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Electron shells

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1 hour ago, Brainee said:

If electrons are smeared out how do several electrons occupy same shell?

Electrons in atoms can be thought of as standing waves corresponding to resonant frequencies, ie. a series of harmonics. In fact the shapes of atomic orbitals are spherical harmonics, akin to the modes of vibration of a rubber ball if you hit it and look at how it vibrates with a strobe light. 

Each electron occupies a different quantum state. It has to, as electrons are fermions.

"Shells" are simply groupings of related, but different states that are possible for an electron to occupy in an atom. Each shell comprises all the states that have the same principal quantum number, n. But n is only one of 4 quantum numbers needed to specify individual possible states. They others are:

- l, which denotes the angular momentum and determines which subshell the electron is in (i.e. s, p, d, f etc),

- m(l), which determines which member of the sets of s, p,d, f orbitals the electron is in (e.g p(z), d(x²-y²), etc),

- and finally m(s) which determines the spin orientation within that orbital.

So one can have a maximum of 2 electrons per orbital, one with spin orientation "up" and the other "down".  

In chemistry, this accounts for the pattern of the Periodic Table of the elements, each row corresponding to the highest occupied principal shell that is occupied, 1st row n=1 2nd row n=2 etc. (cf. Aufbau Principle.) 


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3 hours ago, exchemist said:

So one can have a maximum of 2 electrons per orbital, one with spin orientation "up" and the other "down".  

To add to this excellent summary, +1,

It is important to distinguish between shells and orbitals.

Shells are groupings in space of several orbitals.

The orbitals in a given shell are so shaped as to not intefere with each other in the space occupied by a given shell

atomic orbitals electron orbitals

Note these are not solid shapes but surfaces.

Imagine them as the skins of balloons, like the party balloons we twist together to form dogs etc.

Edited by studiot
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On 1/9/2023 at 3:00 AM, Brainee said:

What is difference between shell and orbital?

OK I didn't explain this very clearly in my previous post. A shell is a set of orbitals sharing the same principal quantum number, n. All the elements in a given row of the Periodic Table have their outermost electrons in the same shell, i.e. with the same principal quantum number. For example, elements of the second row, starting with Li, have outermost electrons in the n=2 shell.

 Next there are subshells. A sub-shell is is a set of orbitals having the same principal, n, and azimuthal (or angular momentum) quantum number, l. So in the second row, electrons can go into the 2s or 2p subshells. The s subshells have l=0, p subshells have l=1, d subshells have l=2 and f subshells have l=3.  

Finally we have orbitals themselves. These are distinguished by the orientation of the angular momentum, which is set by the 3rd quantum number m(l). Each orbital comprises a pair of quantum states which have identical orientation in space, but with opposite spin orientation of the electron. So for example every p subshell has 3 p orbitals, perpendicular to each other, which you can treat as orientated along x, y and z axes. Each one can have 2 electrons in it, one with spin "up" and one with spin "down".

In chemistry we tend to treat orbitals as if they are quantum states, each of which can have zero, one or two electrons in it. Strictly speaking they are not, because you need to specify the spin quantum number too in order to define an individual quantum state properly. But since spin orientation can only have 2 values "up" or "down", and since the spatial orientation of the orbital is what is relevant for chemical bonding, it is convenient to think of  the orbital as the basic building block of electronic structure in the atom, each of which can accept a pair of electrons.  


Edited by exchemist
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