3. One interesting consequence of quantum mechanics is the idea that bound particles cannot be stationary...

 

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3. One interesting consequence of quantum mechanics is the idea that bound particles cannot be stationary - even at absolute zero. A "bound" particle is one that is confined in some finite region of space, as is the case for an atom in a solid. There is a non-zero lower limit on the kinetic energy of such a particle. (a) Suppose an electron is confined in one dimension to a region of width L. Obtain an approximate formula for its minimum kinetic energy using the uncertainty principle. Be sure to justify your steps. (b) How does this expression compare to the approximate formula we derived in class for the energy of an electron in a Hydrogen atom? 3. One interesting consequence of quantum mechanics is the idea that bound particles cannot be stationary - even at absolute zero. A "bound" particle is one that is confined in some finite region of space, as is the case for an atom in a solid. There is a non-zero lower limit on the kinetic energy of such a particle. (a) Suppose an electron is confined in one dimension to a region of width L. Obtain an approximate formula for its minimum kinetic energy using the uncertainty principle. Be sure to justify your steps. (b) How does this expression compare to the approximate formula we derived in class for the energy of an electron in a Hydrogen atom?