Question

A golf ball has a mass of 50 g, and a speed of 30 m/s. If the speed can be measured within accuracy of 1%, then the uncertainty in the position will be

Answer 1

Given : A golf ball has a mass of 50g, and a speed of 30 m/s. the speed can be measured within accuracy of 1 %.

To find : The uncertainty in the position.

solution : mass of golf ball, m = 50g = 0.05kg

speed of golf ball, v = 30 m/s.

uncertainty in the speed, ∆v = 1% of v = 1/100 × 30 = 0.3 m/s

using Heisenberg's uncertainty principle,

∆p × ∆x = h/4π

⇒m∆v × ∆x = h/4π

⇒∆x = h/4πm∆v

= (6.63 × 10¯³⁴ J.s)/(4 × 3.14 × 0.05 kg × 0.3 m/s)

= 35.19 × 10¯³⁴ m

= 3.519 × 10¯³³ m

Therefore the uncertainty in the position will be 3.519 × 10¯³³ m.