Intro to Quantum Physics questions

In summary, the minimum kinetic energy of a nucleon confined within a nucleus of radius 5x10^-15m is 1.65*10^-14J.
  • #1
Odyssey
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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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  • #2
According to the posting guidelines, we can't help you unless you start.

What do you know about the Uncertainty Principle?
 
  • #3
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
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
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
[tex]\hbar[/tex] should be [tex]1.05*10^{-34} Js[/tex]
 
  • #7
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].
 

1. What is quantum physics?

Quantum physics is a branch of physics that studies the behavior and interactions of particles at a microscopic level, such as atoms and subatomic particles. It explores the fundamental laws and principles that govern the behavior of matter and energy at this scale.

2. How does quantum physics differ from classical physics?

Classical physics describes the behavior of macroscopic objects, while quantum physics explains the behavior of particles at a microscopic level. In quantum physics, particles can exist in multiple states simultaneously and can exhibit properties of both particles and waves, unlike classical particles which have well-defined properties.

3. What are some real-world applications of quantum physics?

Quantum mechanics has many practical applications in modern technology, such as transistors, lasers, and computer memory. It is also essential in the development of quantum computing, cryptography, and quantum communication.

4. What is the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that it is impossible to know both the exact position and momentum of a particle simultaneously. This means that there will always be a degree of uncertainty in our measurements of these properties.

5. Can quantum physics explain the concept of entanglement?

Yes, entanglement is a phenomenon in quantum physics where two particles become linked in a way that their states are dependent on each other, even when separated by large distances. This concept has been experimentally proven and has potential applications in quantum computing and communication.

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