Range of speeds of particle confined in box

AI Thread Summary
The discussion centers on estimating the speed range of a proton confined within a nucleus of diameter 3.80 femtometers using the uncertainty principle. The calculation involves the relationship between position uncertainty and momentum, leading to a derived speed of approximately 5.22 x 10^7 m/s. There is confusion regarding the use of Planck's constant (h) versus the reduced Planck's constant (h-bar) in the calculations. Participants clarify that the uncertainty principle should use h-bar for accurate results. The original poster is encouraged to revisit their setup and calculations for consistency with quantum mechanics principles.
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1. A proton is confined within an atomic nucleus of diameter 3.80 fm. Estimate the smallest range of speeds you might find for a proton in the nucleus.



2. Uncertainty Principle



3. 3.80fm * mv = h/2

Soliving for h, using mass of proton = 1.67*10-27kg, I obtain v = 5.22*107. Then, dividing by two I obtain a final answer:

0 less than/equal to v less than/equal to 2.6*107

Is this correct?
 
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That is how I would set it up. I got a different answer though. You are using h-bar not h right?
 
Why h-bar? The uncertainty principle is delta(x)delta(p) greater than/equal to h/2
 
any luck with this question? I have the same question with different values am not sure how to approach it
 
dc5itr888 said:
any luck with this question? I have the same question with different values am not sure how to approach it

Op set it up right he just used h instead of h-bar.
 

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