Question

Employing the uncertainty principle, estimate the minimum kinetic energy of an electron confined within a region whose sizes is `l=0.20nm`.

Answer 1

Clearly `Deltax le l" so" Delta p_(x),ge(ħ)/(l)`
Now `p_(x)geDeltaP_(x)` and so
`T=(p_(x)^(2))/(2m) ge (ħ^(2))/(2ml^(2))`
Thus `T_(min)=(ħ^(2))/(2m l^(2))~=0.95eV`