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### Course: Chemistry library>Unit 5

Lesson 3: Quantum numbers and orbitals

# Quantum numbers

An orbital is a region around an atom's nucleus where electrons are likely to be found. Different types of orbitals (s, p, d, f) have different shapes and can hold different numbers of electrons. Learn how quantum numbers are used to describe the orbitals, and compare Bohr model orbits with the quantum mechanical model of atom. Created by Jay.

## Want to join the conversation?

• I m confused with the word orbital! Is orbital and sub-shell or sub-energy level the same thing? If not, then what is the difference ?
• An orbital is a "3D cloud" of possible positions of an electron (quantum mechanics states that the position is not certain). The quantum model is different from the Bohr model where the position is certain and the electron is in an orbit. There are many different individual shells of these orbital "clouds", which is described by the quantum number n. n describes the electron's distance from the nucleus, which also gives the energy of the electron. A subshell is contained within a shell. It's possible that there is more than one subshell per shell. The shape of a subshell is described by the quantum number ℓ. ℓ can be any positive integer from 0 to n-1. So, there is the possibility of many subshells of many shapes. Since subshells of a shell share the space of that shell, they must have the same energy levels.

For Example:

There is an electron with n=4. Therefore there is individual shells of electrons, each with a larger energy level than the previous. Since ℓ can be from any positive integer 0 all the way to n-1, and if n=4, then ℓ can be 0, 1, 2, and 3. So, there are 4 subshells of 4 different shapes within the n=4 shell. The 4 subshells, though they have different shape (and orientation through the other quantum numbers), are contained within the shell, therefore they all have the same level of energy.
• Why even give a spin quantum number if the electron isn't really spinning on an axis in reality?
• I think it's to account for the fact that in each orbital the electrons are "spinning" in opposite directions. Basically while they move around in the orbital they also have angular momentum. So the 1/2 and -1/2 is to account for that. We just call it "spin" to make it easier to understand the concept of what the 1/2 and -1/2 describe.
• Why is the spin quantum number +1/2 up or -1/2 down ? Where does the 1/2 come from ?
• That value comes from some very difficult math involved in quantum physics. You need to have mastered calculus at least through differential equations and vector calculus even to be able to read the equations properly. So, at this level of study we typically just tell the students the results of all the math, but skip the actual computations.
• What is the shape of a d- and f- orbital?
• In this video, we talk about n as the number of shell but the hydrogen atom has only one shell of type s so why the electron in this atom can "jump" down (up) to lower energy levels to emit light with different frequencies when there is only the case where n = 1 because otherwise we would have l > 0 so we would also have p orbitals, right?. I'm confused :D . Can someone help me understand?
• The shells still exist (or, more accurately, are available) even if there are no electrons occupying them. Thus, an electron can absorb just the right amount of energy and change from its usual state to an excited state.

By analogy, suppose that someone usually sings in the baritone range. Well, that person might be able to sing in a falsetto and reach the alto range. When they do that, their voice has jumped from its normal state to a higher state. Something no completely unlike that happens with electrons. They have their ordinary states, but if they absorb just the right amount of energy they can jump from their normal state to an excited state.

And, yes, the shell n=1 has only an s subshell, so a 1s electron must move into a different shell in order to achieve an excited state. Similarly shell n=2 has only s and p subshells, so a 2p electron would have to move into a greater shell in order to achieve an excited stated. However a 2s electron could jump to a 2p orbital (if they weren't all full) and achieve an excited state that way.

Thus, when we say that an atom does not have this or that shell, what we mean is that in its ground state that shell is not occupied.
• according to the quantum mechanics how many energy levels can be found ?
• In theory, there are an infinite number of energy levels. Practically, there are 7 energy levels(k,l,m,n,o,p,q -- we also assign these numbers 1-7) and there are 4 sublevels (s,p,d,f)
• What's the reason of introducing four quantum numbers only? And why is ( l ) always equal to zero when ( n ) is equal to 2?
And why are the orbitals named as s, p, d and f? How do we know how many electrons an orbital contains?
• A quantum number describes a specific aspect of an electron. Just like we have four ways of defining the location of a building (country, state, city, and street address), we have four ways of defining the properties of an electron, or four quantum numbers.

The minimum value of "l" is zero because no atom can exist without a subshell. If l = 0, we know that the shape of the s subshell is spherical. And we also know that every atom must have at least one s subshell. So, considering any atom, "l" must start from zero and go on till n-1

The s, p, d, and f stand for sharp, principal, diffuse and fundamental, respectively.
The letters and words refer to the visual impression left by the fine structure of the spectral lines which occurs due to the first relativistic corrections, especially the spin-orbital interaction.

The maximum number of electrons an orbital can hold is two. So, the capacity of each subshell is:
s-subshell : maximum of 2 electrons (as it contains only 1 orbital)
p-subshell : maximum of 6 electrons (as it contains 3 orbitals)
d-subshell : maximum of 10 electrons (as it contains 5 orbitals)
f-subshell : maximum of 14 electrons (as it contains 7 orbitals)
• But in my NCERT textbook, it says that An electron
spins around its own axis, much in a similar
way as the earth spins around its own axis while
revolving around the sun. I'm confused.
• They’re teaching you a simplification in a way that you can relate it to something you know. But electrons do not really spin around an axis.