Question

way U nodal calculate the appropriate integra areas under the curve graphi i probability maxima for (b) Describe the motion of the part UUh atom that is 43. Consider the wave function Val Wis dot structure. (You may priate integrals or estimate the relevant a cubic box. Figure 4 A5a shows plane at 2 = 0.75. curve graphically.) Then recalculate the (a) Convince yourself that the co by approximating the integral as y(xo) Ax, 0.25 would have the same uated in the middle of the range from xy to peak would become negativ (b) Describe the shape of this v lly explain why you can't approximate the integral probabilities by appro where xo is evaluated in the middle x2. Finally, explain why 39. Chapter 3 introdu needed for Problem 37(a) in this way. nter 3 introduced the concept of a double bond between carbon atoms, represented by C=C, with a length 1 34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three low- est allowed states if it is confined to move in a one-dimen- sional box of length 1.34 A. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state. at y = 0.5. 44. Consider the wave function a cubic box. Figure 4.45a sh plane at ž = 0.75. (a) Describe the shape of th at š = 0.5. (b) Describe the shape of t at j = 0.5. ADDITIONAL PROBLEMS

Answer 1

for particle in a one dimensional box at wave function is Y 2 2 2 2 sin na x. sohing for energy for 1D box is E2 none n = Positive integers me mass of particle ha planck's constant Now from question, C=C is treated as a iD box and length is 1.34 &. three The lowest, allowed states is nz 1,2,3. 8mL? La length of the box. .. E1 z 22 h 2 E 17 h 8m L² SMLE E228 E3² sm Lr. 8 km L². 84(9:11 X 10 -98.g) * (1.34*10-8 cm) - 54 0.336 X 10 0.335 * 10004 10-44 -10 = - 10-28 x 10-16 0.335 X 100

E1 2 1 x 3.35 x 10 oog E22 277 3.35*10 & 2) 13.4 x 1011 erg 232 32 x 3.358 10 2 30.1510 erg. Es 2 3.35 x 10-18 I E2 2 13.4 x 10-18 ] 3 2 30.65 x 1018 J ground state Ist Excited state. 2nd Excited state. Energy difference from ground State to di excited state is (E2 - E 1) 2 (13.4-3.85x10-18 ] AB 3 10.05x1018 he e 10-05 X10-18 az hac ore 6.625x10x3x108 10.05x10-17 7 2 2 10.05 810-18 - 3 1.977 410-8 m 2 197.7 810lm > ,197.7 Å