The simple answer is that the dz2 orbital has the correct symmetry. Its all about orthogonallity, orthogonal orbitals do not hybridise. I'm sorry you need to have a grounding in group theory as it applies to quantum mechanics to go further with this answer.
The electron configuration of an atom with electrons in the dz2 orbital is 3d10.
3rd to onward all energy levels have 5 d-orbitals their name assign are dxy,dxz,dyz,d(x2 - y2) and dz2
You can break down the shell and orbitals of an atom on several levels of detail.First, there are the main shells of the atom, and these are numbered 1, 2, 3, 4, etc. (or like some doing it alphabetically K, L, M, N, ...).In the periodic table you will encounter them as seven periods.Each shell holds orbitals (sometimes called sub-shells, but they are not), and different shells have different numbers of orbitals associated with it. The higher the number of the main shell, the more orbitals it contains. In fact, the number of the main shell is equal to the number of orbitals it contains. The types of orbitals are labeled like this: s, p, d, f, and not so very important: g, h, i, etc (alphabetically after i).So far we have:Main shell #1-- contains one orbital (s-orbital)Main shell #2-- contains two orbitals (s-orbital, and p-orbital)Main shell #3-- contains three orbitals (s-orbital, p-orbital, and d-orbital)Main shell #4-- contains four orbitals (s-orbital, p-orbital, d-orbital, and f-orbital)etc...Now we can further break down orbitals! The p-orbital is actually composed of three sub-orbitals and the d-orbital is composed of 5 sub-orbitals and f-orbital in 7 sub-orbitals.So we have:s-orbital: just a single orbital, called just the s-orbitalp-orbitals: composed of 3 sub-orbitals, called the px-, py-, and pz-orbitalsd-orbitals: composed of 5 sub-orbitals, called the dxy-, dxz-, dyz-, dx2-y2, and dz2-orbtialsf-orbitals: composed of 7 sub-orbitals, called fz3, fxz2, fyz2, fxyz, fz(x2-y2), fx(x2-3y2), fy(3x2-y2).etc...And at last, but not least: each sub-orbital has a maximum of TWO electrons in it, only differing in electron spin number.So the maxima per orbital are:s-orbital: just a single orbital, max. 2 electronsp-orbitals: composed of 3 sub-orbitals, max. 6 electronsd-orbitals: composed of 5 sub-orbitals, max. 10 electrons (= number of transitional elements)f-orbitals: composed of 7 sub-orbitals, max. 14 electrons (= number of lanthanides, actinides)(Thanks to JEK, who's original answer I completed with the last paragraph and some minor add's in the first ones)
There is no such level as 2d. In 1st level there is just 1s. In the 2nd level there is 2s and 2p. Only in the 3rd level is there 3s, 3p and 3d. The sublevels of 3d are 3 dxy dyz dxz d(x2-y2) dz2 so 5 sublevels of 3d.
The s sublevel has just one orbital, so can contain 2 electrons max. The p sublevel has 3 orbitals, so can contain 6 electrons max. The d sublevel has5orbitals, so can contain 10 electrons max. And the 4 sublevel has 7 orbitals, so can contain 14 electrons max.
The electron configuration of an atom with electrons in the dz2 orbital is 3d10.
A sigma bond is a molecular bond made by the joining of the wavefunctions of either an s to an s orbital, an s to a pz orbital, a pz to a pz orbital or a dz2 to a dz2 orbital. Sigma bonds are the strongest of the molecular bonds (the others being the pi and delta bonds) and has the maximum electron density directly between the nuclei with no nodal planes and cylindrical symmetry (for the bonding variety, since sigma antibonds have no electron density between the nuclei). For bonds between small elements (such as hydrogen, carbon, oxygen), one bond in a single, double, or triple bond is always a sigma bond (the others are pi bonds).
There are five d orbitals in one energy level. These orbitals are designated as dxy, dyz, dxz, dz2, and dx2-y2. Each d orbital can hold a maximum of 2 electrons.
The "s" orbital is circular; the "p" orbital is shaped like a dumbell. The "d" orbitals are like a double dumbell, though the dz2 sub orbital is like a dumbell with an annulus around it. Finally, the f orbital are much more complex. They are like a quadruple dumbell with the lobes pointing towards the 8 corners of a cube.
You have to be more specific if you want a specific answer. The shape is the biggest thing that you should notice straight away. dz2 looks like a p orbital with a ring around the centre. All other d suborbitals look like 2 p orbitals perpendicular to each other
D orbitals like any other orbital can form bonds through overlap. They can form sigma bonds (only between dz2) and pi bonds (seen in transition metal complexes) and delta bonds (overlap of two d orbitals again seen in complexes))
The d-subshell has a total of 5 orbitals, labeled as dxy, dyz, dzx, dx2-y2, and dz2. For an electron in the third energy level, the principal quantum number (n) is 3. The possible sets of quantum numbers for an electron in the d-subshell of the third energy level are: n=3, l=2, ml=-2, ms= +1/2 (for dxy orbital) and n=3, l=2, ml=0, ms= +1/2 (for dyz orbital) and so on for the other orbitals in the d-subshell.
3rd to onward all energy levels have 5 d-orbitals their name assign are dxy,dxz,dyz,d(x2 - y2) and dz2
For a three-dimensional del operator in Cartesian coordinates: del2 = delT del = del dot del = d/dx2 + d/dy2 + d/dz2
There are five d orbitals, known as dz2, dxy, dxz, dyz , and dx2-y2. The special properties of transition metals are because of the d-orbitals.
Each orbital contains at maximum 2 electrons. there is one s-orbital: 2 in this alone there are three p-orbitals (px, py, pz) with 2 in each there are five d-orbitals (dz2, dxz, dyz, dxy dx2-y2) with 2 in each there are seven f-orbitals (fz3, fxz2, fyz2 ,fxyz ,fz(x2-y2) ,fx(x2-3y2) ,fy(3x2-y2) with 2 in each
You can break down the shell and orbitals of an atom on several levels of detail.First, there are the main shells of the atom, and these are numbered 1, 2, 3, 4, etc. (or like some doing it alphabetically K, L, M, N, ...).In the periodic table you will encounter them as seven periods.Each shell holds orbitals (sometimes called sub-shells, but they are not), and different shells have different numbers of orbitals associated with it. The higher the number of the main shell, the more orbitals it contains. In fact, the number of the main shell is equal to the number of orbitals it contains. The types of orbitals are labeled like this: s, p, d, f, and not so very important: g, h, i, etc (alphabetically after i).So far we have:Main shell #1-- contains one orbital (s-orbital)Main shell #2-- contains two orbitals (s-orbital, and p-orbital)Main shell #3-- contains three orbitals (s-orbital, p-orbital, and d-orbital)Main shell #4-- contains four orbitals (s-orbital, p-orbital, d-orbital, and f-orbital)etc...Now we can further break down orbitals! The p-orbital is actually composed of three sub-orbitals and the d-orbital is composed of 5 sub-orbitals and f-orbital in 7 sub-orbitals.So we have:s-orbital: just a single orbital, called just the s-orbitalp-orbitals: composed of 3 sub-orbitals, called the px-, py-, and pz-orbitalsd-orbitals: composed of 5 sub-orbitals, called the dxy-, dxz-, dyz-, dx2-y2, and dz2-orbtialsf-orbitals: composed of 7 sub-orbitals, called fz3, fxz2, fyz2, fxyz, fz(x2-y2), fx(x2-3y2), fy(3x2-y2).etc...And at last, but not least: each sub-orbital has a maximum of TWO electrons in it, only differing in electron spin number.So the maxima per orbital are:s-orbital: just a single orbital, max. 2 electronsp-orbitals: composed of 3 sub-orbitals, max. 6 electronsd-orbitals: composed of 5 sub-orbitals, max. 10 electrons (= number of transitional elements)f-orbitals: composed of 7 sub-orbitals, max. 14 electrons (= number of lanthanides, actinides)(Thanks to JEK, who's original answer I completed with the last paragraph and some minor add's in the first ones)