Two electrons exert a force of repulsion of
0.96 N on each other.
How far apart are they? The elemental
charge is 1.602 × 10
−19
C .
To determine the distance between the two electrons, we can use Coulomb's law, which states that the force of repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb's Law:
F = (k * q1 * q2) / r^2
Where:
F is the force of repulsion between the electrons (0.96 N)
k is the electrical constant or Coulomb's constant (9 × 10^9 N m^2/C^2)
q1 and q2 are the charges of the electrons (equal to the elementary charge, 1.602 × 10^-19 C)
r is the distance between the electrons (unknown)
Now, we can rearrange the formula to solve for r:
r = sqrt((k * q1 * q2) / F)
Substituting the given values:
r = sqrt((9 × 10^9 N m^2/C^2 * 1.602 × 10^-19 C * 1.602 × 10^-19 C) / 0.96 N)
Simplifying the equation:
r = sqrt((2.5804864 × 10^-28 N^2 m^2)/(0.96 N))
r = sqrt(2.6884 × 10^-28 N m^2)
r ≈ 1.64 × 10^-14 meters
Therefore, the distance between the two electrons is approximately 1.64 × 10^-14 meters.
0.96 newtons = k e^2/r^2
k is the Coulomb constant,
8.99*10^9 N*m^2/C^2.
You already know what e is.
Solve for r