The Photoelectric Effect: Difference between revisions
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==Mechanism and Mathematical Model== | ==Mechanism and Mathematical Model== | ||
When electromagnetic waves are shone onto a surface (often a metal), an electron can be emitted, dependent on the energy of the photons of that light. Electrons emitted in this way are referred to as photoelectrons. The photon transfers energy to the electron, causing it to excite and by ejected from the material. This energy transfer manifests as kinetic energy with the electron. Each photon of light has an energy <math>{E=hf}</math> where '''h''' is Planck's constant and '''f''' is the frequency. When the photon contacts the electron on the surface of the material, its energy can be modeled by the relation <math>{E_f = K+Φ}</math> The quantity Φ is known as the work function of the material and is a unique value for each metal. This can be rewritten as <math>{K= hf-Φ}</math> to model the kinetic energy. From this, the mathematical reasoning for a threshold frequency can be observed. The minimum kinetic energy the particle can have is 0, it may not be negative. Thus, the frequency must be great enough for K to take on a non-negative value<ref name=" | When electromagnetic waves are shone onto a surface (often a metal), an electron can be emitted, dependent on the energy of the photons of that light. Electrons emitted in this way are referred to as photoelectrons. The photon transfers energy to the electron, causing it to excite and by ejected from the material. This energy transfer manifests as kinetic energy with the electron. Each photon of light has an energy <math>{E=hf}</math> where '''h''' is Planck's constant and '''f''' is the frequency. When the photon contacts the electron on the surface of the material, its energy can be modeled by the relation <math>{E_f = K+Φ}</math> The quantity Φ is known as the work function of the material and is a unique value for each metal. This can be rewritten as <math>{K= hf-Φ}</math> to model the kinetic energy. From this, the mathematical reasoning for a threshold frequency can be observed. The minimum kinetic energy the particle can have is 0, it may not be negative. Thus, the frequency must be great enough for K to take on a non-negative value<ref name="OSX">[https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect | ||
]</ref>. | ]</ref>. | ||
Revision as of 13:27, 22 April 2022
Claimed by Joe Baldino 4/16/2022 Short Description of Topic
The Main Idea
The photoelectric effect is the phenomena in which electrons are emitted from a material that is bombarded by electromagnetic radiation. First observed in the 19th century, the effect was confounding to scientists because of its violation of classical electromagnetism. These discrepancies ultimately led to Albert Einstein making groundbreaking proposals about the nature of light.
History
German physicist Heinrich Hertz is credited with the discovery of the photoelectric effect in 1887 when he observed a changing of sparking voltage between electrodes when ultraviolet light is shined on them[1]. The effect was subsequently studied by various other notable physicists, including Aleksandr Stoletov and J.J. Thomson. Most significant of this period, however, were the studies undertaken by Philipp Lenard. Lenard extensively worked on researching the photoelectric effect and determined that the velocity at which electrons are emitted from a material is independent of the intensity of the light[2]. This was one of the major discoveries that directly violated what was though to be known about electromagnetic radiation. This, compounded with later studies showing that there is a threshold frequency for electron emission and an absence of lag time, suggested the current understanding of the nature of light was insufficient.
Albert Einstein worked to solve this conundrum. Using Max Planck's theories about how light was carried in "packets", Einstein theorized that light was quantized in discrete particles, which he ended up dubbing as photons. He postulated that the absorption of a quanta of energy is what causes the ejection of an electron. This explained the dependence on frequency instead of intensity that was experimentally observed. Light with a high intensity but only low-energy quanta would not result in an emission. The frequency needed to be high enough- hence the idea of a threshold frequency. Einstein's ideas about the photoelectric effect paved the way for the modern-day interpretation of light's wave-particle duality.
Mechanism and Mathematical Model
When electromagnetic waves are shone onto a surface (often a metal), an electron can be emitted, dependent on the energy of the photons of that light. Electrons emitted in this way are referred to as photoelectrons. The photon transfers energy to the electron, causing it to excite and by ejected from the material. This energy transfer manifests as kinetic energy with the electron. Each photon of light has an energy [math]\displaystyle{ {E=hf} }[/math] where h is Planck's constant and f is the frequency. When the photon contacts the electron on the surface of the material, its energy can be modeled by the relation [math]\displaystyle{ {E_f = K+Φ} }[/math] The quantity Φ is known as the work function of the material and is a unique value for each metal. This can be rewritten as [math]\displaystyle{ {K= hf-Φ} }[/math] to model the kinetic energy. From this, the mathematical reasoning for a threshold frequency can be observed. The minimum kinetic energy the particle can have is 0, it may not be negative. Thus, the frequency must be great enough for K to take on a non-negative value[3].
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