Question

4. (20 pts) Show that two of the set of four equivalent orbitals appropriate for sp hybridization, hi = 12 (-s + px + Py + P2) h2 = 12 (-S - Px - Py + P2) are normalized and orthogonal.

Answer 1

& let us take an orbital - 0,= 4, 4; 4 (z 4'2 d, will be normalised ja seda, a 11.4, +4% 2) (6, 4, + 2 % 2 ) de 21 orthogored. a1. Bis482 + 6C2% 4,4% dy + y 2 " +4,454,428Y21 a 142 +5=17 – This is the condition Now, hi = £ 1-st Put Py + P2) 2-45 +LPx + 4 Py +ļpę. 4 , C9 z C4. 1 2 2 + z ten = 1-4)²+14) ² + 2)² + ( ₂² 2 bat tote* 5 + + 2). - Thus, h, is normalised be suite=i 4 = b 1-5 + Pu - Py + Pe) 2-45+ Pue - Py + { P . 21-4)+14) +1+4)*+14)*= £ + + + + + = 1 This he is normalised se. S ha dx = 1 1 New; h, & he will be orthogonal if sh, he de =0 su kedy = 4S 1-5 tlu+ Py +Pz) 1-5--Px – Py + P3) ay -Ispo de ISM Piet (Py Pedro + f Pq lde]

This h, and hq are or thogonal
NOTE: Every atomic orbital is normalised and orthogonal to other orbitals.