   Chapter 17, Problem 8P

Chapter
Section
Textbook Problem

An aluminum wire having a cross-sectional area of 4.00 × 10−6 m2 carries a current of 5.00 A. The density of aluminum is 2.70 g/cm3. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire.

To determine
The drift velocity of electrons in aluminum wire.

Explanation

Given Info: The aluminum wire having cross sectional are 4.00×106m2 carries steady current 5.00A . The density of aluminum is 2.70gcm3 . Each aluminum atom supplies one conduction electron per atom.

Explanation:

Formula to calculate the number of conduction electrons is

n=ρNAM

• n is the number of conduction electrons in unit volume,
• ρ is the density of aluminum,
• NA is the Avogadro number,
• M is the molecular mass of aluminum,

Since each aluminum atom contributes only one conduction electron, number of atoms per unit volume is same as the number of electrons per unit volume.

Substitute 2.70gcm3 for ρ , 6.022×1028electrons/m3 for NA and 27.0grammol-1 for M in the above equation to find n

n=(2.70gcm3)(1kg103g)(1cm-310-6m3)(6.022×1023atomsmole)(27.0 grammole(10-3kg1gm))=6.022×1028electrons/m3

The conduction electron density is 6

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