A 45.0 g ball of copper has a net charge of 1.5 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.)
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.
The charge of the copper ball is given as 1.5 µC (microcoulombs). To determine the charge of a single electron, we can use the elementary charge, which is approximately 1.6 x 10^-19 C (coulombs). Since 1 µC is equal to 10^-6 C, the charge of a single electron is:
1.5 µC x (10^-6 C/1 µC) = 1.5 x 10^-6 C
Now we need to calculate the number of electrons in the copper ball. To do this, we need to know the total charge of the copper ball in terms of electrons. Since each proton has a positive charge equal in magnitude to the electron's negative charge, the total charge of the copper ball will be positive. This means that some electrons have been removed.
The atomic mass of copper is given as 63.5 g/mol, which means that one mole of copper has a mass of 63.5 grams. We can use the atomic mass to find the number of moles of copper in the ball:
45.0 g copper x (1 mol/63.5 g) = 0.7087 mol
Since one mole of a substance contains Avogadro's number (6.022 x 10^23) particles, we can calculate the number of atoms in the copper ball:
0.7087 mol x (6.022 x 10^23 atoms/mol) = 4.265 x 10^23 atoms
Since each copper atom has 29 protons, we know that the total charge of the copper ball is positive:
Total charge = 1.5 x 10^-6 C (positive)
To find the number of electrons that have been removed, we need to calculate the charge of the copper ball in terms of electrons. Each electron has a charge of 1.6 x 10^-19 C. The total charge in terms of electrons is:
Total charge in terms of electrons = Total charge / Charge of a single electron
Total charge in terms of electrons = (1.5 x 10^-6 C) / (1.6 x 10^-19 C)
Total charge in terms of electrons = (1.5 x 10^-6 C) x (1/(1.6 x 10^-19 C))
Total charge in terms of electrons ≈ 9.375 x 10^12 electrons
Now we can find the fraction of electrons that have been removed. Remember that the total number of electrons in the copper ball is the same as the total number of protons since copper is neutral without any net charge:
Fraction of electrons removed = (Total number of electrons removed) / (Total number of electrons)
Fraction of electrons removed ≈ (9.375 x 10^12 electrons) / (4.265 x 10^23 electrons)
Fraction of electrons removed ≈ 2.2 x 10^-11
Therefore, approximately 2.2 x 10^-11 or 0.000000000022 (2.2 parts per trillion) fraction of the copper's electrons have been removed.