An electron in a hydrogen atom moves with speed 6.76 × 10⁶ m s⁻¹ in an orbit of radius 0.52 Å. Find the magnetic field at the nucleus, in tesla.

Question

G1 Physics · Accepted Answer

An orbiting electron constitutes a current: I = q/T = qv/(2πr) Magnetic field at the centre of a circular orbit: B = μ₀I/(2r) Therefore: B = μ₀qv/(4πr²) Using: μ₀/(4π) = 10⁻⁷ q = 1.6 × 10⁻¹⁹ C v = 6.76 × 10⁶ m s⁻¹ r = 0.52 Å = 0.52 × 10⁻¹⁰ m B = 10⁻⁷ × (1.6 × 10⁻¹⁹)(6.76 × 10⁶)/(0.52 × 10⁻¹⁰)² ≈ 40 T Final answer: 40.