Difference between revisions of "GChemPaint/C3/Orbital-Overlap/English"

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Title of the tutorial: '''Orbital overlap'''
+
Title of the tutorial: '''Orbital Overlap'''
  
 
Author: '''Madhuri Ganapathi'''
 
Author: '''Madhuri Ganapathi'''
  
 
Key words: Atomic orbital, Add or modify an atomic orbital tool, rotation  and resize of  orbitals, positive, negative overlaps and zero overlap, Video tutorial
 
Key words: Atomic orbital, Add or modify an atomic orbital tool, rotation  and resize of  orbitals, positive, negative overlaps and zero overlap, Video tutorial
 +
  
 
<font size="2">
 
<font size="2">
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If not, for relevant tutorials,  please visit our website.  
 
If not, for relevant tutorials,  please visit our website.  
 
|-
 
|-
−
||Switch to '''GChemPaint''' application.
+
||'''Slide Number 5'''
−
||I have opened a new '''GChemPaint''' application.
+
−
|-
+
−
||
+
−
'''Slide Number 5'''
+
  
 
'''Atomic Orbital'''
 
'''Atomic Orbital'''
−
||
+
||Let's first see what an '''atomic orbital''' is.
  
−
Let's first see what an atomic orbital is.
+
An '''atomic orbital''' is a mathematical function.  
−
 
+
−
An atomic orbital is a mathematical function.  
+
  
 
It describes the wave-like behavior of an electron in an atom.  
 
It describes the wave-like behavior of an electron in an atom.  
  
−
An orbital is a region of space with maximum probability of finding an electron.
+
An '''orbital''' is a region of space with maximum probability of finding an electron.
 
|-
 
|-
−
||Slide Numbers 6
+
||'''Slide Numbers 6'''
 +
 
 
'''‘s’ and ‘p’ Orbitals'''
 
'''‘s’ and ‘p’ Orbitals'''
  
−
Point to the orbitals
+
Point to the '''orbitals'''.
−
||This is an 's'  orbital.
+
||This is an 's'  '''orbital'''.
  
 
It has '''spherical''' shape.
 
It has '''spherical''' shape.
−
Here are 'p'  orbitals in different axes.
 
  
−
'p' orbitals are '''dumb-bell''' shaped.
+
Here are 'p'  '''orbitals''' in different axes.
 +
 
 +
'p' '''orbitals''' are '''"dumb-bell"''' shaped.
 
|-
 
|-
−
||‘d’ Orbitals
+
||'''Slide Numbers  7'''
−
||Next, we have 'd' orbitals in different axes.
+
  
−
'd' orbitals are '''double dumb-bell''' shaped.
+
'''‘d’ Orbitals'''
 +
||Next, we have 'd' '''orbitals''' in different axes.
 +
 
 +
'd' '''orbitals''' are '''double "dumb-bell"''' shaped.
 
|-
 
|-
 
||Switch to '''GChemPaint''' application.
 
||Switch to '''GChemPaint''' application.
  
−
I have opened a new '''GChemPaint''' application.   
+
||I have opened a new '''GChemPaint''' application.   
 
|-
 
|-
 
||
 
||
−
||Let's first learn about orbitals.  
+
||Let's first learn about '''orbitals'''.
 +
|-
 +
||Click on '''Add or modify an atomic orbital''' tool
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
|-
 +
||Point to the properties window.
 +
||'''Orbital''' property window opens.
 +
|-
 +
||Point to the properties.
 +
||This window contains fields like- '''Coefficient, Rotation''' and '''Type'''.
 +
|-
 +
||Point to Type field.
 +
||First, I will begin with '''Type'''.
 +
|-
 +
||Point to 's'
 +
||By default,  's'  '''orbital''' is selected.
 
|-
 
|-
 +
||Click on '''p, dxy''' and '''dz^2'''  radio buttons.
  
  
 +
Point to the '''orbital''' shapes.
 +
||Let's click on '''p, d xy''' and '''d z square orbital''' radio buttons.
  
 +
Notice the different '''orbital''' shapes displayed alongside.
 +
|-
 +
||Point to  '''Coefficient''' and '''Rotation'''
 +
||Next let's check the '''Coefficient''' and '''Rotation''' properties.
 +
|-
 +
||Cursor on the value box
 +
||'''Coefficient''' property has values from -1.00 to 1.00.
 +
|-
 +
||Press the down arrow continuously.
 +
||Using '''Coefficient''' field values, we can vary the size of the '''orbital'''.
  
 +
Notice that size of the ''' orbital''' alongside, has changed.
 +
|-
 +
||Cursor on the value box.
 +
||'''Rotation''' property has values from -180(minus) to 180.
 +
|-
 +
||Press the down arrow continuously.
 +
||We can rotate the '''orbitals''' clockwise or anticlockwise.
  
 +
Values can be changed using the up and down arrows.
  
 +
|-
 +
||
 +
||Let's see how to use '''orbitals''' to show different types of '''Positive overlaps'''.
 +
|-
 +
||'''Slide Number 8'''
  
 +
'''Positive Overlaps'''
 +
||
 +
Here is a slide for '''Positive overlap''' of different orbitals.
  
 +
''''s-s'overlap, 's-p'overlap, 'p-p'overlap''' and ''''p-p' side-wise overlap'''.
 +
|-
 +
||Switch to '''GChemPaint''' window.
 +
||Let's draw '''Hydrogen''' molecule on the '''Display area'''.
 +
|-
 +
||Press H on the Key board.
 +
||Press H on the keyboard.
 +
|-
 +
||Set '''Co-efficient''' value to 1.
 +
||Set the '''Co-efficient''' value to one.
 +
|-
 +
||Click on '''Add or modify an atom''' tool.
 +
||Click on '''Add or modify an atom''' tool.
 +
|-
 +
||Click '''Add a bond''' tool.
 +
||Click '''Add a bond''' tool.
  
 +
Ensure that bond length is around 130.
 +
|-
 +
||Click on the '''Display area'''.
 +
||Click on the''' Display area'''.
  
 +
'''Hydrogen''' molecule is formed.
 +
|-
 +
||
 +
||Let's start with 's-s' end-on overlap.
 +
|-
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
|-
 +
||Click on 's' orbital>>click on the '''Hydrogen''' atoms of''' Hydrogen''' molecule.
  
−
||'''Slide Number'''
+
Point to the s-s end on overlap.
 +
||Click on 's' '''orbital''',
  
−
'''Assignment'''
+
Then click on '''Hydrogen''' atoms of '''Hydrogen''' molecule.
 +
 
 +
Observe 's-s' end-on overlap.
 +
|-
 
||
 
||
 +
||Now to 'p-p' end-on overlap.
 +
|-
 +
||Press F on the keyboard
 +
||Press F on the keyboard.
 +
|-
 +
||Click on '''Add or modify an atom''' tool.
 +
||Click on '''Add or modify an atom''' tool.
 +
|-
 +
||Click '''Add a bond ''' tool.
 +
 +
Point to the molecule.
 +
||Click '''Add a bond''' tool.
 +
 +
Ensure that bond length is around 200.
 +
 +
Click on the '''Display area'''.
 +
 +
'''Fluorine''' molecule is formed.
 +
|-
 +
||Click on '''Add or modify an atomic orbital''' tool
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
|-
 +
||Click on the ''''p' orbital'''.
 +
||Click on the ''''p' orbital'''.
 +
|-
 +
||Point to ''''p' orbital'''
 +
||To form 'p-p' end-on overlap, we need 'p' '''orbitals''' in horizontal direction.
 +
|-
 +
||Click and hold the up arrow triangle
 +
||Let's increase the '''Rotation''' value to 90.
 +
|-
 +
||Click on the horizontal p orbital>> Click on '''Fluorine''' atom.
 +
||Click on the ''''p'''' '''orbital'''.
 +
 +
Click on one '''Fluorine''' atom.
 +
|-
 +
||Click on the other '''Fluorine''' atom.
 +
||Likewise, repeat the process and rotate the 'p' '''orbital''' to '-90'(minus90).
 +
 +
Click on the other '''Fluorine''' atom.
 +
|-
 +
||Right click on the '''orbital'''>> select '''Orbital''' >> click on '''Properties'''.
 +
||In case you are not able to view the overlap clearly, you can resize the '''orbital'''.
 +
 +
To do so, we have to change the '''Coefficient''' value.
 +
 +
Right click on the orbital, select ''' Orbital''' then click on '''Properties'''.
 +
|-
 +
||'''Orbital properties''' dialog box opens.
 +
||'''Orbital properties''' dialog box opens.
 +
|-
 +
||Point to 'p-p' end-on overlap.
 +
||Reduce the '''Coefficient''' value till you see a proper overlap.
 +
 +
Click on '''Close''' button
 +
|-
 +
||Point to the overlap
 +
||I will repeat the process for the other orbital 
 +
 +
Observe 'p-p' end-on overlap.
 +
|-
 +
||Point to 'dz^2' orbital
 +
||Now to 'd-d' end-on overlap using  ''''dz^2' orbital'''.
 +
|-
 +
||Press capital '''F''' on the keyboard.
 +
 +
Point to the list.
 +
||Come to the '''Display Area''' and press capital '''F''' on the keyboard.
 +
 +
Select '''Fe''' from the list.
 +
|-
 +
||Click on '''Add or modify an atom''' tool>>Click on the '''Display area'''.
 +
||Click on '''Add or modify an atom''' tool.
 +
 +
Click on the '''Display area'''.
 +
|-
 +
||Click on '''Add a bond''' tool>>Click on Display area.
 +
||Click on '''Add a bond ''' tool.
 +
 +
Click on iron atom(Fe) to draw a bond.
 +
|-
 +
||Click on '''Add or modify an atomic orbital''' tool>>Select '''dz^2 orbital'''.
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
 +
Select ''''dz^2'''' '''orbital''' radio button.
 +
|-
 +
||Point to the arrow triangles.
 +
||For proper overlap, decrease the '''Coefficient''' value to 0.8.
 +
|-
 +
||Click on the bonded iron atoms to overlap '''dz^2 orbitals'''.
 +
||Click on the bonded Iron atoms to overlap '''"dz^2" orbitals'''.
 +
 +
Observe 'd-d' end-on overlap.
 +
|-
 +
||
 +
||Now let's learn about side-wise overlap of 'p' orbitals.
 +
 +
Ensure that current element is '''Carbon'''.
 +
|-
 +
||Click on '''Add a bond''' tool.
 +
||Click on '''Add a bond''' tool.
 +
 +
Ensure '''Bond length''' is around 90.
 +
 +
Click on the '''Display area'''.
 +
|-
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
 +
Increase the '''Coefficient''' value to one
 +
|-
 +
||Click on 'p' '''orbital''' radio button>>
 +
 +
Click on the edges of the bonds.
 +
||Click on 'p' '''orbital''' radio button.
 +
 +
Rotate the '''orbital''' to vertical position if it is in horizontal position.
 +
 +
Click on the edges of the bonds.
 +
|-
 +
||Point to the overlap.
 +
||Observe the 'p-p' side-wise overlap.
 +
 
 +
In this type of overlap, lobes of '''orbitals''' are of same sign.
 +
|-
 +
||
 +
||Next, we will move to '''negative''' and '''zero overlaps'''.
 +
|-
 +
||'''Slide Number 9'''
 +
 +
'''Negative overlaps'''
 +
||Here is a slide for '''negative''' overlaps.
 +
|-
 +
||Switch to '''GChemPaint''' window.
 +
||I have opened a new '''GChempaint''' application.
 +
|-
 +
||
 +
||Now, I will demonstrate how to draw a '''negative overlap'''.
 +
|-
 +
||Click on '''Add a bond''' tool >>Click on the '''Display area'''.
 +
||Click on '''Add a bond''' tool.
 +
 +
Ensure that Bond length is around 90.
 +
 +
Click on the '''Display area'''.
 +
|-
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
|-
 +
||Click on the ''''p' orbital''' radio button >>click on one edge of the bond.
 +
||Click on ''''p' orbital''' radio button then click on one edge of the bond.
 +
|-
 +
||Cursor on '''Rotation''' arrow triangle.
 +
 +
Click on the other edge of the bond.
 +
||Rotate ''''p' orbital''' to 180 degree to flip it upside down.
 +
 +
Then click other edge of the bond.
 +
|-
 +
||Point to the '''overlap'''.
 +
||Observe '''negative overlap'''.
 +
 +
In this type of overlap, lobes of '''orbitals''' are of opposite sign.
 +
|-
 +
||
 +
||Now, let's learn how to create a '''zero overlap'''.
 +
|-
 +
||'''Slide Number 10'''
 +
 +
'''Zero Overlap'''
 +
||Here is a slide for '''zero overlap'''.
 +
|-
 +
||Click on '''Add a bond''' tool>>
 +
 +
Click on the '''Display area'''.
 +
||Click on '''Add a bond''' tool.
 +
 +
Click on the ''' Display area.'''
 +
|-
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
||Click on '''Add or modify an atomic orbital''' tool.
 +
|-
 +
 +
||Click on the 'p' >>Rotate the ''''p' orbital''' to original position>>
 +
 +
Click on one edge of the bond.
 +
||Click on the 'p' orbital.
 +
 +
Rotate the''' 'p' orbital''' to original position.
 +
 +
Click on one edge of the bond.
 +
|-
 +
||Click on the ''''s' orbital'''  >>click on one edge of the bond.
 +
||Click on ''''s' orbital''' and then click on other edge of the bond.
 +
|-
 +
||Point to the overlap
 +
||Observe '''zero overlap'''.
 +
 +
In this type of overlap, orientation of the '''orbitals''' is not same.
 +
|-
 +
||
 +
||Let's summarize what we have learnt.
 +
|-
 +
||'''Slide Number 11'''
 +
 +
'''Summary'''
 +
||In this tutorial we have learnt,
 +
 +
* About different types of '''orbitals'''
 +
 +
* End-on and side-wise overlaps
 +
 +
* Rotation and resize of orbitals
 +
 +
* Positive, negative and zero overlap.
 +
|-
 +
||'''Slide Number 12'''
 +
 +
'''Assignment'''
 +
||Here is an assignment.
 +
 +
* Draw  's-p' end-on overlap with Hydrogen chloride(H-Cl) molecule
 +
 +
* Draw side-wise overlap of 'dxy-dxy' orbitals
 +
 +
* Draw other negative and zero overlaps.
 +
 +
* Hint: Rotate and resize the orbitals for proper overlap.
 +
 
Your completed assignment should look like this.
 
Your completed assignment should look like this.
 
|-
 
|-
Line 128: Line 433:
 
||Spoken Tutorial Project is a part of the Talk to a Teacher project  
 
||Spoken Tutorial Project is a part of the Talk to a Teacher project  
  
−
It is supported by the National Mission on Education through ICT, MHRD, Government of India
+
It is supported by the National Mission on Education through ICT, MHRD, Government of India.
  
 
More information on this Mission is available at this link  
 
More information on this Mission is available at this link  
Line 135: Line 440:
 
|-
 
|-
 
||
 
||
−
||This is '''Madhuri Ganapathi''' from '''IIT Bombay''' signing off. Thank you for joining.  
+
||Drawings are contributed by '''Arathi'''
 +
 
 +
This is '''Madhuri Ganapathi''' from '''IIT Bombay''' signing off. Thank you for joining.  
 
|}
 
|}

Latest revision as of 15:16, 28 October 2020

Title of the tutorial: Orbital Overlap

Author: Madhuri Ganapathi

Key words: Atomic orbital, Add or modify an atomic orbital tool, rotation and resize of orbitals, positive, negative overlaps and zero overlap, Video tutorial


Visual Cue Narration

Slide Number 1

Title Slide

Hello everyone.

Welcome to this tutorial on Orbital Overlap in GChemPaint.

Slide Number 2

Learning Objectives

In this tutorial, we will learn
  • About different types of orbitals
  • Rotation and resize of orbitals
  • Types of orbital overlaps
Slide Number 3

System Requirement

Here I am using

Ubuntu Linux OS version 12.04.

GChemPaint version 0.12.10.

Slide Number 4

Pre-requisites

To follow this tutorial, you should be familiar with

GChemPaint chemical structure editor.

If not, for relevant tutorials, please visit our website.

Slide Number 5

Atomic Orbital

Let's first see what an atomic orbital is.

An atomic orbital is a mathematical function.

It describes the wave-like behavior of an electron in an atom.

An orbital is a region of space with maximum probability of finding an electron.

Slide Numbers 6

‘s’ and ‘p’ Orbitals

Point to the orbitals.

This is an 's' orbital.

It has spherical shape.

Here are 'p' orbitals in different axes.

'p' orbitals are "dumb-bell" shaped.

Slide Numbers 7

‘d’ Orbitals

Next, we have 'd' orbitals in different axes.

'd' orbitals are double "dumb-bell" shaped.

Switch to GChemPaint application. I have opened a new GChemPaint application.
Let's first learn about orbitals.
Click on Add or modify an atomic orbital tool Click on Add or modify an atomic orbital tool.
Point to the properties window. Orbital property window opens.
Point to the properties. This window contains fields like- Coefficient, Rotation and Type.
Point to Type field. First, I will begin with Type.
Point to 's' By default, 's' orbital is selected.
Click on p, dxy and dz^2 radio buttons.


Point to the orbital shapes.

Let's click on p, d xy and d z square orbital radio buttons.

Notice the different orbital shapes displayed alongside.

Point to Coefficient and Rotation Next let's check the Coefficient and Rotation properties.
Cursor on the value box Coefficient property has values from -1.00 to 1.00.
Press the down arrow continuously. Using Coefficient field values, we can vary the size of the orbital.

Notice that size of the orbital alongside, has changed.

Cursor on the value box. Rotation property has values from -180(minus) to 180.
Press the down arrow continuously. We can rotate the orbitals clockwise or anticlockwise.

Values can be changed using the up and down arrows.

Let's see how to use orbitals to show different types of Positive overlaps.
Slide Number 8

Positive Overlaps

Here is a slide for Positive overlap of different orbitals.

's-s'overlap, 's-p'overlap, 'p-p'overlap and 'p-p' side-wise overlap.

Switch to GChemPaint window. Let's draw Hydrogen molecule on the Display area.
Press H on the Key board. Press H on the keyboard.
Set Co-efficient value to 1. Set the Co-efficient value to one.
Click on Add or modify an atom tool. Click on Add or modify an atom tool.
Click Add a bond tool. Click Add a bond tool.

Ensure that bond length is around 130.

Click on the Display area. Click on the Display area.

Hydrogen molecule is formed.

Let's start with 's-s' end-on overlap.
Click on Add or modify an atomic orbital tool. Click on Add or modify an atomic orbital tool.
Click on 's' orbital>>click on the Hydrogen atoms of Hydrogen molecule.

Point to the s-s end on overlap.

Click on 's' orbital,

Then click on Hydrogen atoms of Hydrogen molecule.

Observe 's-s' end-on overlap.

Now to 'p-p' end-on overlap.
Press F on the keyboard Press F on the keyboard.
Click on Add or modify an atom tool. Click on Add or modify an atom tool.
Click Add a bond tool.

Point to the molecule.

Click Add a bond tool.

Ensure that bond length is around 200.

Click on the Display area.

Fluorine molecule is formed.

Click on Add or modify an atomic orbital tool Click on Add or modify an atomic orbital tool.
Click on the 'p' orbital. Click on the 'p' orbital.
Point to 'p' orbital To form 'p-p' end-on overlap, we need 'p' orbitals in horizontal direction.
Click and hold the up arrow triangle Let's increase the Rotation value to 90.
Click on the horizontal p orbital>> Click on Fluorine atom. Click on the 'p' orbital.

Click on one Fluorine atom.

Click on the other Fluorine atom. Likewise, repeat the process and rotate the 'p' orbital to '-90'(minus90).

Click on the other Fluorine atom.

Right click on the orbital>> select Orbital >> click on Properties. In case you are not able to view the overlap clearly, you can resize the orbital.

To do so, we have to change the Coefficient value.

Right click on the orbital, select Orbital then click on Properties.

Orbital properties dialog box opens. Orbital properties dialog box opens.
Point to 'p-p' end-on overlap. Reduce the Coefficient value till you see a proper overlap.

Click on Close button

Point to the overlap I will repeat the process for the other orbital

Observe 'p-p' end-on overlap.

Point to 'dz^2' orbital Now to 'd-d' end-on overlap using 'dz^2' orbital.
Press capital F on the keyboard.

Point to the list.

Come to the Display Area and press capital F on the keyboard.

Select Fe from the list.

Click on Add or modify an atom tool>>Click on the Display area. Click on Add or modify an atom tool.

Click on the Display area.

Click on Add a bond tool>>Click on Display area. Click on Add a bond tool.

Click on iron atom(Fe) to draw a bond.

Click on Add or modify an atomic orbital tool>>Select dz^2 orbital. Click on Add or modify an atomic orbital tool.

Select 'dz^2' orbital radio button.

Point to the arrow triangles. For proper overlap, decrease the Coefficient value to 0.8.
Click on the bonded iron atoms to overlap dz^2 orbitals. Click on the bonded Iron atoms to overlap "dz^2" orbitals.

Observe 'd-d' end-on overlap.

Now let's learn about side-wise overlap of 'p' orbitals.

Ensure that current element is Carbon.

Click on Add a bond tool. Click on Add a bond tool.

Ensure Bond length is around 90.

Click on the Display area.

Click on Add or modify an atomic orbital tool. Click on Add or modify an atomic orbital tool.

Increase the Coefficient value to one

Click on 'p' orbital radio button>>

Click on the edges of the bonds.

Click on 'p' orbital radio button.

Rotate the orbital to vertical position if it is in horizontal position.

Click on the edges of the bonds.

Point to the overlap. Observe the 'p-p' side-wise overlap.

In this type of overlap, lobes of orbitals are of same sign.

Next, we will move to negative and zero overlaps.
Slide Number 9

Negative overlaps

Here is a slide for negative overlaps.
Switch to GChemPaint window. I have opened a new GChempaint application.
Now, I will demonstrate how to draw a negative overlap.
Click on Add a bond tool >>Click on the Display area. Click on Add a bond tool.

Ensure that Bond length is around 90.

Click on the Display area.

Click on Add or modify an atomic orbital tool. Click on Add or modify an atomic orbital tool.
Click on the 'p' orbital radio button >>click on one edge of the bond. Click on 'p' orbital radio button then click on one edge of the bond.
Cursor on Rotation arrow triangle.

Click on the other edge of the bond.

Rotate 'p' orbital to 180 degree to flip it upside down.

Then click other edge of the bond.

Point to the overlap. Observe negative overlap.

In this type of overlap, lobes of orbitals are of opposite sign.

Now, let's learn how to create a zero overlap.
Slide Number 10

Zero Overlap

Here is a slide for zero overlap.
Click on Add a bond tool>>

Click on the Display area.

Click on Add a bond tool.

Click on the Display area.

Click on Add or modify an atomic orbital tool. Click on Add or modify an atomic orbital tool.
Click on the 'p' >>Rotate the 'p' orbital to original position>>

Click on one edge of the bond.

Click on the 'p' orbital.

Rotate the 'p' orbital to original position.

Click on one edge of the bond.

Click on the 's' orbital >>click on one edge of the bond. Click on 's' orbital and then click on other edge of the bond.
Point to the overlap Observe zero overlap.

In this type of overlap, orientation of the orbitals is not same.

Let's summarize what we have learnt.
Slide Number 11

Summary

In this tutorial we have learnt,
  • About different types of orbitals
  • End-on and side-wise overlaps
  • Rotation and resize of orbitals
  • Positive, negative and zero overlap.
Slide Number 12

Assignment

Here is an assignment.
  • Draw 's-p' end-on overlap with Hydrogen chloride(H-Cl) molecule
  • Draw side-wise overlap of 'dxy-dxy' orbitals
  • Draw other negative and zero overlaps.
  • Hint: Rotate and resize the orbitals for proper overlap.

Your completed assignment should look like this.

Slide Number 13

Acknowledgement

Watch the video available at this link.

http://spoken-tutorial.org/What_is_a_Spoken_Tutorial

It summarizes the Spoken Tutorial project

If you do not have good bandwidth, you can download and watch it

Slide Number 14 The Spoken Tutorial Project Team:

Conducts workshops using spoken tutorials

Gives certificates to those who pass an on-line test

For more details, please write to contact@spoken-tutorial.org

Slide number 15 Spoken Tutorial Project is a part of the Talk to a Teacher project

It is supported by the National Mission on Education through ICT, MHRD, Government of India.

More information on this Mission is available at this link

http://spoken-tutorial.org/NMEICT-Intro

Drawings are contributed by Arathi

This is Madhuri Ganapathi from IIT Bombay signing off. Thank you for joining.

Contributors and Content Editors

Madhurig, PoojaMoolya

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