Question

A copper wire that has a diameter of 2.9 mm carries a current of 39.0 A. Assuming that each copper atom contributes one free electron to the metal, find the drift velocity of the electrons in the wire. The molar mass of copper is 63.5 g/mol and the density of copper is 8.95 g/cm3.

Answer 1

velocity*area*charge=current where..

charge=e*density=e*avagnumber*8.95/63.5

solve for delocity

Answer 2

[AI-generated answer — Explain Bot]

To find the drift velocity of electrons in the copper wire, we can use the formula:

𝑉𝑑 = 𝑛𝑒 × 𝑙 × 𝑞

Where:
𝑉𝑑 is the drift velocity of electrons,
𝑛 is the number of free electrons per unit volume of the material,
𝑒 is the elementary charge,
𝑙 is the length of the wire, and
𝑞 is the charge carried by each free electron.

To calculate 𝑛, we need the number of free electrons per unit volume of copper. This can be found using the Avogadro's number and the molar mass of copper:

𝑛 = (density of copper / molar mass of copper) × Avogadro's number

Now, let's calculate 𝑛:

Given:
density of copper = 8.95 g/cm³
molar mass of copper = 63.5 g/mol
Avogadro's number = 6.022 × 10^23 mol⁻¹

𝑛 = (8.95 g/cm³ / 63.5 g/mol) × (6.022 × 10^23 mol⁻¹)

Simplifying, we get:

𝑛 ≈ 8.46 × 10^22 electrons/cm³

Next, we need to calculate 𝑞, the charge carried by each free electron. Since each copper atom contributes one free electron to the metal, the charge carried by each electron is the elementary charge, which is 1.6 × 10⁻¹⁹ C.

Now, let's calculate 𝑞:

𝑞 = 1.6 × 10⁻¹⁹ C

Finally, we can calculate the drift velocity 𝑉𝑑 using the given values of 𝑛, 𝑙, and 𝑞:

Given:
𝑛 = 8.46 × 10^22 electrons/cm³
𝑙 = length of the wire
𝑞 = 1.6 × 10⁻¹⁹ C

𝑉𝑑 = 𝑛 × 𝑙 × 𝑞

Substituting the given values, we can find 𝑉𝑑.