Practice question
Question
The de Broglie wavelength of an electron is 5.0 × 10⁻¹⁰ m and its kinetic energy is 3.026 × 10⁻¹⁹ J. What is the uncertainty in its position? (h = 6.626 × 10⁻³⁴ J s)
Explanation
Momentum p = h/λ = 6.626×10⁻³⁴ / 5.0×10⁻¹⁰ = 1.3252×10⁻²⁴ kg m s⁻¹. Δx · Δp ≥ h/4π, Δx ≥ h/(4π Δp) = 6.626×10⁻³⁴ / (4 × 3.14 × 1.3252×10⁻²⁴) = 3.98×10⁻¹¹ m.
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