Hey there! Sign in to join this conversationNew here? Join for free

Uncertainty principle, electrons and the nucleus. Watch

    • Thread Starter
    Offline

    1
    ReputationRep:
    I have a question I'm not entirely sure how to answer, if I work out the uncertainty of an electron's momentum confined in a space of one femtometer using the uncertainty principle, why does this result tell me that an electron cannot be bound inside a nucleus? I don't really understand why. Any help/tips appreciated.
    Offline

    1
    ReputationRep:
    (Original post by Sasukekun)
    I have a question I'm not entirely sure how to answer, if I work out the uncertainty of an electron's momentum confined in a space of one femtometer using the uncertainty principle, why does this result tell me that an electron cannot be bound inside a nucleus? I don't really understand why. Any help/tips appreciated.
    Well work out the uncertainty of the electron's momentum...
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by TableChair)
    Well work out the uncertainty of the electron's momentum...
    Well yeah I know to do that bit, I got  1.055*10^{-19} kgm/s..how does that show it won't be within the nucleus?
    Offline

    1
    ReputationRep:
    (Original post by Sasukekun)
    Well yeah I know to do that bit, I got  1.055*10^{-19} kgm/s..how does that show it won't be within the nucleus?
    Work out what speed it would have to be moving at. (Ignore SR)
    Offline

    0
    ReputationRep:
    You know that for a particle to be confined in a potential, the wavefunction must be a standing wave, and you need to be able to fit an integer number of half wavelengths within the distance over which is it confined. You can work out the electron's wavelength from the momentum, and then compare it to a typical nuclear radius.
    (you should find that the wavelength is too long for a standing wave to be possible)
    Offline

    1
    ReputationRep:
    (Original post by laeti)
    You know that for a particle to be confined in a potential, the wavefunction must be a standing wave, and you need to be able to fit an integer number of half wavelengths within the distance over which is it confined. You can work out the electron's wavelength from the momentum, and then compare it to a typical nuclear radius.
    No, that's completely circular. By imposing that it is confined to such a potential, you have picked it's wavelength. All you'll do is show that it is possible, since you've defined it to be possible.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by TableChair)
    Work out what speed it would have to be moving at. (Ignore SR)
    Non-relativistically that would be  1.158*10^{11} which is clearly wrong, I do not have the formulas for relativistic speeds.
    Offline

    1
    ReputationRep:
    (Original post by Sasukekun)
    Non-relativistically that would be  1.158*10^{11} which is clearly wrong, I do not have the formulas for relativistic speeds.
    Basically, ignoring SR, it would have to be travelling about 10^3 times the speed of light. The point is it would be travelling too fast to be bound. What level is this by the way?
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by TableChair)
    Basically, ignoring SR, it would have to be travelling about 10^3 times the speed of light. The point is it would be travelling too fast to be bound. What level is this by the way?
    Oh right. That's what has confused me. I wasn't sure how a femtometer linked to the size of a nucleus - after all, isn't one fm close to the value of a proton's radius? How big is a nucleus?

    This is first year university stuff, I've just left my notes at my home for relativity.
    Offline

    1
    ReputationRep:
    (Original post by Sasukekun)
    Oh right. That's what has confused me. I wasn't sure how a femtometer linked to the size of a nucleus - after all, isn't one fm close to the value of a proton's radius? How big is a nucleus?

    This is first year university stuff, I've just left my notes at my home for relativity.
    A nucleus is of the order of 10^-15 m (a femtometre) if I remember correctly, and it would make sense.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by TableChair)
    A nucleus is of the order of 10^-15 m (a femtometre) if I remember correctly, and it would make sense.
    Thanks for the help, apologies that you had to pretty much spell it out for me. Dx
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.