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## Homework Statement

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.

## Homework Equations

Δx*Δp≥ h/4*pi

E=sqrt(p²c²+m²c

^{4})

## The Attempt at a Solution

Searching for the minimum value of the energy

Δx ≈ x

Δp ≈ p

x*p≈h/4*pi

so x=10

^{-14}

p=h/(4*pi*x)

sqrt(p²c²+m²c

^{4})=sqrt(h²/(4²*pi²*x²)+m²c

^{4})

E=sqrt(h²/(4²*pi²*x²)+m²c

^{4})

I found ≈ 5 Mev for the minimum energy for an electron in a nucleus, is my method correct ?

Thanks !