Q32E By the 鈥渧ector鈥� technique of... [FREE SOLUTION]

Chapter 10: Q32E (page 468)

By the 鈥渧ector鈥� technique of example 10.1 , show that the angles between all lobes of the hybrid ${sp}^{3}$ states are $109.5 掳 .$ .

Short Answer

Expert verified

The Angle between all lobes of hybrid ${sp}^{3}$ states are $109.5 掳$

Step by step solution

Finding Four States that participate in hybrid.

$蠄_{1} = 蠄_{2 s} - 蠄_{2 p z} 蠄_{2} = 蠄_{2 s} + \frac{1}{3} 蠄_{2 p z} - \frac{\sqrt{8}}{3} 蠄_{2 p x} 蠄_{3} = 蠄_{2 s} + \frac{1}{3} 蠄_{2 p z} - \frac{\sqrt{2}}{3} 蠄_{2 p x} - \frac{\sqrt{6}}{3} 蠄_{2 p x} 蠄_{4} = 蠄_{3} = 蠄_{2 s} + \frac{1}{3} 蠄_{2 p z} - \frac{\sqrt{2}}{3} 蠄_{2 p x} - \frac{\sqrt{6}}{3} 蠄_{2 p x}$

Now We will Use Dot product to Find The Angle.

A.B=AB Cos $胃$ (Here A and B are vectors).

To Calculate the Dot Product.

Ignoring the 2s state contribution, to calculate the length of each state.

$|蠄_{1}| = {(- 1)}^{2} = 1 {|蠄_{1}|}^{2} = (\frac{1}{3}) + {(\frac{\sqrt{8}}{3})}^{2} = 1 蠄_{3 or 4} l^{2} = {(\frac{1}{3})}^{2} + {(\frac{\sqrt{2}}{3})}^{2} + {(\frac{\sqrt{6}}{3})}^{2} = 1 For Dot Products Calculation . . 蠄_{1 .} 蠄_{2} = (0, 0, 1) . (\frac{- \sqrt{8}}{3}, 0, \frac{1}{3}) = \frac{- 1}{3} 蠄_{2} . 蠄_{3 or 4} = (0, 0, - 1) . (\frac{\sqrt{2}}{3} 卤 (\frac{\sqrt{6}}{3}, \frac{1}{3}) = \frac{- 1}{3} 蠄_{2} . 蠄_{3 or 4} = (\frac{\sqrt{2}}{3} - (\frac{\sqrt{6}}{3}, \frac{1}{3}) . (\frac{\sqrt{2}}{3}, (\frac{\sqrt{6}}{3}, \frac{1}{3}) = \frac{2}{9} - \frac{6}{9} + \frac{1}{9} = \frac{- 1}{3} In all cases the Dot Product is \frac{- 1}{3} and the length is always 1 . So, Cos 胃 = \frac{AB}{|AB|} = \frac{- 1}{3} 胃 = \cos^{- 1} (\frac{- 1}{3}) = 109.5 掳 . . Hence, The Angle between all lobes of hybrid {sp}^{3} states are 109.5 掳$

For Dot Products Calculation..

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

By the 鈥渧ector鈥� technique of example 10.1 , show that the angles between all lobes of the hybrid ${sp}^{3}$ states are $109.5 掳 .$ .

Short Answer

Step by step solution

Finding Four States that participate in hybrid.

To Calculate the Dot Product.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Kinematics Physics

Atoms and Radioactivity

Fundamentals of Physics

Rotational Dynamics

Electrostatics

Study anywhere. Anytime. Across all devices.

91影视

By the 鈥渧ector鈥� technique of example 10.1 , show that the angles between all lobes of the hybridsp3states are 109.5掳..

Short Answer

Step by step solution

Finding Four States that participate in hybrid.

To Calculate the Dot Product.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Kinematics Physics

Atoms and Radioactivity

Fundamentals of Physics

Rotational Dynamics

Electrostatics

Study anywhere. Anytime. Across all devices.

By the 鈥渧ector鈥� technique of example 10.1 , show that the angles between all lobes of the hybrid ${sp}^{3}$ states are $109.5 掳 .$ .