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.