Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
A hydrogen atom consists of one proton and one electron. It may be assumed that the electron revolves in a circle of radius 0.53 angstrom ( 1 angstrom = 10⁻¹⁰ m and is abbreviated as Å) with the proton positioned at the centre. The hydrogen atom is said to be in the ground state in this scenario. Determine the magnitude of the electric force between the proton and the electron of a hydrogen atom in its ground state.
Options
- A8.2 10⁻¹⁰ N
- B4.3 10⁻¹⁸ N
- C4.1 10⁻⁸ N
- D8.2 10⁻⁸ N
Correct answer
D. 8.2 10⁻⁸ N
Step-by-step solution
The magnitude of the electric force between the proton and the electron is given by Coulomb's law: F = 1 4 ₀ e^2 r^2 Substituting the values e = 1.6 10⁻¹⁹ C , r = 0.53 10⁻¹⁰ m , and 1 4 ₀ = 9 10^9 N m ^2 C ⁻² : F = 9 10^9 (1.6 10⁻¹⁹)^2 (0.53 10⁻¹⁰)^2 F = 9 10^9 2.56 10⁻³⁸ 0.2809 10⁻²⁰ F = 23.04 10⁻²⁹ 0.2809 10⁻²⁰ F 82.02 10⁻⁹ N F 8.2 10⁻⁸ N