Problem 1 B.27

Moderators: Chem_Mod, Chem_Admin

Melody Haratian 2J
Posts: 112
Joined: Wed Sep 30, 2020 9:48 pm
Been upvoted: 1 time

Problem 1 B.27

Postby Melody Haratian 2J » Fri Oct 23, 2020 7:01 pm

Hi everyone! I’m having trouble with problem 1 B.27 in the textbook. The problem is “ A bowling ball with a mass 8.00 kg is rolled down a bowling alley lane at 5.00 ± 5.0 m/s . What is the minimum uncertainty in its position?” Can someone help me with the first step of getting started with this problem?
Thank you!

Jiapeng Han 1C
Posts: 91
Joined: Wed Sep 30, 2020 9:50 pm

Re: Problem 1 B.27

Postby Jiapeng Han 1C » Fri Oct 23, 2020 7:15 pm

To calculate the uncertainty in position, you firstly have to determine the uncertainty in momentum. The speed is 55m/s, so the uncertainty in speed is 10-0=10m/s. We then calculate the uncertainty in momentum using p=mv. Finally, we plug the value of momentum into Heisenberg's equation, and the answer should be 6.59*m.

Eliana Carney 3E
Posts: 91
Joined: Wed Sep 30, 2020 9:31 pm

Re: Problem 1 B.27

Postby Eliana Carney 3E » Sat Oct 24, 2020 1:02 pm

Hey Melody!

The first step to this problem is calculating the uncertainty of the bowling ball's momentum using the formula: Δp = (mass(m)) x Δv. The uncertainly of the velocity is going to be 5.0 m/s because as the problem states, the velocity is 5.00 ± 5.0 m/s. This shows that the uncertainly in velocity is ± 5.0 m/s.

Once you calculate the uncertainty of the bowling ball's momentum, you use this value in Heisenberg's indeterminacy equation, which is ΔpΔx ≥ (h/(4π)). By plugging in your known values and solving for Δx, you will be given the minimum uncertainty in the bowling ball's position.

Hope this helps!

Return to “Heisenberg Indeterminacy (Uncertainty) Equation”

Who is online

Users browsing this forum: No registered users and 1 guest