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Electron vs. Proton - 2/2m Energy needed to confine an...

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Why does the proton stay in the nucleus but the electron doesn’t? The Heisenberg Uncertainty Principle helps answer this question. ΔxΔp = h/4π For a large atom, we can assume the atomic diameter is 4 Å (4.0 x 10 - 10 m). Assume the diameter of the nucleus 1/20,000 of that or 2 x 10 - 14 m (20 fm) We want to calculate the energy needed to hold the electron or proton in the nucleus. First use ΔxΔp = h/4π to find the momentum . Then, convert this to energy using a kinetic energy equation: E = p
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Unformatted text preview: 2 /2m Energy needed to confine an electron to an atom 9.4 eV (in the range of accepted ionization energies) Energy needed to confine an electron to the nucleus 3.7 GeV (way outside the acceptable range by a factor of 1000) Energy needed to confine a proton to the nucleus 2.05 MeV (in the range of accepted nuclear binding energies) In summary, to confine something to a smaller volume requires a higher energy . ↓ Δx ↑ Δp = h/4π...
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