Use the Heisenberg uncertainty principle to estimate the uncertainty in momentum resulting from confining an electron...

Use the Heisenberg uncertainty principle to estimate the uncertainty in momentum resulting from confining an electron to an atom (~10^-10 m) and to the size of an atomic nucleus (~10^-15 m). Calculate the corresponding uncertainty in the energy (in eV) of the confined electron and briefly comment on the physical implications of your results.

Expert Solution

From Heisenberg uncertainty principle, the minimum uncertainty possible will be given by

a) = 10^-10 m. Then = 1.055 x 10^-34 / (2 x 10^-10) = 5.275 x 10^-25 kg m s^-1.

b) = 10^-15 m. Then = 1.055 x 10^-34 / (2 x 10^-15) = 5.275 x 10^-20 kg m s^-1.

The difference between the two energies are of the order of 10¹⁰. This shows that when the electrons are confined to a very small space, their uncertainty in energy increases. This arrises from the Heisenberg uncertainty principle.

genius_generous answered 2 years ago

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