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What is the uncertainty in its mass?

  1. Apr 30, 2006 #1
    This is a really simple problem, but I cannot seem to find the equation. Any help? Thank you.

    1) A free neutron has a mean life of 900 s. What is the uncertainty in its mass?
     
    Last edited by a moderator: Jan 7, 2014
  2. jcsd
  3. Apr 30, 2006 #2

    jtbell

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    Hints: for exponential-decay processes, the uncertainty in the lifetime, [itex]\Delta t[/itex], equals the mean lifetime. Also, remember Einstein's mass-energy equivalence.
     
  4. Apr 30, 2006 #3
    Okay... still do not see an equation. It is from our chapter on Quantum Mechanic of Atoms.
     
  5. May 1, 2006 #4

    Hootenanny

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    HINT: Heisenberg's uncertainty principle
     
  6. May 1, 2006 #5
    Yes, that would be:

    (delta p)(delta x) > h or (energy)(time) > h....

    So how does that help?

    All I know is a time = 900 s.

    So am I solving for energy? e =(1.06 x 10^-34 J)/(900 s) = 1.2 x 10^-37 J

    ? ? ?
     
  7. May 1, 2006 #6

    Hootenanny

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    The full expression is;

    [tex]\Delta E \Delta t \geq \frac{h}{4\pi}[/tex]

    And jtbell gave you a bit hint

    ~H
     
  8. May 1, 2006 #7
    So I did it incorrectly? I am getting a bit confused...
     
  9. May 1, 2006 #8
    Yes I know E = mc^2, but I still lost as to how to solve for uncertainty...
     
  10. May 1, 2006 #9

    Hootenanny

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    Delta E is the uncertainty in energy of the neutron, you need to solve for delta E then convert this into mass using E = mc2.

    ~H
     
  11. May 2, 2006 #10
    Btw, my book doe snot use 4 pie.

    So I solve for E by : E = h/900 s = =1.06 x 10^-34 J/900 s? = 1.2 x 10^-37 J

    Then I use E = mc^2
    1.2 x 10^-37 J = m(3.0 x 10^8)^2
    m = 1.54 x 10^-54 m

    Is that correct! =)
     
  12. May 2, 2006 #11

    Hootenanny

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    Your text uses a modified plank constant ( I think it is correct, I haven't checked it). Your working is right, but be careful, you are inducing rounding errors in you calculations. Also check your units of uncertainty in mass.

    ~H
     
  13. May 2, 2006 #12
    Opps. I mean kg! :-S
     
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