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 1.308e+4 m/s if the velocity has an uncertainty of 1.398%?
delta x = solve
delta p = mass*velocity
You know h and 4*pi
Multiply velocity by +/- 0.01398 and solve for delta x.
To find the uncertainty in the position of the neutron, we can use the uncertainty principle equation and some additional information given in the problem.
First, we need to find the uncertainty in the momentum (Δp) of the neutron. We know that the mass of the neutron is given as 1.675e-27 kg, and we also have the velocity of the neutron (v) and the uncertainty in velocity (Δv), which is given as 1.398% of the velocity.
Δv = (1.398/100) * v
Next, we can find the uncertainty in the momentum using the formula:
Δp = m * Δv
Substituting the values:
Δp = (1.675e-27 kg) * [(1.398/100) * (1.308e+4 m/s)]
Now, we can calculate the uncertainty in the position (Δx) using the uncertainty principle equation:
Δx * Δp = h / (4 * π)
Rearranging the equation to solve for Δx:
Δx = h / (4 * π * Δp)
Substituting the values of h (Planck's constant = 6.626e-34 J·s) and Δp, we can calculate the uncertainty in the position of the neutron.