Here my project incorporates with the 12th grade level.In this lessons we are discussing about the orbitals.As we know that the orbitals are bit confusing for a 12th grader.Especially it's very hard to visualize the shapes of the orbitals and to pull out the logic behind it by merely looking on a 2D image.By pulling out the potential of TINKERCAD,i have just made 3D Orbital shapes which can be easily visualized by projecting these models on a screen.So teachers can ease make out their lessons with these models.These models can also be 3D printed to make intense feeling of orbital shape in the minds of students.

### Teacher Notes

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## Step 1: Why TINKERCAD?

Tinkercad is an easy,browser based 3D design and modelling tool.It allows users to imagine anything and then design with in couple of minutes.So teachers can easily make out these 3D orbital shapes with the help of Tinkercad.They can actually create a good feeling about that concept in the mind of students.Students are very bored with the existing teaching methodology.So always try to use advanced technologies to make out the lessons for students like this.

## Step 2: Lesson Objectives

At the end of the lesson, students will be able to

- Describe the number and relative energies of the s,p,d and f orbitals for the principal quantum numbers1,2,3 and 4 including the 4 s orbital.
- Describe the shape of all orbitals.
- Describe the radial and angular distribution ie, distribution of the electron from the nucleus.

## Step 3: Orbital Shapes and Energies

An atom is composed of a nucleus containing neutrons and protons with electrons dispersed throughout the remaining space. Electrons, however, are not simply floating within the atom; instead, they are fixed within electronic orbitals. Electronic orbitals are regions within the atom in which electrons have the highest probability of being found.

There are multiple orbitals within an atom. Each has its own specific energy level and properties. Because each orbital is different, they are assigned specific quantum numbers: 1s, 2s, 2p 3s, 3p,4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. The numbers, (n=1,2,3, etc.) are called principal quantum numbers and can only be positive numbers. The letters (s,p,d,f) represent the orbital angular momentum quantum number (ℓ) and the orbital angular momentum quantum number may be 0 or a positive number, but can never be greater than n-1. Each letter is paired with a specific ℓ value

s: subshell = 0 p: subshell = 1 d: subshell = 2 f: subshell = 3

An orbital is also described by its magnetic quantum number (mℓ). The magnetic quantum number can range from –ℓ to +ℓ. This number indicates how many orbitals there are and thus how many electrons can reside in each atom. Orbitals that have the same or identical energy levels are referred to as degenerate. An example is the 2p orbital: 2px has the same energy level as 2py. This concept becomes more important when dealing with molecular orbitals. The Pauli exclusion principle states that no two electrons can have the same exact orbital configuration; in other words, the same quantum numbers. However, the electron can exist in spin up (ms = +1/2) or with spin down (ms = -1/2) configurations. This means that the s orbital can contain up to two electrons, the p orbital can contain up to six electrons, the d orbital can contain up to 10 electrons, and the f orbital can contain up to 14 electrons.

## Step 4: Visualizing Electron Orbitals

As discussed in the previous section, the magnetic quantum number (ml) can range from –l to +l. The number of possible values is the number of lobes (orbitals) there are in the s, p, d, and f subshells.The s subshell has one lobe, the p subshell has three lobes, the d subshell has five lobes, and the f subshell has seven lobes. Each of these lobes is labeled differently and is named depending on which plane the lobe is resting in. If the lobe lies along the x plane, then it is labeled with an x, as in 2px. If the lobe lies along the xy plane, then it is labeled with a xy such as dxy. Electrons are found within the lobes. The plane (or planes) that the orbitals do not fill are called nodes. These are regions in which there is a 0 probability density of finding electrons. For example, in the dyx orbital, there are nodes on planes xz and yz.Then we can discuss about the shapes of different orbitals.Actually Orbitals are generally drawn as three-dimensional surfaces that enclose 90% of the electron density.

## Step 5: S Orbital

Boundary surface diagram for **s **orbital looks like a sphere having the nucleus as its center which in two dimensions can be seen as a circle. Hence, we can say that s-orbitals are spherically symmetric having the probability of finding the electron at a given distance equal in all the directions. The size of the s orbital is also found to increase with the increase in the value of principal quantum number **(n)**, thus,__ 4s > 3s> 2s > 1s.__

Three things happen to s orbitals as n increases

- They become larger, extending farther from the nucleus.
- They contain more nodes. This is similar to a standing wave that has regions of significant amplitude separated by nodes, points with zero amplitude
- .For a given atom, the s orbitals also become higher in energy as n increases because of their increased distance from the nucleus.

## Step 6: P Orbitals

Each p orbital consists of two sections better known as lobes which lie on either side of the plane passing through the nucleus. The three p orbitals differ in the way the lobes are oriented whereas they are identical in terms of size shape and energy. As the lobes lie along one of the x, y or z-axis, these three orbitals are given the designations 2px, 2py, and 2pz. Thus, we can say that there are three p orbitals whose axes are mutually perpendicular. Similar to s orbitals, size, and energy of p orbitals increase with an increase in the principal quantum number (4p > 3p > 2p).They have a shape that is best described as a "dumbbell". A 3D view of this distribution can be found here for a 2p.p orbitals have one angular node (one angle at which the probability of electron is always zero. The radial probability distribution (the probability of finding the electron at a particular radius) for a 2p, looks nearly identical to a 1s.

## Step 7: D Orbitals

d orbitals are wavefunctions with ℓℓ = 2. They have an even more complex angular distribution than the p orbitals. For most of them it is a "clover leaf" distribution (something like 2 dumbbells in a plane). dorbitals have two angular nodes (two angles at which the probability of electron is always zero.Hence, we can say that there are five d-orbitals. These orbitals are designated as dxy, dyz, dxz, dx2–y 2 and dz2. Out of these five d orbitals, shapes of the first four d-orbitals are similar to each other, which is different from the dz2 orbital whereas the energy of all five d orbitals is same.

There are five different d orbitals that are nearly identical (n=2, ℓℓ =1) for the five different mℓmℓ values (-2,-1,0,+1,+2). These different orbitals essentially have different orientations. There is one that is a little different than the others (this is the mℓmℓ=0). The shapes of the d orbitals can be seen here for a 3d.As n increases there are ever larger available ℓℓ numbers. These give even more complex angular distributions with more angular nodes. After the d orbitals ℓℓ=2, come the f ℓℓ=3, then g ℓℓ=4, then hℓℓ=5, ....

There are five 3d orbitals called**3dxy 3dxz 3dyz 3dx2 - y2 3dz2** To make sense of it, we need to look at these in two groups:

__3dx2 - y2 and 3dz2__

The names tell you that these orbitals lie in the x-y plane, the x-z plane and the y-z plane respectively. Each orbital has four lobes. Notice that each of the lobes is pointing between two of the axes - not along them. For example, the 3dxy orbital has lobes that point between the x and y axes. No lobe actually points in the x or y direction. It is really important for what follows that you understand that.

__3dx2 - y2 and 3dz2__

Although these two orbitals look totally different, what they have in common is that their lobes point along the various axes. That's different from the first three where the lobes pointed in between the axes.

The 3dx2 - y2 orbital looks exactly like the first group - apart, of course, from the fact that the lobes are pointing along the x and y axes, not between them.Be absolutely sure that you can see the difference between this orbital and the 3dxy orbital.

The 3dz2 looks like a p orbital wearing a collar! The main lobes point along the z axis.

## Step 8: F Orbitals

An f orbital is an orbital for which the secondary quantum number l = 3.

There are seven f orbitals, with ml = -3, -2, -1, 0, 1, 2, and 3. The f orbitals aren't occupied in the ground state until element 58 (cerium). The electron configuration of cerium is [Xe] 6s24f5d. Even for elements beyond cerium, the f orbitals are deeply buried beneath the valence shell. They rarely play an important role in chemical change or bonding. But the orbital shapes are useful in interpreting spectra. So here they are.Actually f orbitals are very complex in nature and has complex symmetry.Fortunately, you will probably not have to memorize the shapes of the f orbitals by merely looking on a 2D image.By exploiting these 3D images most of the students can memorize these complex shapes.

## Step 9: How to Teach These Elements?

Teachers can use any 3D viewer to project these models on that.By these models they can easily demonstrate the shapes of any orbitals including complex shapes of **f **orbitals.The **.stl** file(3D file) can be downloaded from here.It can also be 3D printed(.stl file) for low cost.Actually by making these 3D prints can create a very good impact on students about these concepts.In these elements i didn't marked up the axes because it's very difficult to mark the axes in tinkercad.To refer the axes i have attached an image.

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