Respuesta :
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
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
(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
[tex]n_{e}[/tex] = number of electrons per atom = 13
[tex]N_{e}[/tex] = total number of electrons
Total number of electrons are given as
[tex]N_{e}[/tex] = [tex]n_{e}[/tex] N
[tex]N_{e}[/tex] = (13) (5.6 x 10²³)
[tex]N_{e}[/tex] = 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/[tex]N_{e}[/tex] = (5.25 x 10¹⁵)/(72.8 x 10²³) = 7.2 x 10⁻¹⁰
