Question

A ping-pong ball weighing 2.5 g has a speed of 20 m/sec . If the speed can be measured within the

accuracy 1 % , Calculate the uncertainty in speed & position​

Answer 1

A ping - pong ball weighing 2.5 g has a speed of 20 m/s. the speed can be measured within the accuracy 1%.

To find : The uncertainty in the position.

solution : According to Heisenberg's uncertainty principle,

∆x = h/4πm∆v

here m = 2.5g = 2.5 × 10¯³ kg ,

∆v = 1 % of 20 m/s = 1 × 20/100 = 0.2 m/s

h = 6.63 × 10¯³⁴ Js

here ∆x = (6.63 × 10¯³⁴)/(4 × 3.14 × 2.5 × 10¯³ × 0.2)

= (6.63)/(4 × 3.14 × 0.5) × 10¯³¹ m

= 6.63/(6.28) × 10¯³¹ m

= 1.0557 × 10¯³¹ m

Therefore the uncertainty in the position is 1.0557 × 10¯³¹ m.