In the Bohr model of the hydrogen atom, the electron moves in a circular orbit of radius 5.3 × 10⁻¹¹ m with a speed of 2.2 × 10⁶ m/s. What is the magnitude of the centripetal force acting on the electron? (Electron mass m = 9.1 × 10⁻³¹ kg)
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Correct answer
A. 8.3 × 10⁻⁸ N
Principle or equation
Centripetal force is given by F = m v² / r. In the Bohr model, this force is provided by the electrostatic attraction between the electron and the proton.
Why this answer is correct
Substitute the values: F = (9.1 × 10⁻³¹ kg) × (2.2 × 10⁶ m/s)² / (5.3 × 10⁻¹¹ m) = (9.1 × 10⁻³¹) × (4.84 × 10¹²) / (5.3 × 10⁻¹¹) = (4.4044 × 10⁻¹⁸) / (5.3 × 10⁻¹¹) = 8.31 × 10⁻⁸ N, approximately 8.3 × 10⁻⁸ N.
Example
For a satellite of mass 1000 kg in orbit at speed 7000 m/s and radius 7×10⁶ m, F = 1000 × (7000)² / (7×10⁶) = 7000 N.
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