# Why are orbitals are shown bubble shaped in the books when they exist in only in one particular dimension

I am utterly confused here: In our books orbitals $s$, $p$, $d$ are shown to be bubble or sphere like but ain't $s$-orbital exist only in $x$-axis so only a particular underline should be shown to denote it, just like when you mark open intervals in maths and the same goes for $p$-orbital for $x$, $y$ and $z$.

So why draw a bubble like shape encompassing all the dimensions/axes/planes?

Secondly, I can understand $d_{xy}$, $d_{xz}$, and $d_{yz}$ but what does $d_z^{2}$ and $d_z^{2} - y^{2}$ means ($x^{2} - y^{2}$ looks like $d_{xy}$, it just seems to be oriented by $90^{\circ}$)?

FYI, I am a high school student.

• No. All of the orbitals are three dimensional. Can you explain why you think they exist only in 1d? (Please be careful when typing ... do you mean "D" or "d"? And please use MathJax. Here’s a MathJax tutorial) – garyp Aug 8 '16 at 14:25
• What is the reason you believe s orbitals only exist in one axis? – Cort Ammon Aug 8 '16 at 14:25
• Respected Sir/Madame(s):I have told as such by my teacher.I first suspected this at first but then I consulted other chemistry/physics teacher who said s_x or p_x/d_x mean it exist only in x-axis/plane or along x-axis.I couldnt understand what they meant by along.That's why assumed as such (tho it still seemed to me invalid whenever the equation integral wave dx dy dz = 1 comes to my mind since we integrate over 3-dimensional space).Kindly correct me wherever I am wrong with firm reasoning and enlighten me more on this @garyp – groak_master Aug 8 '16 at 14:46
• @garyp:I meant d ..Is there something D too?Can you tell me more about this – groak_master Aug 8 '16 at 14:47
• The subtext on something like $s_x$ does mean that it exists only in the x-dimension. However, when they told you that, they meant that specifically $s_x$ exists only in x. There may or may not be other components of $s$, such as $s_y$, which exist in other dimensions. What they told you was the truth, but misleading. They should have said it is the component of $s$ that exists solely in the x-dimension – Jim Aug 8 '16 at 14:55

Your teacher may have misinterpreted your question about the s orbitals. The s orbital never has a subscript. It is always spherical.

As you move into the p and d orbitals, the subscripts describe the shape of the orbital. For example $p_z$ is symmetric around the z axis. This does not mean the electron is confined to the z axis, merely that the probability of finding it at a given place is higher as you get close to the z axis. The shapes given for the orbitals are defined by probability. When they show you a shell of an orbital, it is usually rendered as "the electron has a 90% probability of being within this volume at any moment" or some similar construction.

The exact meaning of the subscripts is a bit more complicated. They deal with what are called Cubic harmonics. These cubic harmonics are solutions to the angular momentum operator: meaning they keep spin angular momentum conserved. The subscripts are actually key parts out of the cubic harmonic equations which uniquely identify that solution to the angular momentum operator. I find they are related to symmetries in the shape of the orbital, but I don't yet know if that's coincidence or something fundamental about how the equations operate.

Also note that these are really probabilistic solutions for a the wave equation describing the electrons. Wikipedia has a very nice set of animations showing an analogue of these orbitals in 2 dimensions using a drum to show the resonance of this wave. It may be a helpful tool for developing a more intuitive grasp on what an orbital means. It's not a 1:1 match to how electrons work, but its close enough that it may help with the visualization (and it comes with a verbal explanation of how the two connect, if you're curious)

• You assume the questioner has accurately represented what their teacher said, despite their otherwise imperfect undetstanding. Perhaps the point was only that the single subscript orbitals may be biased along a single axis? – benjimin Aug 8 '16 at 15:20
• "pzpz is symmetric around the z axis. This does not mean the electron is confined to the z axis, merely that the probability of finding it at a given place is higher as you get close to the z axis". since P-x and P_y both are symmetric doesn't it indirectly implies a sphere again? And what do interepret of the pear shape bulging outwards and what about d-orbital .I can't understand the later part can you please explain a toned-down version of it apporpriate for High school studentt?(I already mentioned my background in question but somebody edited out that part) – groak_master Aug 8 '16 at 15:52
• @groak_master P_x is symmetric around the x axis and P_y is symmetric around the y axis. However, this is only one axis of symmetry. A sphere (like the s orbital) is symmetric about any axis. For example, if you have a cardboard tube, it is symmetric about one axis. As for interpretations of the shapes, that's an entirely different field. Interpreting them as anything except "the correct answer for a set of equations we believe governs electrons" is difficult. – Cort Ammon Aug 8 '16 at 16:25
• You might be able to get some insight into what is going on from the patterns on a Chlandi plate (youtube.com/watch?v=YedgubRZva8). Interpreting those patterns with respect to the sound waves on the Chlandi plate may be very helpful for helping you interpret the orbital shapes. And, if not, it's a really pretty experiment! – Cort Ammon Aug 8 '16 at 16:31
• @groak_master I fixed that over-zealous edit. Let me know if you don't approve. – garyp Aug 8 '16 at 17:19