium...

Light with a wavelength of $405 \mathrm{~nm}$ fell on a strontium surface, and electrons were ejected. If the speed of an ejected electron is $3.36 \times 10^{5} \mathrm{~m} / \mathrm{s}$, what energy was expended in removing the electron from the metal? Express the answer in joules (per electron) and in kilojoules per mole (of electrons).

Key Concepts

Photoelectric Effect

The photoelectric effect describes the process by which electrons are ejected from a material when it is exposed to light of sufficient energy. This phenomenon provided early experimental evidence for quantum mechanics by showing that light can behave as a particle, with each photon delivering a quantized packet of energy to an electron.

Photon Energy

Photon energy is determined by the relationship E = hf or E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the light. This energy must be sufficient to overcome the binding energy of electrons in the material for photoemission to occur.

Kinetic Energy of Ejected Electrons

Upon absorption of a photon, any energy in excess of the binding energy (or work function) is converted into the kinetic energy of the ejected electron. This kinetic energy can be calculated using the classical formula K = ½mv², linking the observable speed of the electron to the energy transferred during photon absorption.

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, it represents the energy needed to overcome the binding forces holding the electron in the material, and it can be determined by subtracting the kinetic energy of the ejected electron from the incident photon energy.

Energy Unit Conversion

Converting energy per electron into energy per mole involves using Avogadro's number, which bridges the gap between the microscopic scale (individual electrons) and macroscopic quantities (moles). This is essential for expressing energy in terms commonly used in chemistry and physics, such as kilojoules per mole.

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