Name: electron drift in metallic conduction
Uploaded: 2023-09-18T17:11:19.000Z
Duration: 1 min 17 s
Channel: JoVE

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North Carolina K-12 Science Standard Course of Study

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Motion and Stability- Forces and Interactions

PS.PSc.6.3

Theory of Metallic Conduction

Wenn ein elektrisches Feld an einen Leiter angelegt wird, driften freie Elektronen in die entgegengesetzte Richtung des Feldes, während sie mit den Ionen des Kristalls kollidieren.
Wenn das angewendete Feld Null wäre, würde die zufällige Bewegung im Durchschnitt zu einer Nettodrift von Null führen, da die Kollisionen ihre Richtung zufällig ändern würden. Die durchschnittliche Zeit zwischen Kollisionen wird als mittlere freie Zeit bezeichnet.
Die Beschleunigung des Elektrons ist durch die elektrische Kraft über die Masse gegeben. Seine Geschwindigkeit zu einem beliebigen Zeitpunkt wird durch die Anfangsgeschwindigkeit, die Beschleunigung und die Zeit ausgedrückt.
Die Mittelung beider Seiten über die Kollisionen ergibt die durchschnittliche Geschwindigkeit. Da die durchschnittliche Drift durch Kollisionen jedoch Null ist, ist die Driftgeschwindigkeit durch das Produkt aus Beschleunigung und mittlerer freier Zeit gegeben.
Unter Verwendung des Verhältnisses zwischen der Stromdichte und der Driftgeschwindigkeit wird die Stromdichte mit dem elektrischen Feld in Beziehung gesetzt, was das Ohmsche Gesetz ist.
Die elektrische Leitfähigkeit wird also durch die Anzahl der freien Elektronen pro Volumeneinheit, die Ladung und Masse des Elektrons und die mittlere freie Zeit ausgedrückt.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson; Abschnitt 25.6; Seiten 838–839.</li>
	<li>Griffiths, David J. (1999). Einführung in die Elektrodynamik (3. Aufl.). Upper Saddle River, New Jersey 07458; Abschnitt 7.1.1; Seiten 289–290.</li>
</ol>

theorie der metallischen leitung

Die Leitung freier Elektronen innerhalb eines Leiters wird am besten durch die Quantenmechanik beschrieben. Allerdings liefert ein klassisches Modell Vorhersagen, die nahe an den Ergebnissen der Quantenmechanik liegen. Es wird als Theorie der metallischen Leitung bezeichnet.

In dieser Theorie wird das zweite Newtonsche Gesetz der Bewegung verwendet, um die Beschleunigung eines Elektrons in Anwesenheit eines angelegten elektrischen Feldes zu bestimmen. Dann wird die Geschwindigkeit über diese Beschleunigung ausgedrückt.

Ein Elektron bewegt sich durch ein Kristallgitter, das positive Ionen enthält, und kollidiert mit den Ionen. Diese Zusammenstöße werfen es in verschiedene Richtungen ab. Wenn kein angelegtes elektrisches Feld vorhanden wäre, wäre die durchschnittliche Geschwindigkeit des Elektrons über die Zusammenstöße hinweg null. In Gegenwart des elektrischen Feldes beschleunigt das Elektron jedoch zwischen den Zusammenstößen entgegengesetzt zum Feld, so dass die durchschnittliche Geschwindigkeit, die so genannte Driftgeschwindigkeit, in Richtung des Feldes verläuft.

Die durchschnittliche Zeit zwischen den Zusammenstößen wird als mittlere freie Zeit definiert.

Die Beziehung zwischen der Stromdichte und der Driftgeschwindigkeit verbindet die Stromdichte mit dem elektrischen Feld. Diese Beziehung hat die Form des Ohmschen Gesetzes, aus dem die elektrische Leitfähigkeit des Materials ermittelt werden kann.

Diese Theorie sagt die richtige Temperaturabhängigkeit der Leitfähigkeit voraus. Mit zunehmender Temperatur des Materials nehmen die Schwingungen der Ionen zu, und damit auch die Zusammenstöße der Elektronen mit diesen Ionen. Die mittlere freie Zeit nimmt ab, was bedeutet, dass die Leitfähigkeit abnimmt. Die Vorhersage, dass die elektrische Leitfähigkeit des Materials mit zunehmender Temperatur abnimmt, wird in Experimenten beobachtet, wobei die genaue Abhängigkeit nur mithilfe der Quantenmechanik ermittelt werden kann.

Theorie der metallischen Leitung

Die Leitung freier Elektronen innerhalb eines Leiters lässt sich am besten durch die Quantenmechanik beschreiben. Ein klassisches Modell macht jedoch Vorhersagen nahe an der ...

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electron drift in metallic conduction

Electron drift in metallic conduction explains how free electrons move through a conductor. A classical model can describe this motion closely, even though quantum mechanics gives the best overall picture. This model is called the theory of metallic conduction.

In this theory, Newton's second law is used to find the acceleration of an electron when an electric field is applied. The electron's velocity is then found from that acceleration. The electron travels through a crystal of positive ions and collides with them. These collisions send the electron in different directions.

If no electric field is present, the average velocity of the electron is zero over many collisions. When an electric field is applied, the electron accelerates opposite to the field between collisions. As a result, the average velocity, called the drift velocity, points in the direction of the field. The average time between collisions is called the mean free time.

The link between current density and drift velocity gives the relationship between current density and electric field. This relationship has the form of Ohm's law, and it can be used to find the electrical conductivity of the material. The theory also predicts the correct temperature trend for conductivity.

As temperature rises, ion vibrations increase. Electrons then collide more often with the ions. The mean free time decreases, so the conductivity decreases. Experiments show this drop in conductivity with increasing temperature. The exact temperature dependence, however, requires quantum mechanics.

Electron Drift in Metallic Conduction

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theory of metallic conduction

Electron drift in metallic conduction explains how free electrons move through a conductor. A classical model can describe this motion closely, even though quantum mechanics gives the best overall picture. This model is called the theory of metallic conduction. In this theory, Newton's second law is used to find the acceleration of an electron when an electric field is applied. The electron's velocity is then found from that acceleration. The electron travels through a crystal of positive ions...

key terms and concepts

Explore electron drift, mean free time, and conductivity in metallic conduction. See how electric fields and temperature affect current in metals.

Electron Drift in Metallic Conduction | JoVE K12

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Electron Drift in Metallic Conduction

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