A copper atom has 29 electrons revolving around the nucleus. A copper ball has 4x10^23 atoms. What fraction of the electrons be removed to give the ball a charge of +9.6uC?
To determine the fraction of electrons that need to be removed to give the copper ball a charge of +9.6uC, we need to first find the total charge of the electrons in the copper ball.
Given that a copper atom has 29 electrons, we can calculate the total charge of one copper atom by multiplying the charge of a single electron with the number of electrons. The charge of a single electron is -1.6 x 10^-19 Coulombs (uC):
Charge of one copper atom = 29 electrons * (-1.6 x 10^-19 uC/electron)
= -46.4 x 10^-19 uC
Now, let's determine the total charge of the copper ball which contains 4x10^23 copper atoms. We can multiply the charge of one copper atom by the number of copper atoms in the ball:
Total charge of the copper ball = Charge of one copper atom * Number of copper atoms
= (-46.4 x 10^-19 uC) * (4 x 10^23 atoms)
= -185.6 x 10^4 x 10^-19 uC
= -185.6 x 10^-15 uC
Now, we want the copper ball to have a positive charge of +9.6 uC. To find the fraction of electrons that need to be removed, we need to determine the ratio of the desired charge to the actual charge:
Fraction of electrons removed = (Desired charge - Actual charge) / Actual charge
Plugging in the values:
Fraction of electrons removed = (9.6 x 10^-6 uC - (-185.6 x 10^-15 uC)) / (-185.6 x 10^-15 uC)
Simplifying the equation:
Fraction of electrons removed = (9.6 x 10^-6 uC + 185.6 x 10^-15 uC) / (185.6 x 10^-15 uC)
Therefore, the fraction of electrons that need to be removed to give the copper ball a charge of +9.6 uC is the calculated result of the above equation.
To calculate the fraction of electrons that need to be removed to give the copper ball a charge of +9.6uC, we need to compare the amount of charge carried by one electron with the desired charge.
1. Determine the charge carried by one electron:
The charge of one electron is equal to the elementary charge, which is approximately -1.6 x 10^-19 Coulombs (C).
2. Calculate the total charge of the copper ball:
The total charge of the copper ball is given as +9.6 uC (microCoulombs). To convert this to Coulombs, multiply by 10^-6:
9.6 uC x 10^-6 = 9.6 x 10^-6 C.
3. Find the total charge carried by all the electrons in the copper ball:
The total charge carried by all the electrons in the copper ball is equal to the product of the charge carried by one electron (-1.6 x 10^-19 C) and the number of electrons in the ball (4x10^23):
Total charge = (-1.6 x 10^-19 C) x (4x10^23) = -6.4 x 10^4 C.
4. Calculate the number of electrons that need to be removed:
To find the number of electrons that need to be removed, we divide the desired charge (+9.6 x 10^-6 C) by the charge carried by one electron (-1.6 x 10^-19 C):
Number of electrons removed = (9.6 x 10^-6 C) / (-1.6 x 10^-19 C) = -6.0 x 10^13 electrons.
5. Calculate the fraction of electrons removed:
To find the fraction of electrons removed, divide the number of electrons removed by the total number of electrons in the copper ball (4x10^23 electrons):
Fraction of electrons removed = (6.0 x 10^13 electrons) / (4x10^23 electrons) = 1.5 x 10^-10.
Therefore, the fraction of electrons that need to be removed to give the copper ball a charge of +9.6 uC is approximately 1.5 x 10^-10.