1. Understand the Concepts
* Electrostatic Force: The force between charged objects is described by Coulomb's law:
* F = k * (q1 * q2) / r²
* Where:
* F is the force
* k is Coulomb's constant (approximately 8.98755 × 10⁹ N⋅m²/C²)
* q1 and q2 are the charges of the two objects
* r is the distance between the centers of the objects
* Alpha Particle: An alpha particle consists of two protons and two neutrons, giving it a charge of +2e (where e is the elementary charge, approximately 1.602 × 10⁻¹⁹ C).
* Gold Nucleus: A gold nucleus has 79 protons, giving it a charge of +79e.
2. Set up the Calculation
* Charges:
* q1 = +2e = 2 * 1.602 × 10⁻¹⁹ C
* q2 = +79e = 79 * 1.602 × 10⁻¹⁹ C
* Distance:
* r = 1 pm = 1 × 10⁻¹² m
3. Plug the Values into Coulomb's Law
F = (8.98755 × 10⁹ N⋅m²/C²) * (2 * 1.602 × 10⁻¹⁹ C) * (79 * 1.602 × 10⁻¹⁹ C) / (1 × 10⁻¹² m)²
4. Calculate the Force
F ≈ 2.90 × 10⁻² N
Therefore, the force of repulsion between an alpha particle and a gold nucleus at a distance of 1 pm is approximately 2.90 × 10⁻² Newtons.
Important Notes:
* Units: Make sure all units are consistent (meters for distance, Coulombs for charge).
* Direction: The force is repulsive, meaning it acts to push the alpha particle and gold nucleus away from each other.
* Approximation: This calculation assumes the alpha particle and gold nucleus are point charges. In reality, they have a small, but non-zero, size, which can slightly affect the force.
