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CGP EDU Academic Team
Published on: September 12, 2026
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10 – 7 m 2 carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0 × 10 3 kg m – 3 and its atomic mass is 63.5 amu.
Text Solution
Verified by ExpertsThe correct answer is:
0.0017 m/s
Step 1: Determine the number density of conduction electrons in copper.
The density of copper (ρ) is given as 9.0 × 103 kg/m3, and the atomic mass (M) of copper is 63.5 amu. First, we convert the atomic mass from amu to kg:
1 amu = 1.66 × 10-27 kg, therefore, M = 63.5 amu = 63.5 × 1.66 × 10-27 kg = 1.055 × 10-25 kg.
Step 2: Calculate the number of moles of copper in 1 m3:
Number of moles = density / molar mass = 9.0 × 103 kg/m3 / (63.5 × 10-3 kg/mol) = 141.4 mol/m3.
Step 3: Use Avogadro's number (NA = 6.022 × 1023 particles/mol) to find the number of conduction electrons:
Number of conduction electrons per m3 = number of moles × NA = 141.4 mol/m3 × 6.022 × 1023 electrons/mol = 8.50 × 1024 electrons/m3.
Step 4: Now, calculate the average drift speed (v_d) using the formula:
I = n × A × q × vd
where I is the current (1.5 A), n is the number density of conduction electrons (8.50 × 1024 m-3), A is the area (1.0 × 10-7 m2), and q is the charge of an electron (q = 1.6 × 10-19 C).
Step 5: Rearranging the equation gives:
vd = I / (n × A × q)
= 1.5 A / (8.50 × 1024 m-3 × 1.0 × 10-7 m2 × 1.6 × 10-19 C)
= 1.5 / (1.36 × 1019)
= 0.0017 m/s.
Therefore, the average drift speed of conduction electrons in the copper wire is approximately 0.0017 m/s.
The density of copper (ρ) is given as 9.0 × 103 kg/m3, and the atomic mass (M) of copper is 63.5 amu. First, we convert the atomic mass from amu to kg:
1 amu = 1.66 × 10-27 kg, therefore, M = 63.5 amu = 63.5 × 1.66 × 10-27 kg = 1.055 × 10-25 kg.
Step 2: Calculate the number of moles of copper in 1 m3:
Number of moles = density / molar mass = 9.0 × 103 kg/m3 / (63.5 × 10-3 kg/mol) = 141.4 mol/m3.
Step 3: Use Avogadro's number (NA = 6.022 × 1023 particles/mol) to find the number of conduction electrons:
Number of conduction electrons per m3 = number of moles × NA = 141.4 mol/m3 × 6.022 × 1023 electrons/mol = 8.50 × 1024 electrons/m3.
Step 4: Now, calculate the average drift speed (v_d) using the formula:
I = n × A × q × vd
where I is the current (1.5 A), n is the number density of conduction electrons (8.50 × 1024 m-3), A is the area (1.0 × 10-7 m2), and q is the charge of an electron (q = 1.6 × 10-19 C).
Step 5: Rearranging the equation gives:
vd = I / (n × A × q)
= 1.5 A / (8.50 × 1024 m-3 × 1.0 × 10-7 m2 × 1.6 × 10-19 C)
= 1.5 / (1.36 × 1019)
= 0.0017 m/s.
Therefore, the average drift speed of conduction electrons in the copper wire is approximately 0.0017 m/s.
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