Question

In a hydrogen atom, an electron with a charge of -1.6e-19 C orbits a proton with the same but positive charge at a distance 71 picometers away (that's trillionths of a meter or 10⁻¹² m). What is the magnitude of the electric force F (in nN nano Newton) that binds the two particles together?

Answer 1

The magnitude of the electric force that binds the electron and proton together in a hydrogen atom is approximately 6.36e4 nN (nano Newtons).

Step-by-step explanation:

The magnitude of the electric force that binds the electron and proton together in a hydrogen atom can be calculated using Coulomb's law. Coulomb's law states that the magnitude of the electric force between two charged particles is equal to the product of their charges divided by the square of the distance between them.

In this case, the charge of the electron is -1.6e-19 C and the charge of the proton is +1.6e-19 C. The distance between them is 71 picometers, which is equal to 71e-12 m.

Using Coulomb's law, we can calculate the force as:

F = (|q1 * q2|) / r^2

Plugging in the values:

F = ((1.6e-19 C) * (1.6e-19 C)) / (71e-12 m)^2

Simplifying the expression gives us:

F = 3.2e-19 / (5.041e-24)

Therefore, the magnitude of the electric force that binds the electron and proton together is approximately 6.36e4 nN (nano Newtons).