Assuming an electron is confined to a 1nm wide region,

Question:

Assuming an electron is confined to a 1nm wide region, find the uncertainty in momentum using the Heisenberg Uncertainty principle. You can assume the uncertainty in position ∆x as 1nm. Assuming p = ∆p, find the energy of the electron in electron volts.

Solution:

As the electrons rotate in a circular path, ∆r = 1 nm = 10-9 m

∆p = h/∆x

∆p = (331/314) × 10-25

E = 1/2 mv2 = ∆p2/2m

E = 3.8 × 10-2 eV

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