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Intro to Quantum Physics questions

  • Thread starter Odyssey
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  • #1
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Hello everybody, I got two questions on my assignment that I am stuck on...it'd be great if you guys can give me some hints to get me in the right direction. :smile:

1) Using the uncertainty principle, find the minimum value (in MeV) of the kinetic energy of a nucleon confined within a nucleus of radius [tex]R=5x10^-15 m.[/tex]

2) Show that the electron orbits in the semi-classical Bohr model are not real. Do this by showing that any attempt to measure the orbit radius to an accuracy [tex] \Delta{x}<<R_{n+1}-R_{n}[/tex] is the radius of the electron in the hydrogen atom, would cause an uncertainty in the energy [tex]E_{n}[/tex] which is larger than the binding energy in that orbit. (Hint: This problem requires that you make suitable approximations).

Of the two questions, I am more desperate for number 2 :cry:...I don't know where to begin!!
 
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Answers and Replies

  • #2
Gokul43201
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According to the posting guidelines, we can't help you unless you start.

What do you know about the Uncertainty Principle?
 
  • #3
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About the uncertainty principle...I just know the basics...that if [tex]\Delta{x}[/tex] and [tex]\Delta{p}[/tex] are the uncertainties in position and momentum, respectively, then their product must be at least [tex]\hbar /2[/tex]. Do I set the radius equal to [tex]\Delta{X}[/tex]??
 
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  • #4
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Correct, you would set the radius to [tex]\Delta x[/tex].

If you solved the uncertainty principle for the minimum momentum in this case, you could easily find the minimum kinetic energy.
 
  • #5
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Thank you for the help. Here's what I got after setting the radius equal to [tex]\Delta{x}[/tex]...please check my work. :)

[tex]\Delta{p}\geq{\hbar /2\Delta{x}}[/tex]
[tex]\Delta{p}\geq{(1.05*10^-34Js)/(2)(5*10^-15m))}[/tex]
[tex]\Delta{p}\geq{1.05*10^-20kgm/s}[/tex]

Then I used the minimum value of momentum and the mass of the nucleon to find the minimum kinetic energy...
[tex]E_{k}\geq{p^2/2m}[/tex]
[tex]E_{k}\geq(1.05*10^-20kgm/s)^2/(2)(3.34*10^-27kg)[/tex]
[tex]E_{k}\geq1.65*10^-14J[/tex]
 
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  • #6
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[tex]\hbar[/tex] should be [tex]1.05*10^{-34} Js[/tex]
 
  • #7
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yes, that was a typo there. [tex]\hbar[/tex] should be [tex]1.05*10^{-34} Js[/tex]. The final value I get is [tex]E_{k}\geq1.65*10^-14J[/tex].
 

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