Quantum mechanics minimum uncertainty

In summary, the conversation is about a quantum mechanics question regarding the uncertainty in the velocity of an oxygen molecule trapped in a lung's alveoli, using Heisenberg's uncertainty principle equation. The equation is \Delta x \Delta p \geq \frac{h}{2\pi}, where h is Planck's constant, and it helps determine the uncertainty in the momentum of the particle. The units used are meters, kilograms, and seconds.
  • #1
jalen
25
0
URGENT! quantum mechanics question

Homework Statement



In the lungs there are tiny sacs of air, which are called alveoli. The average diameter of one of these sacs is 0.25nm. Consider an oxygen molecule(mass=5.3x10^-26kg) trapped with a sac. What is the minimum uncertainty in the velocity of this oxygen molecule?

Homework Equations



I'm not sure what equation I should use...then I'll post what the possible answer is

The Attempt at a Solution

 
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  • #2
I'm reading a similar section in my physics textbook, and I came across an equation ... in the section for Heisenberg's uncertainty principle.

[tex]\Delta x \Delta p \geq \frac{h}{2\pi}[/tex], where h is Planck's constant.

Hope that helps?
 
  • #3
Hey LHC, thanks for the quick reply :)

I know that nm=r and kg=m but how would I sub it into the equation you mentioned?
 
  • #4
x--> uncertainty in particle's position...
p--> uncertainty in particle's momentum...
 
  • #5
So the equation will tell you the uncertainty in the momentum. Find that.

p.s. and watch the units ... use meters, kg, & sec for everything.
 

1. What is the uncertainty principle in quantum mechanics?

The uncertainty principle in quantum mechanics, also known as Heisenberg's uncertainty principle, states that it is impossible to know the precise values of certain pairs of physical properties of a particle at the same time. This is because the act of measuring one property affects the value of the other, making it impossible to have complete knowledge of both properties simultaneously.

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

The uncertainty principle challenges our classical understanding of the physical world, where properties such as position and momentum were thought to have well-defined values. In the quantum world, these properties are inherently uncertain and can only be described by probabilities. This means that our understanding of the physical world is limited by the inherent uncertainty of quantum mechanics.

3. What is the minimum uncertainty in quantum mechanics?

The minimum uncertainty in quantum mechanics, also known as the uncertainty principle's lower bound, is a fundamental limit that sets a lower limit on the uncertainty of certain pairs of physical properties. This means that even if we improve our measuring devices, we will never be able to know the precise values of these properties beyond a certain limit.

4. How does the uncertainty principle relate to the wave-particle duality of quantum mechanics?

The uncertainty principle is closely related to the wave-particle duality of quantum mechanics. It states that particles can exhibit both wave-like and particle-like behaviors, and the uncertainty principle arises from this duality. The more precisely we try to measure the position of a particle, the more uncertain its momentum becomes, and vice versa.

5. Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental principle in quantum mechanics and cannot be violated. It is a consequence of the wave-like nature of particles and the statistical nature of quantum mechanics. However, there are ways to decrease the uncertainty in one property while increasing it in another, known as entangled states, but the overall uncertainty will always remain above the minimum limit set by the uncertainty principle.

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