Alright, let's embark on this exciting journey of solving this problem step by step. The electrostatic force between two charged objects is described by Coulomb’s Law:
F = k*q1*q2/r²
where:
- F is the force between the charges,
- q1 and q2 are the magnitudes of the charges,
- r is the distance between the charges, and
- k is Coulomb's constant (k = 9x10⁹ N*m²/C²).
The charge (q) of a proton and an electron is the same in magnitude but opposite in sign. For our calculations, we consider the magnitude, which is approximately 1.6×10⁻¹⁹ Columbs.
In the case of a hydrogen atom, an electron and a proton are separated by a distance (r) of 5.29×10⁻¹¹ meters.
By substituting these values into Coulomb's Law we get:
F = (9.0 * 10⁹ N*m²/C²) * (1.6×10⁻¹⁹ C)² / (5.29×10⁻¹¹ m)²
After careful calculation, we find that the force F comes to be approximately 8.22×10⁻⁸ N.
Remember, this attraction force is what makes the electron stay around the nucleus, creating the basis for atoms and, consequently, matter.
So, that's how you find the magnitude of the electrostatic force between a proton and an electron in a hydrogen atom. Keep practicing to become proficient in working with Coulomb's law and the fascinating world of electrostatics!