A 0.62-mm-diameter copper wire carries a tiny current of 2.0 μA . The molar mass of copper is 63.5 g/mole and its density is 8900 kg/m3. NA=6.02×1023
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To find the number of copper atoms in the wire, we can use the following steps:
1. Calculate the volume of the wire:
The volume of a wire can be calculated using the formula for the volume of a cylinder, which is given by:
V = π * r^2 * h
where V is the volume, π is a mathematical constant (approximately equal to 3.14159), r is the radius, and h is the height.
The radius of the wire is given as half of its diameter (0.62 mm), so the radius (r) would be 0.62/2 = 0.31 mm = 0.00031 m.
The height (h) of the wire is not provided in the question, so we will use a standard value of 1 meter for simplicity.
Plugging in these values, we get:
V = π * (0.00031 m)^2 * 1 m
2. Calculate the mass of the wire:
The mass (m) of the wire can be calculated using the formula:
m = ρ * V
where ρ is the density of copper.
The density of copper is given as 8900 kg/m^3.
Plugging in the previously calculated volume (V), we get:
m = 8900 kg/m^3 * V
3. Calculate the number of moles of copper:
The moles of copper (n) can be calculated using the formula:
n = m / M
where m is the mass of copper and M is the molar mass of copper.
The molar mass of copper is given as 63.5 g/mole.
We need to convert the mass (m) of the wire from kg to g by multiplying it by 1000.
Plugging in these values, we get:
n = (m in g) / 63.5 g/mole
4. Calculate the number of copper atoms:
The number of copper atoms (N) can be calculated using Avogadro's number (NA):
N = n * NA
where n is the number of moles of copper and NA is Avogadro's number, which is approximately 6.02 × 10^23.
Plugging in these values, we get:
N = n * 6.02 × 10^23