Reviewed CSCA Physics question · Easy

In the Bohr model of the hydrogen atom, the electron in the ground state has an orbital radius of 5.3 × 10⁻¹¹ m and a speed of 2.2 × 10⁶ m/s. What is the magnitude of the centripetal force acting on the electron? (Electron mass m_e = 9.1 × 10⁻³¹ kg)

8.3 × 10⁻⁸ N
8.3 × 10⁻⁹ N
4.2 × 10⁻⁸ N
2.2 × 10⁻⁶ N

Show the answer and explanation

Correct answer

A. 8.3 × 10⁻⁸ N

Principle or equation

Centripetal force F = m v² / r.

Why this answer is correct

F = (9.1 × 10⁻³¹ kg) × (2.2 × 10⁶ m/s)² / (5.3 × 10⁻¹¹ m) ≈ 8.3 × 10⁻⁸ N.

Example

For an electron with v = 1.0 × 10⁶ m/s and r = 1.0 × 10⁻¹⁰ m, F = 9.1 × 10⁻³¹ × (1e6)² / 1e-10 = 9.1 × 10⁻⁹ N.

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