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 Vin_Math 91
1 year 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 - 1 year ago

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

Vin_Math 91 - 1 year 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 - 1 year ago

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

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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 - 1 year ago

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

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No, I have just byhearted them.

Aryan Sanghi - 1 year 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!

Vin_Math 91 - 1 year ago

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In class 11 ncert it is given .

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@A Former Brilliant Member Oh, I don't have it, I'll see it on website. Thanks for letting me know!

Vin_Math 91 - 1 year ago

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@Vin_Math 91 Link You will find the exceptions and the reasons are also covered here. Phew! This was tiring to find it for you.

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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!

Vin_Math 91 - 1 year ago

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

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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

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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!

Vin_Math 91 - 1 year ago

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

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

Vin_Math 91 - 1 year ago

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@Vin_Math 91 Are you in class 9th?

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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???

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@A Former Brilliant Member 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?

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@A Former Brilliant Member I just came to 11th.

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

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@A Former Brilliant Member No. But I would soon.

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@Siddharth Chakravarty Have you enrolled in prmo or nsep?

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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!

Vin_Math 91 - 1 year ago

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@Siddharth Chakravarty,is my explanation correct??

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@A Former Brilliant Member 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.

Vin_Math 91 - 1 year ago

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@Vin_Math 91 I am not expert.:-)

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@A Former Brilliant Member But you are better than me, and you can clear my doubt, so for me, you are an expert :)

Vin_Math 91 - 1 year ago

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@Vin_Math 91 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 :-) .

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@A Former Brilliant Member Ok, thank you!

Vin_Math 91 - 1 year ago

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@A Former Brilliant Member Same here, because anybody can be an expert in a different context. You might know something we don't.

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@Vin_Math 91 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!

Vin_Math 91 - 1 year ago

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

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@A Former Brilliant Member 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.

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@A Former Brilliant Member 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.

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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!

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

Vin_Math 91 - 1 year 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 year 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!

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@A Former Brilliant Member It is because they are particles too. Electrons are like light, showing dual nature.

Aryan Sanghi - 1 year 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???

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@A Former Brilliant Member 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 - 1 year ago

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@Aryan Sanghi Ya,you might be right.

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@Aryan Sanghi Electrons have mixed states.

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@A Former Brilliant Member 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.

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

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@A Former Brilliant Member I had talked about only 1 scenario, I made it more precise if it confused you.

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Thanks a lot Sir!

Vin_Math 91 - 1 year ago

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Thanku for the explanation sir. :)

Aryan Sanghi - 1 year ago

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

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

Vin_Math 91 - 1 year ago

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What is the question? There are 22 unique atoms

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

Vin_Math 91 - 1 year ago

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@Vin_Math 91 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.

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@A Former Brilliant Member How can we calculate it?

Vin_Math 91 - 1 year ago

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@Vin_Math 91 LOL I asked that too. I don't know. If you want I can ask her

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@A Former Brilliant Member Yes, please!

Vin_Math 91 - 1 year ago

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@Vin_Math 91 Ok. Maybe it will take a few hours

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@A Former Brilliant Member No problem with that!

Vin_Math 91 - 1 year ago

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@Vin_Math 91 Now I should wait. BTW I think we should know lots of information. Just learn the 22 exceptions! :)

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@A Former Brilliant Member She wrote you should learn more math. Btw she wrote the formula in the pdf is your answer.

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@Vin_Math 91 You can start with this LOL From Szeged, so this won't be perfect :) (Szeged is famous for its dialect)

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I know why. It's almost certainly that the electrons repel each other into other orbitals, which happen to be d orbitals.

Kent Hitchborn - 10 months ago

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