Question

A golf ball has a mass of 100 g, and a speed of 50 m/s. If the speed can be measured

within accuracy of 2%, calculate the uncertainty in the position.​

Answer 1

Explanation:

Use Heisenberg's uncertainty principle.

For example [Δx=

4πmΔv

h

]

Here, Δx is the uncertainty in the position.

Δv is the uncertainty in velocity

m is the mass of Particle.

Given,m=40g=0.04kg

Δv=2%ofv=2×

100

45

=0.9m/s

h=6.626×10

−34

J.s

Now,Δx=

(4×3.14×0.04×0.9)

6.626×10

−34

=1.4654×10

−33

m

Answer 2

∆x=1.465×10^-33

Explanation:

Given : m=40g converted in kg 40/1000=40 ×10^-3

speed =45 m/sec

∆v= 45×2/100=0.9 m/s

∆x=?

formula

∆x×m∆v=h/4π

∆x = h/4π×m×∆v

6.6×10^-34 /4×3.14×40×10^-3 ×0.9

Ans =∆x = 1.4654 ×10^-33 m