how many electrons are there in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm )? express your answer using two significant figures.

Answers

Answer 1

There are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm.

To calculate the number of electrons in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm), you can use the following equation:

n = ρV / m

where:

n is the number of electrons.ρ is the density of copper (8.96 g/cm³).V is the volume of the wire. m is the mass of one copper atom.

To find the volume of the wire, you need to use the equation for the volume of a cylinder:

V = πr²h

Where:

r is the radius of the wire (1.025 mm). h is the length of the wire (30.0 cm).

Therefore, V = π(1.025 mm)²(30.0 cm) = 9.30 cm³The mass of one copper atom is 63.55 g/mol or 1.054 x 10⁻²² g. To find m, you need to use Avogadro's number (6.02 x 10^23 atoms/mol):m = (63.55 g/mol) / (6.02 x 10^23 atoms/mol) = 1.055 x 10⁻²² g

Now, you can plug in the values:

n = (8.96 g/cm³)(9.30 cm³) / (1.055 x 10⁻²² g) = 7.86 x 10²³ electrons

Therefore, there are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm. This should be rounded to 2 significant figures, so the final answer is 7.9 x 10²³ electrons.

Learn more about electrons: https://brainly.com/question/26084288

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