Material Science HW 1
1. Using a Modulus of Elasticity versus Density materials selection chart, which materials would you choose to achieve the best performance for a bicycle frame, and why?
Discuss the cost of different material options.
2. Bromine has two naturally occurring isotopes: 79Br, with an atomic weight of 78.918 amu, and 81Br, with an atomic weight of 80.916 amu. If the average atomic weight for Br is 79.903 amu, calculate the fraction-of-occurrences of these two isotopes.
3. The net potential energy EN between two adjacent ions is sometimes represented by the expression
in which r is the interionic separation and C, D, and ρ are constants whose values depend on the specific material.
(a) Derive an expression for the bonding energy E0 in terms of the equilibrium interionic separation r0 and the constants D and ρ using the following procedure:
1. Differentiate EN with respect to r and set the resulting expression equal to zero.
2. Solve for C in terms of D, ρ, and r0.
3. Determine the expression for E0 by substitution for C in the Equation above.
(b) Derive another expression for E0 in terms of r0, C, and ρ using a procedure analogous to the one outlined in part (a).
4. The atomic radii of Li+ and O2- ions are 0.068 and 0.140 nm, respectively.
(a) Calculate the force of attraction between these two ions at their equilibrium interionic separation (i.e., when the ions just touch one another).
(b) What is the force of repulsion at this same separation distance?