Two electrons in an atom are separated by
1.6 × 10^−10 m, the typical size of an atom.
What is the force between them? The
Coulomb constant is 9 × 10^9 N · m^2
/C^2
.
Answer in units of N.
To calculate the force between two electrons separated by a distance of 1.6 × 10^−10 m, we can use Coulomb's law. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = (k * q1 * q2) / r^2
Where F is the force between the two charges, k is the Coulomb constant (9 × 10^9 N · m^2 / C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
In this case, both electrons have the same charge, which is -1.6 × 10^-19 C (the charge of an electron). Therefore, q1 = q2 = -1.6 × 10^-19 C.
Plugging in the values into the formula, we have:
F = (9 × 10^9 N · m^2 / C^2) * (-1.6 × 10^-19 C) * (-1.6 × 10^-19 C) / (1.6 × 10^-10 m)^2
Simplifying the equation, we get:
F = (9 × 10^9 N · m^2 / C^2) * 2.56 × 10^-38 C^2 / 2.56 × 10^-20 m^2
F = 9 × 10^9 N * 2.56 × 10^-38 C / 2.56 × 10^-20
F = 9 × 10^9 N * 10^-18
F = 9 × 10^-9 N
Therefore, the force between the two electrons is 9 × 10^-9 N.