Understanding Electron Movement with Heisenberg's Uncertainty Principle

[jaydnul]

I'm trying to work out why electrons don't crash down into the nucleus using HUP. So if we take 10^-10 meters, the diameter of hydrogen, and use 10^-13 meters as our Δx, the HUP should come out unequal.

So I get Δp=10^-35*10^13 or

Δp=10^-22 and p=mv, so

Δv=10^10

This is where I am confused. I don't know how to think about the Δv. What values do we choose for v final and v initial?

 

[jaydnul]

Also, I didn't use the relativistic momentum because that is not what I am confused about. I thought it would be simpler with just the classical momentum.

 

[jaydnul]

Nevermind, think I figured it out. HUP doesn't describe the actual system, it describes the information we can get from the system.

 

[Rishi Gangadhar]

Some time ago I saw a video relating the large hadron collider. They said that the particles could be accelerated to a velocity of 99.999% the speed of light and they also added that the measured velocities were to an extremely high degree of accuracy. They also showed where the particles actually collide( to be precise, made to collide). If they were so accurate in measuring simultaneously the velocity and position of the particles, are they not violating the uncertainty principle?

 

[bhobba]

They also showed where the particles actually collide( to be precise, made to collide).

Where they collided was not known to much accuracy.

The way such things are calculated is by so called in and out states. We know the states going in, and calculate the transition probabilities of states going out - what's going on in between, and exactly where it occurs, we don't know.

Interestingly this was one of the first things figured out in QM by Max Born leading to the statistical interpretation:
http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Born_1926_statistical_interpretation.pdf

Thanks
Bill

 

[Finny]

JD:
You might find this of interest:
https://en.wikipedia.org/wiki/Atomic_orbital

especially :
https://en.wikipedia.org/wiki/Atomi...tions_to_the_Heisenberg_Uncertainty_Principle

 

[Rishi Gangadhar]

Thanks