ECE 480 Introduction to Nanotechnology
Home Work 1 (Due date 28.10.2014)
1) Chromium has four naturally occurring isotopes: 4.34% of 50Cr, with an atomic weight
of 49.9460 amu; 83.79% of 52Cr, with an atomic weight of 51.9405 amu; 9.50% of 53Cr, with an
atomic weight of 52.9407 amu; and 2.37% of 54Cr, with an atomic weight of 53.9389 amu. On
the basis of these data, confirm that the average atomic weight of Cr is 51.9963 amu.
2) The net potential energy between two adjacent ions, EN, may be represented as,
Calculate the bonding energy E0 in terms of the parameters A, B, and n using the following
procedure:
1. Differentiate EN with respect to r, and then set the resulting expression equal to zero, because
the curve of EN versus r is a minimum at E0.
2. Solve for r in terms of A, B, and n, which yields r0, the equilibrium interionic spacing.
3. Determine the expression for E0 by substituting r0 into Equation above.
3) Iron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight
of 55.85 g/mol. Compute its theoretical density.
4) Rhodium has an atomic radius of 0.1345 nm and a density of 12.41 g/cm3. Determine
whether it has an FCC or BCC crystal structure.
5) What are the indices for the directions indicated by the two vectors in the following
sketch?
6) An unknown semiconductor has Eg = 1.1 eV and Nc = Nv. It is doped with 1015 cm-3
donors, where the donor level is 0.2 eV below Ec. Given that EF is 0.25 eV below Ec, calculate ni
and the concentration of electrons and holes in the semiconductor at 300 K.