Q. Given : The mass of electron is 9.11 × 10⁻³¹ kg, Planck constant is 6.626 × 10⁻³⁴ Js, the uncertainty involved in the measurement of velocity within a distance of 0.1 Å is :
A) 5.79 × 10⁶ m s⁻¹
B) 5.79 × 10⁷ m s⁻¹
C) 5.79 × 10⁸ m s⁻¹
D) 5.79 × 10⁹ m s⁻¹
Explanation
[Solution from source] Heisenberg: Δx·mΔv ≥ h/4π, so Δv = 6.626 × 10⁻³⁴/(4 × 3.1416 × 9.11 × 10⁻³¹ × 1 × 10⁻¹¹) = 6.626 × 10⁻³⁴/1.145 × 10⁻⁴⁰ ≈ 5.79 × 10⁶ m s⁻¹. Remember 0.1 Å = 10⁻¹¹ m; using 10⁻¹⁰ m would change the power of ten. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.