Question

Heisenberg's uncertainty principle can be expressed mathematically as Δx*Δp = h/4π, where Δx and Δp denote the uncertainty in position and momentum respectively and h is Planck's constant. What would be the uncertaintry in the position of a snail (mass = 0.005178 kg) that was traveling at a velocity of 0.00004313 m/s if the velocity has an uncertainty of 2.368%?

Answer 1

Here:

velocity = 4.313*10^-5 m/s

deltav = 2.368% of velocity

deltav = 2.368*4.313*10^-5/100

deltav = 1.021*10^-6 m/s

use Heisenberg uncertainty principle,

deltax*deltav = h/(4*pi*m)

Here:

deltav = 1.021*10^-6 m/s

mass, m = 5.178*10^-3 Kg

Putting values,

deltax*(1.021*10^-6) = (6.626*10^-34)/(4*3.14*5.178*10^-3)

deltax*(1.021*10^-6) = 1.019*10^-32

deltax = 9.976*10^-27 m

Answer:9.976*10^-27 m