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Uncertainty principle for electron in nucleus

  • Thread starter Dassinia
  • Start date
Hello, I have this exercise and want to check if what i did is correct
1. The problem statement, all variables and given/known data

Nuclei, typically of size $10^{-14}$ m, frequently emit electrons with energies of 1-10 MeV. Use the uncertainty principle to show that electrons of energy 1 MeV could not be contained in the nucleus before the decay.

2. Relevant equations

Δx*Δp≥ h/4*pi

3. The attempt at a solution
Searching for the minimum value of the energy
Δx ≈ x
Δp ≈ p
so x=10-14
I found ≈ 5 Mev for the minimum energy for an electron in a nucleus, is my method correct ?
Thanks !


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I think you did it backwards. You want to assume the electron has an energy of 1 MeV and show that this implies ##\Delta x > 10^{-14}\text{ m}##.

Off the top of my head, I'd expect your calculation to give E ~ 10 MeV.
I don't get how i can do it following what you're saying

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