CH101 SPRING 2012 MID TERM REVIEW QUESTIONS (CHAPTERS 1-3) SOLUTIONS 1. A modification of the de Broglie matter wave equation that accounts for the presence of potential energy is h λ(r) = 2m[ E V (r )] Calculate the de Broglie wavelength in Å for an electron in helium (assume 4.00 amu for the He nucleus) at a fixed total energy E of − 3.40 eV at a distance of 2.0 Å from the nucleus. Electron-electron repulsion may be ignored. [Planck’s constant h = 6.626 x 10-34 Js; mass of electron m = 9.109 x 10-31 kg] V (eV ) 14.40 q1q2 2 1 14.40 14.40 eV 2.3110 18 J r 2.0 6.626 1034 J s 2 (9.109 10 31 kg ) (3.40 (1.602 10 19 J ) 2.3110 18 3.75 1010 m J) 3.75 Å or 0.375 nm 2. Determine the wavelength of the first line in the emission spectrum of H in the Paschen series (based on n = 3). [RH (Rydberg constant) = 3.29 x 1015 /s; c (speed of light) = 3.00 x 108 m/s] The Paschen series is the one based on n = 3 and the first line (the one of longest wavelength) in the emission spectrum is formed by n4 n3. 1 (/s) = R (/s) _ n32 = 3.29 x 1015 (/s) 1 n42 1 _ 1 9 16 = 1.599 x 1014 /s Since = c/ , = (3.00 x 108 m/s) / (1.599 x 1014 /s) = 1.88 x 10-6 m or 1880 nm 3. Determine the maximum wavelength of light that is needed to eject electrons from the surface of sodium, if the work function of sodium is 4.41 x 10-19 J. [Planck’s constant h = 6.626 x 10-34 Js; speed of light c = 2.998 x 108 m/s] The maximum wavelength of light here is the one that supplies just enough energy to overcome the work function ( ) at the surface of Na. The electron kinetic energy here is zero and hence, from the Einstein equation, E = 6.626 x 10-34 (Js) x 2.998 x 108 (m/s) E = = hc Hence, = 4.41 x 10-19 (J) = 4.50 x 10-7 m or 450 nm (visible region) 4. Identify and sketch the boundary surface for the orbital with the following wave function: 1 = 81 6 a0 _ 3 2 = r/a0, where a0 is the Bohr radius. 2 e _ 3 (3cos2 - 1) 5. Sketch the plot of radial distribution function (r 2[R(r)]2) versus r for 1s, 2p, 3d and 4f orbitals, relating the value of r for the maximum value of the function with a0, the Bohr radius. 6. Give n, l, number of orbitals, number of radial nodes and number of angular nodes for the orbitals, 3s, 2p, 6d, 5f and 5p. Orbital 3s 2p 6d 5f 5p n l 3 2 6 5 5 0 1 2 3 1 No. orbitals 1 3 5 7 3 No. radial nodes 2 0 3 1 3 No. angular nodes 0 1 2 3 1 7. Predict which of the following pairs of ions have the greatest coulombic attraction in a solid compound (a) K+, O2- : Ga3+, O2- ; Ca2+, O2(b) Mg2+, S2- ; Mg2+, Se2- ; Mg2+ O2(a) K, Ca and Ga are all in the 4th period. Ga3+ is smallest and most highly charged cation and so forms the strongest coulombic attraction with O2-. (b) O, S and Se are all in group VIA, with O 2- being the smallest anion. Hence coullombic attaction is greatest for Mg2+ O2-. 8. Write the best Lewis diagram for the anion PO2Cl2-. P is central atom (group VA) .. _ :O : .. : Cl .. P + .. :O .. .. .. : Cl .. Cl : .. P : O: _ .. Cl : .. : O: _ .. (With fewer formal charges) 9. Write down Lewis diagrams, with formal charges on all atoms, for the molecules cyanic acid (HOCN) and fulminic acid (HCNO). State which molecule is likely to be the more stable. Lewis diagrams (with all formal charges): 0 0 0 0 0 + 0 0 .. .. .. .. H O C N H C N O or H C : .. .. HOCN can be written with no formal charges and hence is more stable + N 0 .. O: 10. Write resonance structures for the formate ion (HCOO -) and comment on the C-O bond length in real formate salts. .. .... _ O: O .. : H C H .. _ C O .. : O: .. O H C _ O Resonance implies equal C-O bond lengths (agrees with experiment) 11. Arrange the following in order of bond strength. (a) HCl; HF; HBr; HI (b) O2; F2; N2 (a) The order of atomic size is F<Cl<Br<I, hence order of bond strength is HF>HCl>HBr>HI. (b) Bond orders are O2 = 2; F2 = 1; N2 = 3, hence order of bond strength is F2<O2<N2. 12. Use the VSEPR theory to determine the shape of the tellurium tetrachloride (TeCl4) molecule. State whether TeCl4 is polar or nonpolar. .. : Cl : .. : Cl .. Lewis diagram xx Te : Cl : .. .. Cl : .. electron pairs = 5: trigonal bipyramidal arrangement, Cl Cl : but “seesaw” or “distorted tetrahedron” shape Te Cl Cl polar 13. Use the Valence bond theory to sketch the molecule ketene (CH2=C=O), showing hybridization modes of C and O, types of sigma bonds, and pi bond formation. 14. Sketch molecular orbital diagrams for the following species, and arrange them in order of increasing bond order. BC, OF-, N2-, NO+, BN. 15. Sketch the molecular orbital energy diagram for NH and predict its magnetic properties. 16. Use MO theory to predict which of the following has the strongest bond: NO +, N2+, O2+. Identify and sketch the MO boundary surface of the NO+ highest occupied MO (HOMO).