Ch 27: Current and Resistance

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 27: Current and Resistance

Problem 8c

Chapter 27, Problem 8c

The mean time between collisions for electrons in a gold wire is 25 fs, where 1 fs = 1 femtosecond = 10⁻¹⁵ s. How many times does the electron collide with an ion while moving this distance?

Verified step by step guidance

Understand the problem: The mean time between collisions (τ) is given as 25 fs, and we need to determine how many collisions occur over a certain time or distance. This requires understanding the relationship between time, velocity, and collisions.

Convert the given mean time between collisions into seconds: Since 1 femtosecond (fs) = 10⁻¹⁵ seconds, multiply 25 fs by 10⁻¹⁵ to express τ in seconds.

Determine the total time or distance over which the electron is moving (if not explicitly given, assume a hypothetical time or distance for calculation). The number of collisions is calculated as the total time divided by the mean time between collisions.

Use the formula for the number of collisions: \( N = \frac{T}{\tau} \), where \( T \) is the total time of motion and \( \tau \) is the mean time between collisions. Substitute the values into this formula.

Interpret the result: The calculated \( N \) represents the number of collisions the electron undergoes while moving over the specified time or distance. Ensure the units are consistent throughout the calculation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mean Free Path

The mean free path is the average distance a particle travels between collisions. In the context of electrons in a conductor, it helps determine how often electrons interact with ions or other particles. This concept is crucial for understanding electrical conductivity and the behavior of charge carriers in materials.

Collision Frequency

Collision frequency refers to the number of collisions a particle experiences per unit time. For electrons in a conductor, this is influenced by factors such as temperature and the density of ions. Understanding collision frequency is essential for calculating how many times an electron collides with ions over a given distance.

Drift Velocity

Drift velocity is the average velocity that a charged particle, such as an electron, attains due to an electric field. It is a key factor in determining how far an electron travels in a given time frame. By knowing the drift velocity and the mean time between collisions, one can calculate the total distance traveled and the number of collisions that occur.

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Related Practice

Textbook Question

The electron drift speed is 2.0 X 10⁻⁴ m/s in a metal with a mean time between collisions of 5.0 x 10⁻¹⁴. What is the electric field strength?

Textbook Question

The current in a 2.0 mm x 2.0 mm square aluminum wire is 2.5 A. What are (a) the current density and (b) the electron drift speed?

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A superconducting magnet carries a 100 A current through a 0.50-mm-diameter superconducting wire that is wound into a coil. How much charge flows through the wire in 15 minutes?

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1.0 x 10²⁰ electrons flow through a cross section of a 2.0-mm-diameter iron wire in 5.0 s. What is the electron drift speed?

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Textbook Question

A hollow copper wire with an inner diameter of 1.0 mm and an outer diameter of 2.0 mm carries a current of 10 A. What is the current density in the wire?

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Textbook Question

The mean time between collisions for electrons in a gold wire is 25 fs, where 1 fs = 1 femtosecond = 10⁻¹⁵ s. What is the electron drift speed in a 35 mV/m electric field?

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