Heisenberg Uncertainty Module Example Question

[Jolie Sukonik 2B]

You are caught in a radar trap and hope to show that the speed measured by the radar gun is in error due to the Heisenberg uncertainty principle. If you assume that the uncertainty in your position was +/- 5 m when your speed was measured, and that the car has a mass of 2150 kg, what is your calculated uncertainty in the speed of your car?
Do you think this calculation will help you?

I know the uncertainty in position =10m, but I keep calculating the wrong answer for the velocity.
First, I found delta p: h/4pi(10) --> 5.28 x 10 ^-2 kgm/s
Then I found delta v: (5.28 x 10^-2 kgm/s) / (10m)

The answer I got for the velocity were none of the answer choices: (and the answer isn't E. none of the above)
A. Delta v >= 4 x 1038 m/s, No, because Delta v is extremely big.

B. Delta v >= 2 x 1038 m/s, No, because Delta v is extremely big.

C. Delta v >= 2 x 10-39 m/s, No, because Delta v is extremely small.

D. Delta v >= 5 x 10-39 m/s, No, because Delta v is extremely small.

E. None of the above

[SamanthaTolentino 3D]

To solve this problem, you can use the Heisenbergs uncertainty principle but instead of delta P, you can simply just use delta V and mass. The equation would look like:

Delta V > h/4pi(mass)(uncertainty in position)

[Arezo Ahmadi 3J]

In your work in which you calculated for the uncertainty in velocity, you are dividing by 10m again when you should be dividing by the mass of the car, which is 2150 kg. This would then look like:

delta p: h/4pi(10 m) = 5.28 x 10^-2 kgm/s

and delta v would look like:

delta v: (5.28 x 10^-2 kgm/s) / 2150 kg.

To look at it another way, the uncertainty in velocity should have the units of m/s, so make sure to always check your units to ensure that you are conducting the correct steps, as looking at the units has helped me a lot personally.

Hope this helps!

[Asia Yamada 2B]

The process you went through was correct, except you divided by the uncertainty in position again when you were supposed to divide by the mass of the car instead. Another way you could have approached the problem is by isolating Δv from Heisenberg’s Uncertainty Equation (Δx • Δp ≥ h/4pi) first, since you know momentum (p) is the product of the mass and velocity. When you reorganize the equation to isolate Δv, you get this: Δv ≥ h/4pi•m•Δx. Then, you can plug in the known values and solve for Δv.