Two small silver spheres with a mass of 10.0g, are separated by 1.00m. Calcuate the fraction of the electrons in one sphere that must be transfered to the other to produce an attractive force of 1.00x10^4 N (about 1 ton) between spheres (number of electrons per atom of silver is 47, and the number of atoms per gram is avogadro's number divided by the molar mass of silver, 107.87g/mol.
I have no idea how to do this.
I know Coulomb's law is Fe= (|q1|q2|)/r^2 but how to find the "fraction" of electrons in one sphere..
help please
You know that q1 must be minus q2 because the electrons that you tranfer from one sphere end up on the other sphere.
You then equate
(|q1|q2|)/r^2 to 1.00x10^4 N
Note that the expression (|q1|q2|)/r^2 for Coulomb force is valid MKS or CGS units not in SI units. The definition of the charge is different in SI units and you then need to include a factor
1/(4 pi epsilon_0).
Once you know the carge q1 you divide it by the charge of an electron. Divide by the total number of electrons to find the fraction.
To calculate the fraction of electrons that needs to be transferred from one sphere to the other, we need to first calculate the total charge on each sphere. We can then determine the fraction by comparing the charges.
1. Calculate the mass of each sphere:
Given that the mass of each sphere is 10.0g, the total mass of silver on each sphere is 10.0g.
2. Calculate the number of silver atoms on each sphere:
To calculate the number of silver atoms, we need to use Avogadro's number divided by the molar mass of silver. Avogadro's number is approximately 6.022 × 10^23.
Number of atoms per gram of silver = Avogadro's number / molar mass of silver
= (6.022 × 10^23) / (107.87g/mol)
Now, multiply the number of atoms per gram by the mass of each sphere to find the number of silver atoms on each sphere.
Number of atoms on each sphere = number of atoms per gram × mass of each sphere
3. Calculate the number of electrons on each sphere:
The number of electrons per silver atom is given as 47. Multiply the number of atoms on each sphere by 47 to find the number of electrons on each sphere.
Number of electrons on each sphere = number of atoms on each sphere × number of electrons per silver atom
4. Calculate the total charge on each sphere:
Since silver has only one electron per atom in its outer shell, the total charge on each sphere is equal to the number of electrons on that sphere.
Total charge on each sphere = number of electrons on each sphere
5. Calculate the fraction of electrons to be transferred:
The fraction of electrons to be transferred will be the ratio of the excess charge on one sphere needed to produce the attractive force of 1.00 × 10^4 N.
Fraction of electrons transferred = (Total charge on other sphere - Total charge on one sphere) / Total charge on one sphere
By substituting the calculated values of the total charges into the equation, you can determine the fraction of electrons that need to be transferred to produce the given attractive force.