An iron wire has a cross-sectional area equal to 2.00 x 106 m². Carry out the following steps to determine the drift speed of the conduction electrons in the wire if it carries a current of 8.0 A. (a) How many kilograms are there in 1.00 mole of iron? kg/mol (b) Starting with the density of iron and the result of part (a), compute the molar density of iron (the number of moles of iron per cubic meter). mol/m³ (c) Calculate the number density of iron atoms using Avogadro's number. atoms/m³ (d) Obtain the number density of conduction electrons given that there are two conduction electrons per iron atom. electrons/m³ (e) Calculate the drift speed of conduction electrons in this wire. m/s

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### Problem: Calculating Drift Speed in an Iron Wire

An iron wire has a cross-sectional area of \(2.00 \times 10^{-6} \, \text{m}^2\). Follow these steps to determine the drift speed of the conduction electrons in the wire, given a current of \(8.0 \, \text{A}\).

#### (a) Mass Calculation
**Question:** How many kilograms are there in 1.00 mole of iron?

- **Answer:** \(\_\_\_\_\_\_\) kg/mol

#### (b) Molar Density of Iron
Starting with the density of iron and the result of part (a), calculate the molar density of iron (number of moles of iron per cubic meter).

- **Answer:** \(\_\_\_\_\_\_\) mol/m\(^3\)

#### (c) Number Density of Iron Atoms
Calculate the number density of iron atoms using Avogadro's number.

- **Answer:** \(\_\_\_\_\_\_\) atoms/m\(^3\)

#### (d) Number Density of Conduction Electrons
Determine the number density of conduction electrons, given there are two conduction electrons per iron atom.

- **Answer:** \(\_\_\_\_\_\_\) electrons/m\(^3\)

#### (e) Drift Speed of Conduction Electrons
Calculate the drift speed of conduction electrons in this wire.

- **Answer:** \(\_\_\_\_\_\_\) m/s

In this exercise, you will learn to integrate physical constants and equations with practical data to solve real-world physics problems related to conduction and electron movement in materials.
Transcribed Image Text:### Problem: Calculating Drift Speed in an Iron Wire An iron wire has a cross-sectional area of \(2.00 \times 10^{-6} \, \text{m}^2\). Follow these steps to determine the drift speed of the conduction electrons in the wire, given a current of \(8.0 \, \text{A}\). #### (a) Mass Calculation **Question:** How many kilograms are there in 1.00 mole of iron? - **Answer:** \(\_\_\_\_\_\_\) kg/mol #### (b) Molar Density of Iron Starting with the density of iron and the result of part (a), calculate the molar density of iron (number of moles of iron per cubic meter). - **Answer:** \(\_\_\_\_\_\_\) mol/m\(^3\) #### (c) Number Density of Iron Atoms Calculate the number density of iron atoms using Avogadro's number. - **Answer:** \(\_\_\_\_\_\_\) atoms/m\(^3\) #### (d) Number Density of Conduction Electrons Determine the number density of conduction electrons, given there are two conduction electrons per iron atom. - **Answer:** \(\_\_\_\_\_\_\) electrons/m\(^3\) #### (e) Drift Speed of Conduction Electrons Calculate the drift speed of conduction electrons in this wire. - **Answer:** \(\_\_\_\_\_\_\) m/s In this exercise, you will learn to integrate physical constants and equations with practical data to solve real-world physics problems related to conduction and electron movement in materials.
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