Question:
Table-tennis ball has a mass 10 g and a speed of 90 m/s. If speed can be measured within an accuracy of 4% what will be the uncertainty in speed and position?
Solution:
According to Heisenberg’s uncertainty principle :
“It is fundamentally impossible to determine accurately both the velocity and the position of a particle at the same time.
∆x. ∆p ≥ h/4π
From the given problem,
mass of the ball = 4 g and speed is = 90 m /s
hence,the uncertainity of speed is ∆v = 4/100 × 90 = 3.6 m/s
∆x is given by ∆x = h/4πm∆v
Hence , the uncertainity of postion is ∆x = 6.26 × 10-34 / 4 × 3.14 × 4× 3.6
= 1.46 x 10-33 m