Help!- Electronic Configuration

I was reading a little bit about the electronic configuration of elements, and don't understand why these elements don't obey the Aufbau Principle. Any help will be greatly appreciated!


According to this principle, the electronic configuration of Lanthanum(La) and Cerium(Ce) should be: Lanthanum(La)=[Xe]6s24f1\text{Lanthanum(La)}= \text{[Xe]}6{\text{s}}^2 4{\text{f}}^1 Cerium(Ce)=[Xe]6s24f2\text{Cerium(Ce)}= \text{[Xe]}6{\text{s}}^2 4{\text{f}}^2

But, according to Google, it is: Lanthanum(La)=[Xe]6s25d1\text{Lanthanum(La)}= \text{[Xe]}6{\text{s}}^2 5{\text{d}}^1 Cerium(Ce)=[Xe]6s24f15d1\text{Cerium(Ce)}= \text{[Xe]}6{\text{s}}^2 4{\text{f}}^1 5{\text{d}}^1

Why are the 4f-{4\text{f-}} orbitals not filling first but the 5d-5{\text{d-}} orbitals are?


I know there are some exceptions to this rule, like Chromium(Cr)\text{Chromium(Cr)} and Copper(Cu)\text{Copper(Cu)}, but those are because the electrons of last orbital tend to gain stability, hence those exceptions seem justified. But, here there is no reason of stability, as none of the last orbitals are half-filled or completely-filled!

Note by Vinayak Srivastava
3 weeks ago

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Actually La and Ce are kinda exceptions only, there are almost 22 exceptions in periodic table. General configuration of f-block elements is ns2ns^2 (n1)d(01)(n-1)d^{(0-1)} (n2)f(114)(n-2)f^{(1-14)} for this reason. And this is the reason why La and Ac are d-block elements. :)

Aryan Sanghi - 3 weeks ago

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Yes, but there are some reasons for exceptions, I could not find any for these! :)

Vinayak Srivastava - 3 weeks ago

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My chemestry teacher said that Nb, Ru, Rh, Pd, La, Ac exeptions have no reasons. They are still not discovered.

Hiviru Palihena - 3 weeks ago

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@Hiviru Palihena All things have some reasons,most chemistry exceptions can be understood by klein-gordon equation.

Kriti Kamal - 3 weeks ago

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Nb-41-[Kr]5s2 4d3 ===> [Kr]5s1 4d4
Ru-44-[Kr]5s2 4d6 ===> [Kr]5s1 4d7
Rh-45-[Kr]5s2 4d7 ===> [Kr]5s1 4d8
Pd-46-[Kr]5s2 4d8 ===> [Kr]4d10
La-57-[Rn]6s2 4f1 ===> [Rn]6s2 5d1
Ac-89-[Rn]7s2 5f1 ===> [Rn]7s2 6d1

Those 6 are the exeptions what I know excepet half-filled & fully-filled.

Hiviru Palihena - 3 weeks ago

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Have you some mnemonic to memorize them??? @Aryan Sanghi .

Kriti Kamal - 3 weeks ago

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No, I have just byhearted them.

Aryan Sanghi - 3 weeks ago

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@Aryan Sanghi Ooo.

Kriti Kamal - 3 weeks ago

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@Aryan Sanghi, can you please write those 22 exceptions? I don't know where I can find all at one place!

Vinayak Srivastava - 3 weeks ago

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In class 11 ncert it is given .

Kriti Kamal - 3 weeks ago

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@Kriti Kamal Oh, I don't have it, I'll see it on website. Thanks for letting me know!

Vinayak Srivastava - 2 weeks, 6 days ago

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@Vinayak Srivastava Link You will find the exceptions and the reasons are also covered here. Phew! This was tiring to find it for you.

Siddharth Chakravarty - 2 weeks, 6 days ago

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@Siddharth Chakravarty Oh, thanks a lot! I would have searched the NCERT, but you still searched it for me! Thank you!

Vinayak Srivastava - 2 weeks, 6 days ago

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@Siddharth Chakravarty Nice,this link covers almost all aspects but i still like wiki .

Kriti Kamal - 2 weeks, 6 days ago

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@Vinayak Srivastava ,As @Aryan Sanghi has said there are many exceptions as such.The reason behind it, is that the aufbau's principle is an empirical formula and doesn't imply for heavier metals. Aufbau's formula of n+l rule is one of the results of schrondiger's wave equation and an interesting fact is that erwin schrondiger had not consider relativity,in its wave equation.The relativistic effects become significant as the mass of the particle increases ,that's why most heavier elements have many exception,however schrondiger's wave equation is rectified to klein-gordon equation. The best example of relativistic effects is color of gold.Since chemistry mainly deals with small atoms of organic compounds,thar's why in most cases we don't consider relatvistic effects.In order to know ,exact answer of your question we have to stydy klein-gordon equations(whose math is a bit harder at least for me.) you can study it completely from given source .

Source

Kriti Kamal - 3 weeks ago

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Oh, so I don't think I need to go into the math, thanks a lot for helping @Kriti Kamal and @Aryan Sanghi!

Vinayak Srivastava - 3 weeks ago

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@Vinayak Srivastava,no problem,have you started atomic structure?

Kriti Kamal - 3 weeks ago

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@Kriti Kamal Yes, I have studied a little bit, but till now struggle with questions of both these chapters, atomic structure, and periodic table.

Vinayak Srivastava - 3 weeks ago

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@Vinayak Srivastava Are you in class 9th?

Kriti Kamal - 3 weeks ago

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@Kriti Kamal Yes.

Vinayak Srivastava - 3 weeks ago

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@Kriti Kamal I am good in the relativistic calculations but I have to still increase the scope i.e study more for the further substitutions done in the chemistry part. I was recently doing some studies for the wave functions, also colour forces it is giving some lead for the question "The moving or not moving neutrons".

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@Siddharth Chakravarty, Nice,but my math is not so good,i am still struggling with classical mechanics and first order calculus.Have you completed,first order calculus???

Kriti Kamal - 3 weeks ago

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@Kriti Kamal Yes, I read some books so I think I know till medium difficulty, but in a way, logic can be done by our simple intuition but that would be too lengthy.

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@Siddharth Chakravarty In which class do you read?

Kriti Kamal - 3 weeks ago

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@Kriti Kamal I just came to 11th.

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@Siddharth Chakravarty Have you started second order calculus such as langrage multipliers.

Kriti Kamal - 3 weeks ago

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@Kriti Kamal No. But I would soon.

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@Siddharth Chakravarty Have you enrolled in prmo or nsep?

Kriti Kamal - 3 weeks ago

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I had the same doubt a few months back. 4f and 5d are supposed to be very near energy shells. But they say 4d is unstable with 1 electron so 5d takes 1 electron to become stable. Similar reason follows for Cerium. Although 1 one of our teachers say they just say this for now, but this is not exactly correct. There is lanthanide contraction also. But the teacher had told to see more about Kohn-Sham orbitals which I have not learnt. There are a lot of things which even I can't explain for now, but there is a lot to study in chemistry. This is beyond the scope I think for now.

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@Vinayak Srivastava as @Aryan Sanghi has mentioned there are many exceptions, you actually find a lot in chemistry, physics or biology i.e whole of science, each law is revised again to match with the new observation, and some law works or some don't.

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Oh, thank you! I think these laws will again be changed like the Periodic Table was again and again changed, until there won't be any exception!

Vinayak Srivastava - 3 weeks ago

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@Siddharth Chakravarty,is my explanation correct??

Kriti Kamal - 3 weeks ago

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@Kriti Kamal However I am also unsure, but few parts I can agree. I shared a little much I knew about this because some things are too complex for now. We need a chemistry expert to help us and @Vinayak Srivastava for more accuracy and info, or some relevant sources.

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@Siddharth Chakravarty There are many maths and physics experts like you all on Brilliant, but I don't know if there is some chemistry expert. Do tell me if there are any! I actually get a lot of doubts in Chemistry, but I don't have any teacher, I have to just Google. In school, these things are not taught.

Vinayak Srivastava - 3 weeks ago

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@Vinayak Srivastava I am not expert.:-)

Kriti Kamal - 3 weeks ago

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@Kriti Kamal But you are better than me, and you can clear my doubt, so for me, you are an expert :)

Vinayak Srivastava - 3 weeks ago

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@Vinayak Srivastava In science and mathematics,no one is ahead and no one is behind . We all are at the same page.

Consider me as a friend rather than a expert :-) .

Kriti Kamal - 3 weeks ago

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@Kriti Kamal Ok, thank you!

Vinayak Srivastava - 3 weeks ago

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@Kriti Kamal Same here, because anybody can be an expert in a different context. You might know something we don't.

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@Vinayak Srivastava You can ask us doubts but we might be able to answer till a certain extent, as we also have doubts.

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@Siddharth Chakravarty Yes, I know, but after that extent, most of the people can't answer!

Vinayak Srivastava - 3 weeks ago

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@Siddharth Chakravarty Yes!

Kriti Kamal - 3 weeks ago

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@Siddharth Chakravarty I don't think a chemistry expert rather than a relativistic quantum mechanics expert.

Kriti Kamal - 3 weeks ago

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@Kriti Kamal A relativistic quantum mechanics expert in a way would know with the chemistry we are dealing here. XD

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@Siddharth Chakravarty Can i know on which parts you disagree?If you have some time,then we can discuss it.

Kriti Kamal - 3 weeks ago

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@Kriti Kamal I mean Idk about some parts thus I said I am unsure.

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I think that they only make stories by introducing exception,if they simply consider relativistic quantum mechanics instead of normal one,then most of the problems will solved. @Siddharth Chakravarty.

Kriti Kamal - 3 weeks ago

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Yes only "most" but I am still unsure about the further things so I won't say because it's good to know nothing rather than 1000 wrong things but humans love to approximate most of the times and believe in patterns which are followed by majority things.

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@Siddharth Chakravarty Yes,you are right!

Kriti Kamal - 3 weeks ago

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@Blake Farrow, Sir, can you please help us? Thanks!

Vinayak Srivastava - 3 weeks ago

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@Kriti Kamal is right on. Heavy atoms have a higher nuclear charge Z, which causes a Coulomb attraction that accelerates the orbiting electrons. Once this gets above 42 or so (Molybdenum or heavier), the ground state electron speeds up beyond 30% of the speed of light, causing a Lorentz correction of more than 5%. You'll find plenty of exceptions in this corner of the periodic table, here there be dragons.

The Aufbau principle doesn't take this stuff into account at all, it's just an approximation. You need many bodied relativistic quantum mechanics to fully describe what's going on here and find the configuration that minimizes the atom's energy.

Check this out for another approximation, but one that gets into a wee bit of relativity and quantum mechanics.

https://brilliant.org/problems/very-small-physics-3/

Blake Farrow Staff - 1 week ago

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Thank you for letting us know more :)

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Sir, i have doubt. If electrons and other particles are wave. How does the electrical force acts between them ? Does it remain same or changes? Thanks!

Kriti Kamal - 6 days, 23 hours ago

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@Kriti Kamal It is because they are particles too. Electrons are like light, showing dual nature.

Aryan Sanghi - 6 days, 23 hours ago

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@Aryan Sanghi I agree. But, an electron is a wave. So,it can be at many places at the same time or we can say all around the nucleus for electrons of s orbital . Then, how many pairs of forces act. And does the expression for electrical force changes???

Kriti Kamal - 6 days, 23 hours ago

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@Kriti Kamal It shows wave nature, like double slit experiment. It doesn't mean that it can exist at many places at once. I think electric force almost remains the same.

Aryan Sanghi - 6 days, 23 hours ago

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@Aryan Sanghi Ya,you might be right.

Kriti Kamal - 6 days, 22 hours ago

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@Aryan Sanghi Electrons have mixed states.

Kriti Kamal - 6 days, 19 hours ago

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@Kriti Kamal But the wave nature comes from the uncertainty principle and other things, so if we don't know the position we could say it having a wave nature so it makes sense to say them to be at many places, no matter how paradoxical it sounds. However, they might be at 1 place actually, excluding the mixed states scenario.

Siddharth Chakravarty - 6 days, 21 hours ago

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@Siddharth Chakravarty I don't agree with last line. Now,i agree

Kriti Kamal - 6 days, 19 hours ago

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@Kriti Kamal I had talked about only 1 scenario, I made it more precise if it confused you.

Siddharth Chakravarty - 6 days, 18 hours ago

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Thanks a lot Sir!

Vinayak Srivastava - 6 days, 22 hours ago

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Thanku for the explanation sir. :)

Aryan Sanghi - 6 days, 21 hours ago

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Yeah. There are exceptions. But there are excited(I used google translator :) ) atoms too.

Páll Márton - 2 weeks, 6 days ago

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@Brilliant Mathematics, @Brilliant Physics, can you please help us?

Vinayak Srivastava - 1 week, 1 day ago

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What is the question? There are 22 unique atoms

Páll Márton - 1 week, 1 day ago

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I want to know why these exceptions, why aren't there any simple reasons?

Vinayak Srivastava - 1 week, 1 day ago

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@Vinayak Srivastava The minimum energy is the answer. My teacher said if we calculate the energy in each scenario, then we will get this is the best result.

Páll Márton - 1 week, 1 day ago

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@Páll Márton How can we calculate it?

Vinayak Srivastava - 1 week, 1 day ago

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@Vinayak Srivastava LOL I asked that too. I don't know. If you want I can ask her

Páll Márton - 1 week, 1 day ago

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@Páll Márton Yes, please!

Vinayak Srivastava - 1 week, 1 day ago

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@Vinayak Srivastava Ok. Maybe it will take a few hours

Páll Márton - 1 week, 1 day ago

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@Páll Márton No problem with that!

Vinayak Srivastava - 1 week, 1 day ago

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@Vinayak Srivastava Now I should wait. BTW I think we should know lots of information. Just learn the 22 exceptions! :)

Páll Márton - 1 week, 1 day ago

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@Páll Márton She wrote you should learn more math. Btw she wrote the formula in the pdf is your answer.

Páll Márton - 6 days, 17 hours ago

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@Vinayak Srivastava You can start with this LOL From Szeged, so this won't be perfect :) (Szeged is famous for its dialect)

Páll Márton - 1 week, 1 day ago

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