A golf ball has a mass of 40g and a speed of 45 ms−1. If the speed can be measured with an accuracy of 2%, calculate the uncertainty in the position.
1.46 × 10−33 m
By Heisenberg uncertainty principle,
△p × △x ≥ h4π ⇒ △v × △x ≥ h4πm
Now,
Mass of the ball = 40 g = 40 × 10−3 kg
The uncertainty in the speed
△v = 45 × 2100 = 0.9 m s−1
So the uncertainty in postion,
△x = h4π△p = h4πm△v
= 6.626×10−344×3.14×(40×10−3kg)×(0.9ms−1)
= 1.46 × 10−33 m