[AdiDex]

I have a statement , write your views on this statement..!!

" Orbitals do not have shape ...!! "

[Arkcon]

What evidence can you offer to support your statement?

[Enthalpy]

Sorry, that's a question too short and vague to invest time in a long answer that wouldn't meet the expectation. Maybe a first glimpse there?
http://winter.group.shef.ac.uk/orbitron/

[AdiDex]

This is my view , I am not saying this is correct . I want to just discuss .

Consider this case ,

you are standing on the origin of a three dimensional graph , can you tell me the shape of the graph ?? Ofcourse no one can tell ..!! similarly all of the orbitals are spread through out the space .
Yes , if you consider a particular fraction volume of a orbital then you can tell its space or in some texts it is refer to the boundary surfaces for orbital .
All of the orbitals have different distribution of electron throughout the space .

So I have reached to a conclusion that there is a difference between "orbitals" and "boundary surface of orbitals" . As orbitals do not have shape but their boundary surface do .

 

[Arkcon]

you are standing on the origin of a three dimensional graph , can you tell me the shape of the graph ?? Ofcourse no one can tell ..!!

I like this explanation.  There are others, you can find them in your text book, and may be required to quote that text book explanation on an exam.  However, I would keep this explanation of yours available for an essay exam, and for the future.  You can build on it as you learn more things.

[AdiDex]

you can find them in your text book, and may be required to quote that text book explanation on an exam.

It is my sorrow that in my country India, There is no original writing . Only some of the books are famous here , most of them belongs to Indian Authors . The funny part is that almost   every book have same writing style (all books are almost fact books with some ugly numericals)  and our education system in which everybody is learning for degree and marks.
We have a catchphrase --> "why do you want to know what is behind of this , do you want to do Ph.D in it ??"

The most funny part is that i can't write my explanation in my exam even this "orbitals do not have shape" . Because it is in my Syllabus --> "Shapes of s, p, d and f orbital" .

In most of the books (Indian author's) it is written that s orbital is spherical and p orbital is dumbbell blah blah . They are very  straight forward . They even don't care from where it came and what does it signifies ..!! They have only facts ...!!

[AdiDex]

Most of the high school (Indian High School) pass out students think that electron is a particle and orbits in circular path around nucleus (even after knowing that orbitals exists) .
Fewer think that they orbit around nucleus in elliptical shape.
A very few student thinks that  Orbital exists and they do not orbit.

After learning in first semester of college.
Most of them think that electron move like Honeybee around the nucleus in their orbitals .(None of them consider wave particle duality)
If You ask them that if electron is like a honeybee then how it can move from one side of node to another side then no one can answer it .

everybody thinks that (spin quantum no.)  s=+1/2 means electron is spinning in anticlockwise direction and s=-1/2 means electron is spinning at their own axis in clockwise direction.

This is not their fault , In all of the Indian Author's books it is mentioned.

[Enthalpy]

I don't really grasp how a surface can have a shape while the enclosed volume wouldn't. It sounds like claiming that a sphere has a shape but a ball doesn't.

[AdiDex]

See,
Your logic seems to be right but it is not (when you are talking about orbitals) .

Boundary surface of orbital consist of only some fraction of the orbital (usually in many textbooks it is written that boundary surfaces consists 95% electron of whole orbital).

Actually i have a question for you ? what is the shape of these curve x²+y²+z²=8 and x²+y²=4 ?? How did you defined them ? How much dimensions do you need to describe each of the curves ?
First answer these questions..!!

[mjc123]

Orbitals may also be represented without using boundary surfaces by shading the volume elements. The higher the probability density (i.e. the quantity ΨΨ*) the more intense the shading. This gives a representation of how the electron density varies in space. The space doesn't have a shape, but the density distribution in space does. It can also show the radial nodes in e.g. 2s and 3s, which a boundary surface doesn't.

[AdiDex]

My point of view says that when we say this it a circle , then we defined a region (or our shape is definite ) Whereas in case of total distribution curves of electron , they decays but do not became zero ,this means electron is spread through out the space. Logically you can't define its shape until it is not definite.
In case of boundary surfaces we are taking an approximation that we are neglecting some of the fraction of orbital so that it become definite.

and if I talk about whatever you said , then I have a counter - reasons to prove why orbitals do not have shape.

 ψ = f(R,θ,Φ) or Ψ=f(x,y,z)  , this equation contains 4 variable therefore if you actually want to visualize a continuous plot of this equation you will need 4 dimensional graph. And you can't visualize any 4-D shape.

and if you are plot it by shading then it will not be continuous . It is equivalent to draw these graphs
i.e x²+y²+z²=8 in 2-D by shading


 or y=2x in 1-D by shading.

you have to take approximation(by considering its boundary surface) or draw a quantized  graph (by shading it) .