An aluminum wire of diameter 2.6 mm carries a current of 12 A. How long on average does it take an electron to move \(12 \mathrm{m}\) along the wire? Assume 3.5 conduction electrons per aluminum atom. The mass density of aluminum is \(2.7 \mathrm{g} / \mathrm{cm}^{3}\) and its atomic mass is $27 \mathrm{g} / \mathrm{mol}$.

#tag_title#Step 3: Determine the charge transferred per second using the current value #tag_content#Now, we will determine the charge transferred per second using the current value of \(3.6 \mathrm{A}\). To do this, we will multiply the current by the charge of one electron: \(3.6 \mathrm{A} \times 1.6 \times 10^{-19} \mathrm{C} = 5.76 \times 10^{-19}\mathrm{C}\) This means that \(5.76 \times 10^{-19} \mathrm{C}\) is transferred per second through the wire. #tag_title#Step 4: Calculate the drift speed of an electron in the wire #tag_content#Now we can calculate the drift speed of an electron in the wire by dividing the charge transferred per second by the product of the number of free electrons per volume, cross-sectional area, and the charge of one electron: Drift speed \(=\frac{5.76 \times 10^{-19} \mathrm{C}}{(2.1077 \times 10^{26} \frac{\mathrm{electrons}}{\mathrm{m}^3})(5.31 \times 10^{-6} \mathrm{m}^2)(1.6 \times 10^{-19}\mathrm{C})} = 5.06 \times 10^{-5} \mathrm{m/s}\) This means that the drift speed of an electron in the wire is approximately \(5.06 \times 10^{-5} \mathrm{m/s}\). #tag_title#Step 5: Calculate the time it takes an electron to move \(12 \mathrm{m}\) along the wire #tag_content#Lastly, we will calculate the time it takes for an electron to move \(12 \mathrm{m}\) along the wire with the drift speed we just calculated. To do this, we will simply divide the distance by the speed: Time \(=\frac{12 \mathrm{m}}{5.06 \times 10^{-5} \mathrm{m/s}} = 2.37 \times 10^5 \mathrm{s}\) So, it takes approximately \(2.37 \times 10^5 \mathrm{s}\) for an electron to move \(12 \mathrm{m}\) along the wire. **In summary, it takes approximately \(2.37 \times 10^5 \mathrm{s}\) for an electron to move \(12 \mathrm{m}\) along the wire at a drift speed of \(5.06 \times 10^{-5} \mathrm{m/s}\).