A copper wire 81.9 cm long and 1.10 mm in diameter has a mass of 6.43 g.
(a) Find the number of electrons in the wire. (Copper has an atomic number of 29; that is, there are 29 protons in the Copper atom. Copper's atomic mass is 63.5.)
how many electrons:
(b) There is one free electron per atom in copper. Find the number of free electrons in the wire.
how many electrons :
To find the number of electrons in the wire, we can use the given information about its length, diameter, and mass.
First, let's calculate the volume of the wire using its dimensions. The volume of a cylinder (the shape of the wire) is given by the formula:
Volume = π * (radius^2) * height
Since the diameter of the wire is given, we can find the radius by dividing it by 2. So, the radius (r) is:
r = diameter / 2 = 1.10 mm / 2 = 0.55 mm = 0.055 cm
Now, we can calculate the volume using the formula:
Volume = π * (0.055 cm)^2 * 81.9 cm
Next, let's convert the mass of the wire (6.43 g) to the number of atoms of copper using its atomic mass (63.5 g). We can use the formula:
Number of atoms = mass / atomic mass
Number of atoms = 6.43 g / 63.5 g/mol
To find the number of electrons, we need to multiply the number of atoms by the number of electrons per atom. Copper has an atomic number of 29, which means it has 29 protons and 29 electrons.
(a) To find the number of electrons in the wire:
Number of electrons = Number of atoms * Number of electrons per atom
Number of electrons = (6.43 g / 63.5 g/mol) * 29 electrons/atom
Now, for part (b), we know that there is one free electron per atom in copper. So, the number of free electrons in the wire is equal to the number of atoms.
(b) Number of free electrons in the wire = Number of atoms
Therefore, to find the answers to both parts (a) and (b), follow the steps provided above.