Heisenberg's uncertainty principle, find uncertainty in position

In summary, using Heisenberg's uncertainty principle, the uncertainty in the position of a proton moving at a speed of (5.00±0.01) x 10^4 m/s can be calculated using the equation \Delta x=\frac{h}{4\pi m\Delta v}. The value of \Delta v, which represents the uncertainty in the speed, needs to be determined in order to solve the problem accurately.
  • #1
Glissando
34
0

Homework Statement


Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of a proton moving at a speed of (5.00±0.01) x 10^4 m/s.


Homework Equations


Δx[itex]\geq[/itex] [itex]\frac{h}{4mΔv\pi}[/itex]


The Attempt at a Solution


x[itex]\geq[/itex] (6.626*10^-34)/(4pi(1.6726*10^-24)(5±0.01 * 10^4)

I get how to solve it, I just don't really understand what to do with the ±0.01. I'm assuming it's in meters, so I have to do 0.01/5 and then multiply that by 5*10^4, but I'm supposed to be getting 3*10^-10

Thanks in advance (:
 
Physics news on Phys.org
  • #2
The formula says [itex]\Delta x=\frac{h}{4\pi m\Delta v}[/itex]
What is [itex]\Delta v[/itex]? Is it a relative or an absolute uncertainty?
 

What is Heisenberg's uncertainty principle?

Heisenberg's uncertainty principle is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

Who discovered the uncertainty principle?

Werner Heisenberg, a German physicist, first proposed the uncertainty principle in 1927 as part of his work on quantum mechanics. He received the Nobel Prize in Physics in 1932 for his contributions to the development of this principle.

What is the uncertainty in position?

The uncertainty in position refers to the range of possible values for the position of a particle. According to Heisenberg's uncertainty principle, the uncertainty in position is inversely proportional to the uncertainty in momentum. This means that the more precisely we know the momentum of a particle, the less precisely we can know its position.

How does the uncertainty principle affect our understanding of the physical world?

The uncertainty principle challenges our traditional understanding of the physical world, which is based on classical mechanics. It suggests that at the subatomic level, the behavior of particles is inherently unpredictable and uncertain. This principle has greatly influenced the development of quantum mechanics and our understanding of the nature of reality.

How is the uncertainty principle applied in modern technology?

The uncertainty principle has numerous practical applications in modern technology, particularly in the development of precision instruments such as atomic clocks and electron microscopes. It also plays a crucial role in quantum computing and cryptography, which rely on the principles of quantum mechanics for their operations.

Similar threads

  • Quantum Interpretations and Foundations
Replies
23
Views
4K
  • Advanced Physics Homework Help
Replies
7
Views
1K
Replies
10
Views
1K
Replies
3
Views
918
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Quantum Physics
Replies
6
Views
3K
  • Quantum Physics
Replies
2
Views
858
Replies
2
Views
1K
Back
Top