HW4-2012
1
MATSE 304 Homework Set #4 due at the beginning of lecture on 2/17/12 1. Starting from the orbitals obtained through carbon s-p hybridization, prove that isolated carbon atoms with sp 3 and sp 2 p configurations are spherically symmetric. 2. By drawing the bonding and anti-bonding levels, compare the dissociation energy of each pair of molecules given (a) Cl 2 and Cl 2 + (b) NO and NO - (c) O 2 + and O 2 - (d) B 2 and B 2 + 3. Assume that, in the vicinity of the equilibrium spacing R 0 , the electron energy for the H 2 + molecular ion can be approximated by the formula E el = -BR -5/6 . (a) Using the experimental value of R 0 (0.108 nm), calculate the constant B. (b) Using this value of B, calculate the bond strength. (c) Using this value of B, calculate the spring constant K at equilibrium. Useful information: For H 2 + the total energy (E t ) is the sum of the electron energy, E el , and the repulsive energy between the two nuclei. At the equilibrium distance, the total energy is at a minimum. The spring constant K is defined as 4. The interaction of two Ar atoms at a distance R can be written with σ = 3.4 Å and ε = 0.01 eV. Calculate (a) Equilibrium distance between atoms (b) Binding energy between the 2 atoms (c) Force required to separate the 2 atoms (d) Distance between the atoms at the point of separation (e) If the Ar atoms crystallize into a close packed structure (fcc), what is the lattice constant? 5. Problem 3.23 in S.O. Kasap – Page 280. Use the hydrogenic model.
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Transcript of HW4-2012
MATSE 304
Homework Set #4 due at the beginning of lecture on 2/17/12
1. Starting from the orbitals obtained through carbon s-p hybridization, prove that isolated
carbon atoms with sp3 and sp2p configurations are spherically symmetric. 2. By drawing the bonding and anti-bonding levels, compare the dissociation energy of each
pair of molecules given
(a) Cl2 and Cl2+
(b) NO and NO- (c) O2
+ and O2-
(d) B2 and B2+
3. Assume that, in the vicinity of the equilibrium spacing R0, the electron energy for the H2
+ molecular ion can be approximated by the formula Eel = -BR-5/6.
(a) Using the experimental value of R0 (0.108 nm), calculate the constant B. (b) Using this value of B, calculate the bond strength. (c) Using this value of B, calculate the spring constant K at equilibrium. Useful information: For H2
+ the total energy (Et) is the sum of the electron energy, Eel, and the repulsive energy between the two nuclei. At the equilibrium distance, the total energy is at a minimum. The spring constant K is defined as
4. The interaction of two Ar atoms at a distance R can be written
with σ = 3.4 Å and ε = 0.01 eV. Calculate (a) Equilibrium distance between atoms (b) Binding energy between the 2 atoms (c) Force required to separate the 2 atoms (d) Distance between the atoms at the point of separation (e) If the Ar atoms crystallize into a close packed structure (fcc), what is the lattice constant?
5. Problem 3.23 in S.O. Kasap – Page 280. Use the hydrogenic model.
![Hw4 solution - University of California, San Diegocontrol.ucsd.edu/mauricio/courses/mae143b-S2012/hw4… · · 2012-05-04Matlab Code: KD=0.4; KP=21.5; T=tf([200*KD 200*KP],[1 12+200*KD](https://static.fdocuments.in/doc/165x107/5acdad6b7f8b9a73128e4bb5/hw4-solution-university-of-california-san-2012-05-04matlab-code-kd04-kp215.jpg)
