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Estimate what fraction of the electrons in a pure copper penny have to be removed to give it a charge of 1uC.

(A copper atom has 29 electrons and the atomic mass of copper is 63. 5 g/mol. There are 6*1023 atoms per mole of atoms. The charge on an electron is e=1. 6*10-19C. Rounding is good)

User Unfrev
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Answer: To estimate the fraction of electrons that need to be removed from a pure copper penny to give it a charge of 1 μC (microcoulomb), we can follow these steps:

  • Calculate the total charge needed for the penny:

1 μC = 1.0 x 10^(-6) C

  • Find the number of copper atoms in the penny:

The molar mass of copper is 63.5 g/mol, and the atomic mass of copper is given. We can calculate the number of moles of copper atoms in the penny and then multiply by Avogadro's number (6.022 x 10^23 atoms/mol) to find the total number of copper atoms.

  • Determine the total number of electrons in the penny:

Since each copper atom has 29 electrons, we can multiply the number of copper atoms by 29 to find the total number of electrons.

  • Find the number of electrons that need to be removed:

Subtract the total charge needed (in coulombs) from the total charge carried by the electrons in the penny (in coulombs).

  • Calculate the fraction of electrons to be removed:

Divide the number of electrons that need to be removed by the total number of electrons to find the fraction.

  • Let's go ahead and do the calculations:

Total charge needed: 1.0 x 10^(-6) C

  • Number of moles of copper atoms in the penny:

Mass of penny (assumed): 1 g

Number of moles = mass / molar mass

Number of moles = 1 g / 63.5 g/mol

  • Total number of copper atoms:

Total number of copper atoms = Number of moles x Avogadro's number

  • Total number of electrons in the penny:

Total number of electrons = Total number of copper atoms x 29 (since each copper atom has 29 electrons)

  • Number of electrons that need to be removed:

Number of electrons to be removed = Total charge needed / Charge on an electron (e = 1.6 x 10^(-19) C)

  • Fraction of electrons to be removed:

Fraction = Number of electrons to be removed / Total number of electrons

  • Now, let's perform the calculations:

Total charge needed = 1.0 x 10^(-6) C

Number of moles of copper atoms = 1 g / 63.5 g/mol ≈ 0.0157 mol

Total number of copper atoms ≈ 0.0157 mol x 6.022 x 10^23 atoms/mol ≈ 9.46 x 10^21 atoms

Total number of electrons ≈ 9.46 x 10^21 atoms x 29 electrons/atom ≈ 2.74 x 10^23 electrons

Number of electrons to be removed ≈ 1.0 x 10^(-6) C / 1.6 x 10^(-19) C ≈ 6.25 x 10^12 electrons

Fraction ≈ 6.25 x 10^12 electrons / 2.74 x 10^23 electrons ≈ 0.0228

So, approximately 0.0228 or 2.28% of the electrons in the pure copper penny need to be removed to give it a charge of 1 μC.

User JimPri
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