Metallic bonding: One can use some simple-minded arguments to explain why metall

Question

Metallic bonding: One can use some simple-minded arguments to explain why metallic bonding is stable. One argument is that allowing the wave functions to be smeared out in space reduces the momentum uncertainty ?p and thereby the highest momentum (and energy) through ?p?x = h 2 (You might recognize this equation as the Heisenberg Uncertainty Principle which is actually ?p?x? h 2 . Here we are interested in the lower limit of the uncertainty, hence the equal sign. Estimate how much ?p would be reduced by allowing the wave function to spread from typical atomic dimensions (Bohr radius) to the typical dimensions of the lattice unit cell (a few Angstrom or 10 times the Bohr radius). If you assume that the highest p would correspond to a highest kinetic energy e E = p2 2m , how much would this reduce the kinetic energy?

Explanation / Answer

calculate p by using bohr radii(assume to be 1) by
σp * σx = h/2

σp = h/2  .................(1)
than by using new radii (10 times the Bohr radius) by putting in (1)
as

σp' * 10 = h/2

σp' = h/20 .....................(2)

now reduced p would be determined by

p = (h/2 - h/20) = 9h/20

%age reduced energy = p/σp *100 = 90 %

put this value of σp & σp' in energy euation respectively & aply same process u will get reduce energy

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---