(a)
m = mass of each aluminium sphere = 0.0250 kg = 0.0250 x 1000 g = 25 g
M = atomic mass = 26.982 g/mol
n = number of moles
Number of moles is given as
n = m/M
n = 25/26.982
n = 0.93
N₀ = Avogadro's number = 6.023 x 10²³
N = number of atoms
Number of atoms is given as
N = n N₀
N = (0.93) (6.023 x 10²³) = 5.6 x 10²³ atoms
= number of electrons per atom = 13
= total number of electrons
Total number of electrons are given as
= N
= (13) (5.6 x 10²³)
= 72.8 x 10²³ electrons
b)
F = magnitude of electric force between the two spheres = 1 x 10⁴ N
r = distance between the spheres = 80 cm = 0.80 m
Q = magnitude of charge on each sphere = ?
Using Coulomb's law, force between the spheres is given as
F = k Q²/r²
inserting the values
1 x 10⁴ = (9 x 10⁹) Q²/(0.80)²
Q = 8.4 x 10⁻⁴ C
n = number of electrons removed
e = magnitude of charge on each electron
using the equation
Q = n e
8.4 x 10⁻⁴ = n (1.6 x 10⁻¹⁹)
n = 5.25 x 10¹⁵
c)
Fraction = n/ = (5.25 x 10¹⁵)/(72.8 x 10²³) = 7.2 x 10⁻¹⁰