Molecular Physics | Thermodynamics Answers

Calculate the first order x-ray diffraction angle from the (113) set of planes in fcc platinum which has a lattice parameter of 0.39 nm, given that the wavelength of the x-rays is 0.154 nm

Calculate the atomic packing fraction of the fcc crystal structure.

Determine the boundaries of the first Brillouin zone for potassium which has a bcc structure and a lattice constant of 5.32 Å.

Calculate the density of bcc iron which has a lattice constant of 2.87 Å and an atomic weight of 55.85.

The energy of the lowest allowed level for an electron in a 1-D box is 10.0 eV. Can the electron ever have an energy of 200 eV? Justify.

In an orthorhombic crystal, a lattice plane makes intercepts of 2a, 3b and 4c on the three axes. Write down the Miller indices for this plane.

The BF_3 molecule has a planar triangular structure with B at the centre. List the symmetries of the BF_3 molecule.

A copper rod ( α = 0.000017 /°C ) is 20 cm longer than an aluminum rod ( α = 0.000022 /°C ). How long should the copper rod be if the difference in their lengths is to be independent of temperature? Hint: For their difference in length not to change with temperature, ΔL must be the same for both rods under the same temperature change.

A particle of mass m moves in a three dimensional box with dimensions a , b , c . Calculate the

allowed energy values.
For a=b=c=L give the first five eigenvalues of the energy and the coresponding degenerate energy levels .


Hint:
Consider solution of this kind: Ψ(x , y , z)=Ψx (x)Ψy ( y )Ψ z(z ) with energy E and solve for
Ψx ,Ψy ,Ψz with energies Ex , Ey ,Ez where E=Ex+Ey+Ez

Derive an expression for adiabatic lapse rate.