Concepts Of Physics MCQ Edition [Volume 1]PhysicsThe Forces
In a hydrogen atom's ground state, the average separation between the proton and the electron is 5.3 10⁻¹¹ m . Determine the Coulomb force between them at this separation.
Options
- A4.3 10⁻¹⁸ N
- B8.2 10⁻⁸ N
- C2.1 10⁻⁸ N
- D8.2 10⁻⁹ N
Correct answer
B. 8.2 10⁻⁸ N
Step-by-step solution
The Coulomb force between the proton and the electron is given by Coulomb's law: F = 1 4 ₀ q₁ q₂ r^2 Substituting the given values: q₁ = e = 1.6 10⁻¹⁹ C q₂ = e = 1.6 10⁻¹⁹ C r = 5.3 10⁻¹¹ m 1 4 ₀ = 9 10^9 N m ^2/ C ^2 F = 9 10^9 (1.6 10⁻¹⁹)^2 (5.3 10⁻¹¹)^2 F = 9 10^9 2.56 10⁻³⁸ 28.09 10⁻²² F = 23.04 10⁻²⁹ 28.09 10⁻²² F 0.82 10⁻⁷ N F = 8.2 10⁻⁸ N