Final answer:
The drift velocity of conduction electrons in a gold wire can be calculated using the equation I = nqAvd, where I is the current, n is the number density of electrons, q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity.
Step-by-step explanation:
The drift velocity of conduction electrons in a gold wire can be calculated using the equation I = nqAvd, where I is the current, n is the number density of electrons, q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity. In this case, the current is given as 20.00 A. The charge of an electron is 1.60 × 10^-19 C. The area of the cross-section of the wire can be calculated using A = πr2, where r is half the diameter of the wire.
To calculate the number density of electrons, we need to use the density of gold and the atomic mass of gold. The density of gold is given as 19.3 g/cm^3. The atomic mass of gold is 196.97 g/mol. We can use these quantities along with Avogadro's number to determine the number of free electrons per cubic meter.
Using the given information, we can calculate the drift velocity of conduction electrons in a gold wire of the given diameter.