A 52.0 g ball of copper has a net charge of 2.1 µC. What fraction of the copper's electrons have been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.)
number electrons removed=2.1microC*/charge on one electron
original number elecrons:
number moles*avagrado's number*29
fraction=removed/original
To find the fraction of electrons that have been removed from the copper ball, we need to compare the charge of the ball to the charge of a single electron.
First, we need to determine the number of electrons in the copper ball. To do this, we can use the atomic mass of copper (63.5 g/mol) and the mass of the copper ball (52.0 g) to calculate the number of moles of copper in the ball using the formula:
Number of moles = Mass (g) / Atomic mass (g/mol)
Number of moles = 52.0 g / 63.5 g/mol
Number of moles = 0.819 mol (rounded to three decimal places)
Since each mole contains Avogadro's number (6.022 x 10^23) of particles, we can calculate the number of copper atoms in the ball using the formula:
Number of atoms = Number of moles x Avogadro's number
Number of atoms = 0.819 mol x 6.022 x 10^23/mol
Number of atoms ≈ 4.928 x 10^23 (rounded to three decimal places)
Since each copper atom has 29 protons and the charge of an electron is 1.6 x 10^-19 C, the total charge of the electrons in the copper ball (assuming none have been removed) would be:
Total charge = Number of atoms x Number of electrons per atom x Charge of an electron
Total charge = 4.928 x 10^23 x 29 x 1.6 x 10^-19 C
Total charge ≈ 2.335 x 10^5 C (rounded to three decimal places)
Now, we can find the fraction of electrons that have been removed by dividing the net charge of the ball by the total charge if no electrons were removed:
Fraction of electrons removed = Net charge / Total charge if no electrons were removed
Fraction of electrons removed = 2.1 µC / 2.335 x 10^5 C
Let's convert 2.1 µC to Coulombs:
2.1 µC = 2.1 x 10^-6 C
Fraction of electrons removed ≈ 9.00 x 10^-12 (rounded to three decimal places)
Therefore, approximately 9.00 x 10^-12 (or 0.000000000009) fraction of the copper's electrons have been removed.