A sample of aluminum metal containing 9.1080 x 10 to the 25 power atoms is drawn into a cylindrical wire with radius r=0.833 mm. how long must the wire be in meters?
mols Al = 9.1080E25 atoms/6.0221E23 = ?
mols Al x atomic mass = grams Al
Look up the density Al. volume = grams/density.
Then volume = pi*(r^2)*h
You know pi, r, and volume. Solve for h = length of the wire.Note that I would change r to meters so the answer will be in meters.
To determine the length of the wire, we need to use the formula to calculate the volume of a cylinder.
The volume of a cylinder is given by the formula:
V = π * r^2 * h,
where V represents the volume, r is the radius of the cylinder, and h is the height (length) of the cylinder.
In this case, the volume of the wire should be equal to the number of aluminum atoms in the wire. Since we know the number of atoms and the radius of the wire, we can calculate the length.
1. Determine the volume of the wire:
Since the formula for the volume of a cylinder is V = π * r^2 * h, we can rearrange the formula to solve for h:
h = V / (π * r^2).
2. Calculate the radius in meters:
The radius, r, is given as 0.833 mm. To convert it to meters, divide by 1000:
r = 0.833 mm / 1000 = 0.000833 m.
3. Calculate the volume of the wire:
The volume should be equal to the number of atoms, so we have:
V = 9.1080 x 10^25 atoms.
4. Substitute the values into the formula and solve for h:
h = (9.1080 x 10^25) / (π * (0.000833)^2).
5. Calculate the length of the wire:
Now that we have the value of h, multiply it by 2 to get the total length of the wire:
length = 2 * h.
Following these steps, you should be able to find the length of the wire in meters.