Question 17.2: DRIFT SPEED OF ELECTRONS GOAL Calculate a drift speed and co...
DRIFT SPEED OF ELECTRONS
GOAL Calculate a drift speed and compare it with the rms speed of an electron gas.
PROBLEM A copper wire of cross-sectional area 3.00 \times 10^{-6} \mathrm{~m}^{2} carries a current of 10.0 \mathrm{~A}. (a) Assuming each copper atom contributes one free electron to the metal, find the drift speed of the electrons in this wire. (b) Use the ideal gas model to compare the drift speed with the random rms speed an electron would have at 20.0^{\circ} \mathrm{C}. The density of copper is 8.92 \mathrm{~g} / \mathrm{cm}^{3}, and its atomic mass is 63.5 \mathrm{u}.
STRATEGY All the variables in Equation 17.2
I = \lim_{\Delta t \to 0} \frac{\Delta Q}{\Delta t} = n q v_d A [17.2]
are known except for n, the number of free charge carriers per unit volume. We can find n by recalling that one mote-of copper contains an Avogadro’s number \left(6.02 \times 10^{23}\right) of atoms, and each atom contributes one charge carrier to the metal. The volume of one mole can be found from copper’s known density and atomic mass. The atomic mass is the same, numerically, as the number of grams in a mole of the substance.
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