Question

Using the tabular method and showing all work in the table (as we did in the lecture example), decompose the following reducible representations into the component irreducible representations in the point group indicated: D3h E 2C33C2 On 25330 T 521 303 Td E 8C33C265460d DS 115 1011- 13 On T E 21 8C3 6C2 604 3C2 0 -1 3 -3 i 654 856 3on 600 -3 -1 0 5 3

Answer 1

Ans: o out the 119 ♡ In the question we chave to find out irreducible representation for the point a st is Dah: for calculation of urreducible repres. entation we need character staple of Dok Charactee Table of Doh Torder=12=h Doh E. RC3 BG on 283 Bor : An B 1 2 1 - 1 2 1 -1 6- To ī- 0 - A," -1 tu I 2 at 0 -1 2 - ho we will find using the reduction irreducible, representation (ER) formula a>A -I [5xixi teXI X2 + 3X1X1 + 3x1*1 + 0 + Bxgx] 07 A 12 - [5+4+2+3 +9] = + x24 = 2 * Ai = by Az - I 5x1x1 + 2X2X1 +3X1X61) + 3x1x1 +0+ 3x3x-1); I r 5+4-373-9] =0 = 124

Date : Expt. No. Experiment : Date :_ c) € - + [OXIX 2 + 2x2x-1 +0+3x1x2 +0+07 - to [10 -4 +6] = { 1 → E' = 1 dy A - • [5x1x1 + 2x2x1 + 3X1X1 +1X3 X-) + 0 + 3x38-17 [5+ 4+3-3-9] = 0 7 AT = 0 ey A," = [5x1x1 + 2x2x1 + 3XIX-1 + 3X1X-1 to +3X3X77 2 L L 5+4-3-3 12L574-3 → A3! = F) E" I 5x2x1+QXQX-1+0+ 3XIX(-2) +oto] LLL [10-4-6] = 0 2 L Pie ITIR = 26; + &' + " - chence * is the love ducible for the Dgh point group. representation CS Scanned with CamScanner

F ay Now meteen in the dimilar way we will find ② the ovreducible representation for Td 120 - point group. Here order = h = 24 Character table for Tel : 1 T É 863 BC 654 60d Am I 1 1 1 1 Agi l -1 -1 E 2 -1 2 0 Ti 8 0 - 1 - Tz 3 0 -1 -1 1 - E 863 362 654 God 15 0 -1 -1 3 Now we will find irreducible representation for Td using reduction formula .. ad A-L [15X1X1 +0+3X(-1881 + 6X1X-1 + 6x 3x1] sto ( 15 +0-3-6+18] - 24 do os ا → A1 = 1 b4y = L [1541x) +0+ 3X-1X1.+ 6X6-7X(-1)+ 6x3x-1] -L115-3 +6-18] = [21-21] = 0 Scanned with CamScanner

Det EXTRA. NO Expertment c) € - Lue lisxix 2 + 0 + Oxume +0+0] [30-6] + = dy T, Pk [ 15X1* 3+ 0.+ 3x-17-1 + 6Y-1X1+ 6X6X4) MC 45+3-6.-18) = 2 = 1 = Tizde es T2 = L 15X1X3+37-1X-1 + 6X-1X+1 + 6X3xı] to [45+3+6+ 18) = 2 = 3 T2 =3 Thus I TER = A, +E + T. +372 - # Hence # is the irreducible representation for Jetrahedrsal point group. you Thank Arabhi Ics Scanned with CamScanner