1. Understand the Concepts
* Coulomb's Law: This law describes the electrostatic force between two charged objects. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
* Alpha Particle: An alpha particle is a helium nucleus, consisting of two protons and two neutrons. Its charge is +2e, where 'e' is the elementary charge (1.602 x 10^-19 Coulombs).
* Gold Nucleus: A gold nucleus has 79 protons, so its charge is +79e.
2. Formula
Coulomb's Law:
F = (k * q1 * q2) / r²
Where:
* F = electrostatic force
* k = Coulomb's constant (8.98755 × 10^9 N⋅m²/C²)
* q1 = charge of the alpha particle (+2e)
* q2 = charge of the gold nucleus (+79e)
* r = distance between the charges (3.0 x 10^-14 m)
3. Calculation
* Convert charges to Coulombs:
* q1 = +2 * (1.602 x 10^-19 C) = 3.204 x 10^-19 C
* q2 = +79 * (1.602 x 10^-19 C) = 1.2656 x 10^-17 C
* Plug values into Coulomb's Law:
F = (8.98755 × 10^9 N⋅m²/C²) * (3.204 x 10^-19 C) * (1.2656 x 10^-17 C) / (3.0 x 10^-14 m)²
* Calculate the force:
F ≈ 4.04 x 10^-3 N
Answer: The electrical force acting on the alpha particle when it's 3.0 x 10^-14 m from the gold nucleus is approximately 4.04 x 10^-3 Newtons.
