Demystifying Quantum Numbers: Understanding the Role of n, l, and ml

[Modernization]

I am still totally confused about the principle quantum number even though i got passed the unit with a A+ on the exam. does the principal quantum number, n, have anything to do with the period? Does the "n" value, which leads to the "l" and "ml" actually indicate all the possible orbitals for a particular atom or just for one electron. When you give an "n" value of 4, what does that mean? does it mean any element on period 4?
Also, why couldn't element Zr (atomic number=40) have at least one electron with an "ml" value of +4?
thanks

 

[Borek]

does the principal quantum number, n, have anything to do with the period?

Yes! 1st period - n=1, 2nd period - n=2. And so on. BUT - that relates only to the valence shell. All valence electrons in all atoms form 3rd period have n=3, but these atoms have also electrons with n=1 and n=2, they are just not taking part in reactions. (In the case of of periods with higher numbers it can get a little bit more cimplicated, but for now that should be enough).

Does the "n" value, which leads to the "l" and "ml" actually indicate all the possible orbitals for a particular atom or just for one electron.

There are many electrons having the same n value, so it probably means "all", but I am not sure what the question is.

When you give an "n" value of 4, what does that mean? does it mean any element on period 4?

No, any atom of any element from period 4th up can have electrons with n=4.

Also, why couldn't element Zr (atomic number=40) have at least one electron with an "ml" value of +4?

Because for n=4 maximum value of ml is 3. To misquote Pauli - treat it as a police ban. You don't have to understand, but you have to obey There is a logic behind, but it is hard to understand without knowing more about where and how quantum numbers appear in wuantum mechanics.

 

[Modernization]

Because for n=4 maximum value of ml is 3. To misquote Pauli - treat it as a police ban. You don't have to understand, but you have to obey There is a logic behind, but it is hard to understand without knowing more about where and how quantum numbers appear in wuantum mechanics.

but the element Zr is on the fifth period, so wouldn't it have an "n" value of 5, which makes ml +4 possible?

 

[Borek]

Sorry, my mistake. You are right, 5th period it is. But now I am not sure what you are asking about.

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[Bohrok]

but the element Zr is on the fifth period, so wouldn't it have an "n" value of 5, which makes ml +4 possible?

An n value of 5 means that an element can have a maximum mℓ value of 4, but an element with electrons in its n = 5 shell doesn't automatically mean it has electrons in all its subshells, or in this case, electrons in its 5g subshell (n = 5, ℓ = 4). Zr (element 30) just has enough electrons to reach its 5d subshell (n = 5, mℓ = 3). On the other hand, no element on the periodic table has enough electrons to reach the 5g subshell (n = 5, ℓ = 4) in its ground state.
By my figuring, the first element to have an electron in its 5g subshell would be element 121.