An aluminum wire having a cross-sectional area equal to 2.20 10-6 m2 carries a current of 5.50 A. The density of aluminum is 2.70 g/cm3. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm

To calculate the number of atoms per volume, you need to know the density and the atomic weight of aluminum. Here's how you do it:

1. Convert the density from g/cm^3 to kg/m^3. The density of aluminum is 2.70 g/cm^3, which is equal to 2700 kg/m^3.

2. The atomic weight of aluminum is approximately 26.98 atomic mass units (u), or 26.98 g/mol. Convert this to kg/mol by dividing by 1000, which gives you 0.02698 kg/mol.

3. Avogadro's number tells us that there are approximately 6.022 x 10^23 atoms in one mole.

4. Therefore, the number of atoms per volume (n) can be calculated using the formula n = density / atomic weight. Substituting the values we have, n = 2700 kg/m^3 / 0.02698 kg/mol = 100037.0631 mol/m^3.

5. Multiply this by Avogadro's number to get the number of atoms per volume: 100037.0631 mol/m^3 * 6.022 x 10^23 atoms/mol = 6.02 x 10^28 atoms/m^3.

Now that we have the number of atoms per volume, we can calculate the drift speed of the electrons in the wire. The formula for drift velocity (v) is I/nAe, where I is the current, n is the number of charge carriers per volume, A is the cross-sectional area of the wire, and e is the charge of an electron (1.6 x 10^-19 C).

Substituting the given values, v = 5.50 A / (6.02 x 10^28 atoms/m^3 * 2.20 x 10^-6 m^2 * 1.6 x 10^-19 C) = 2.57 x 10^-5 m/s.

So, the drift speed of the electrons in the wire is approximately 2.57 x 10^-5 m/s.