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 neutron (mass = 1.675e-27 kg) that was traveling at a velocity of 1.245e+4 m/s if the velocity has an uncertainty of 1.480%?

Answer 1

Here:

velocity = 1.245*10^4 m/s

deltav = 1.48% of velocity

deltav = 1.48*1.245*10^4/100

deltav = 1.843*10^2 m/s

use Heisenberg uncertainty principle,

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

Here:

deltav = 1.843*10^2 m/s

mass, m = 1.675*10^-27 Kg

Putting values,

deltax*(1.843*10^2) = (6.626*10^-34)/(4*3.14*1.675*10^-27)

deltax*(1.843*10^2) = 3.15*10^-8

deltax = 1.709*10^-10 m

Answer: 1.709*10^-10 m