Final answer:
To calculate the drift speed of electrons in the unobtanium wire, we can use the formula I = nqAvd, where I is the current, n is the number of free electrons per unit volume, 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:
To calculate the drift speed of electrons in the unobtanium wire, we can use the formula I = nqAvd, where I is the current, n is the number of free electrons per unit volume, q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity.
To find n, we need to first calculate the number of atoms per unit volume. The density of unobtanium is given as 8.1 g/cm³, which can be converted to kg/m³ by dividing by 1000. Using the molar mass of unobtanium, we can calculate the number of moles per unit volume and then multiply by Avogadro's number to get the number of atoms per unit volume. Finally, multiplying by 2 (since each atom contributes 2 free electrons) gives us the value of n.
To find A, we can use the formula for the area of a circle, A = πr². Since the diameter of the wire is given, we can find the radius by dividing the diameter by 2. Once we have the values of I, n, q, and A, we can rearrange the formula to solve for vd. Plugging in the known values will give us the drift speed of the electrons in the unobtanium wire.