HW 1-Sol - HW 1 Solutions Due January 30th 1(Problem 2.4...

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HW 1 -- Solutions Due: January 30 th 1. (Problem 2.4 from Callister 7 th Ed): In this question, you are asked to list some of the difference between the Bohr’s treatment of the atomic structure vs. the modern quantum mechanical view: a. Cite two important quantum mechanical concepts associated with the Bohr model of the atom. Bohr’s Model: o This model assumes electrons behave like particles, orbiting around the nucleus (wrong!) o The orbits, however, are quantized (good!) o The position of any particular electron is well defined in a particular orbit (completely wrong!!!) b. Cite two important additional refinements that resulted from the wave-mechanical atomic model Quantum View: o Electrons exhibit wave-particle characteristics o ‘Discreteness’ of orbits results from wave-mechanical nature of electron states (only integer wave numbers ‘fit’ in determined orbitals) o At best, you can only say that there is a certain probability of observing an electron around the nucleus o There are four quantum numbers necessary to describe the state of an electron in an atom 2. (Problem 2.7 Callister) Give the electron configurations for the following ions: P 5+ , P 3- , Sn 4+ , Se 2- , I - and Ni+ 2 P [15]: 1s 2 2s 2 2p 6 3s 2 3p 3 = [Ne] 3s 2 3p 3 o P 5+ = [Ne] o P 3- = 1s 2 2s 2 2p 6 3s 2 3p 6 = [Ne] 3s 2 3p 6 =[Ar] Sn [50]: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 2 =[Kr]5s 2 4d 10 5p 2 o Sn +4 = [Kr]5s 0 4d 10 5p 0 (d shells like to be half full or completely full) Se [34] : 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 4 = [Ar]3d 10 4s 2 4p 4 o Se 2- = [Ar] 3d 10 4s 2 4p 6 I [53] : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 =[Kr]4d 10 5s 2 5p 5 o I - = [Kr] 4d 10 5s 2 5p 6 Ni[28]: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 8 = [Ar]3d 8 4s 2 o Ni +2 = [Ar]3d 8
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3. The net potential energy between two adjacent ions, E N , may be represented by the following equation: N n A B E r r = − + (1.1) a. Find an expression for the interatomic force as a function of separation The interatomic force is just the rate of change of the potential energy with respect to separation: ( ) ( ) 2 1 n E r A Bn F r r r r + = = b. Determine the equilibrium separation, r 0 , in terms of A, B and n The equilibrium separation corresponds to the separation where the interatomic force banishes (first instance for this condition, since the force also vanishes at infinite separation!!): ( ) ( ) 2 1 1/ 1 1/1 0 0 n n n E r A Bn F r r r r nB A r A nB + = = = = = c. Determine the expression for bonding energy, E 0 The bonding energy corresponds to the Energy of the system at the equilibrium separation: 0 1/(1 ) /(1 ) 0 0 n n n n A B A B E r r A A nB nB = − + = + 4. List four characteristics of each of the different kinds of primary bonds.
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