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 horse (mass = 403.6 kg) that was traveling at a velocity of 8.441 m/s if the velocity has an uncertainty of 2.496%?

Answer 1

Here:

velocity = 8.441 m/s

deltav = 2.496% of velocity

deltav = 2.496*8.441/100

deltav = 0.2107 m/s

use Heisenberg uncertainty principle,

deltax*deltap = h/(4*pi)

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

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

Here:

deltav = 0.2107 m/s

mass, m = 4.036*10^2 Kg

Putting values,

deltax*(0.2107) = (6.626*10^-34)/(4*3.14*4.036*10^2)

deltax*(0.2107) = 1.307*10^-37

deltax = 6.20*10^-37 m

Answer: 6.20*10^-37 m