Quantum mechanics minimum uncertainty

AI Thread Summary
The discussion revolves around calculating the minimum uncertainty in the velocity of an oxygen molecule trapped in an alveolus, using Heisenberg's uncertainty principle. The relevant equation is Δx Δp ≥ h/2π, where Δx represents the uncertainty in position and Δp represents the uncertainty in momentum. Participants emphasize the importance of using consistent units, specifically meters for distance and kilograms for mass. The conversation highlights the need to substitute the given values correctly into the equation to find the uncertainty in momentum. The focus remains on applying quantum mechanics principles to solve the problem effectively.
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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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I'm reading a similar section in my physics textbook, and I came across an equation ... in the section for Heisenberg's uncertainty principle.

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

Hope that helps?
 
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?
 
x--> uncertainty in particle's position...
p--> uncertainty in particle's momentum...
 
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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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