If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Chemistry archive>Unit 1

Lesson 4: Quantum numbers and orbitals

# Quantum numbers for the first four shells

Calculates number of orbitals and number of electrons in different kinds of orbitals for n = 1 to 4. Explains that only two electrons are allowed per orbital, and gives shortcuts for calculating number of orbitals and total number of electrons for a given n. Created by Jay.

## Want to join the conversation?

• Are orbitals and sub shells the same?
• They are not same. Sub-shell is the l value (Azimuthal Quantum No.) e.g. s, p, d, f, etc, whereas oribitals are within the subshell with same n (Principal Quantum No.) and l. Example: 2py is an orbital in the p subshell.
But generally, they are used synonymously.
• Can the number of electrons in an orbital be increased?or does it just have to be 2?
• Two is maximum number of electrons in an orbital, because the electrons repel each other. If you try to put three electrons in an orbital, the atom wouldn't be stable.
• when electrons are in orbitals, then possess a charge which is cancel out so why they do not slam with nucleus?
• Excellent question. The electron would collapse into the nucleus if we applied classical electrodynamics. This was one of the central problems which quantum mechanics solved. With quantum mechanics, the motion of the electron is replaced with a wave function as described by Schrodinger's equation and solutions to that equation result in quantized energy states that the electron can occupy, and none of those states allow for the electron to collapse into the nucleus due to the boundary conditions required for the wave function to exist.
• I've learned that the formula to determine the no. of elecrons in each shell-2n^2 is only applicable till the elements having atomic no. 20. It was given by Bohr and was proved incorrect. But here, in the video, it seems to be fully correct. I'm confused. Please explain.
• That formula represents the maximum number of electrons per shell, NOT the actual number in any element's particular shells. Most notably, there is no element massive enough to have more than 32 electrons in any of its shells, even though, hypothetically, shells beginning with shell 5 could have more than that number of electrons.

Shells 1 and 2 fill up completely before any higher shells begin filling, but that is not the case thereafter. Starting with scandium, the electrons fill in complicated ways, with higher numbered shells beginning to fill before lower numbered shells are complete.
• how dose the d and the f orbital look like?
• I'm a little confused on the orbitals an atom has as we increase in n shells.
Do, the s,p,d,f, orbitals DIFFER as we go from shell to shell? (I was thinking yes since as 'n' increases we have bigger radius so 's' orbital in n=1 is smaller than 's' orbital in n=2)

Also lets say we took an atom that had n=3. Does that mean it has orbitals of only those in n=3 or does that INCLUDE all the orbitals from n=1 and n=2? (i.e. sulfur atom has a total of 14(1+4+9) different orbitals in which you can find electrons?
• Your both ideas are correct. The s orbital in the first shell has a smaller radius than the s orbital in the second shell, and so on (it is valid for all of the orbitals). An atom can have a lot of orbitals (it just depends on its number of electrons), so, if you have three shells in the atom, you're gonna have all the orbitals from n=1 to n=3, because each electron will be in a specific orbital.
• please tell me if i am right or wrong...
every orbital can hold only 2 electrons. and one of the electrons have up spin and the other down spin.
and the number of orbitals in a shell is given by n^2 where n is the shell number.
• Yes, everything you said is correct. Although, strictly speaking, "spin up" and "spin down" are not official terms.

However, beginning with shell n=3, the shells do NOT completely fill up before the next higher shell begins to fill.

NOTE: there is no element with a large enough atomic number to contain more than 32 electrons (16 orbitals) in any shell. The higher level orbitals (g, h, etc.) do exist but only as excited states. The first theoretical element that would be predicted to have an electron in a g orbital would be Element-125, which does not exist in nature and we do not current know whether it is even possible to make artificially.

So, in summary, although shells 5 and above theoretically could have electrons in 25 or more orbitals, there is no known element that is massive enough for this to actually happen.
• I've not found this anywhere else, so I doubt if it even exists....But are there subshells after 'f' and correspondingly are values of L>3 posiible?
• Yes and No.
There is no element massive enough to have an electron in the g or higher subshell in its ground state. The first element (should it be possible to create it artificially) predicted to have a ground state g subshell with an electron in it would be Element 125.

However, in excited states a lighter element can have an electron in a g or higher subshell. So, in that sense, there is such a thing as a g subshell and higher.
• could you please explain the shape of p and d orbitals because its not explained very well and i could not understand it