Two small aluminum spheres, each of mass 0.0250 kilograms, are separated by 80.0 centimeters.

Asked by maham237 @ 25/12/2020 in Physics viewed by 428 People

Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (a) how many electrons does each sphere contain? (the atomic mass of aluminum is 26.982 g>mol, and its atomic number is 13.) (b) how many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00 * 104 n (roughly 1 ton)? assume that the spheres may be treated as point charges. (c) what fraction of all the electrons in each sphere does this represent?

Answered by maham237 @ 25/12/2020

Part (a):
number of electrons is represented by the atomic number.
So, in order to solve this part, we will get the number of atoms and multiply it by the atomic number to get the number of electrons.
number of moles = mass/molar mass = 0.0250/0.026982 = 0.926 moles
number of atoms = number of moles x Avogadro's number
= 0.926 x 6.022 x 10^23 = 5.579 x 10^23 atoms
number of electrons = number of atoms x atomic number
= 5.579 x 10^23 x 13 = 7.25 x 10^24 electrons

Part (b):
Coulomb's law can be written as follows:
F = (k x q1 x q2) / r^2
We will assume that q1 is equal to q2 in magnitude but opposite in direction
Therefore, q1 = q and q2 = -2
F = (-k x q^2) / r^2
Substitute in the equation by the force, coulomb's constant and the radius to get q and then divide q with the fundamental charge to get number of electrons as follows:
1.00 x 10^4 = -(8.9 x 10^9 x q^2)/(0.8)^2
q = 8.479 x 10^-4 (ignoring the negative sign as it states only direction)
number of electrons = 1.6 x 10^-29 x 8.479 x 10^-4 = 1.35 x 10^-22 electron

Part (c):
To get the fraction, simply divide your answer from part (b) by your answer from part (a) as follows:
fraction = (1.35 x 10^-22) / (7.25 x 10^24) = 1.86 x 10^-47

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