Calculate the inter-atomic equilibrium distance re for for which the equilibrium lattice energy is
,
and the Madelung constant is 1.75.
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Show that the reciprocal lattice of a bcc lattice is an fcc lattice. Calculate the magnitude of the shortest non-zero reciprocal lattice vector.
A metallic element has a density of , a lattice constant of
and an atomic weight
. Calculate the number of atoms per unit cell of this element and predict its lattice crystal structure.
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Note: For the central atom located at (0,0,0) in the bcc unit cell, the nearest neighbours are located at , where a is the lattice constant.
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For Chromium () vapour at
with a number density of atoms
calculate:
i) The Larmor diamagnetic susceptibility assuming the atomic radius to be 1.2 A.
ii) The Curie paramagnetic susceptibility.
In Sommerfeld free electron theory, show that at a temperature T
(i) and (ii)
Calculate the inter-atomic equilibrium distance re for for which the equilibrium lattice energy is
,
and the Madelung constant is 1.75.