Coulomb's Law Explained: How It Applies to Atoms and Electron Shielding

hello everyone and welcome back my name is Mr kovalt and in this video I'm going to go over Coulomb's law and how it

applies to the atom so let's get into this so here we have Coulomb's law and basically what you have here is you have

energy is equal to some constant one over five four uh pi and then this is some some constant that we don't really

need to get into but it's important that this is just a constant whatever that number is

uh but the really important part of this equation is right here so here you have two charges Q is for some charge so you

have charge number one multiplied by charge number two divided by the distance between those

two charges Okay so this equation really does explain a lot

about what's going on in the atom with regard to electrons and uh shielding effect and stuff like that and effective

nuclear charge and things things of that nature and so we have to understand what's going on and so in the atom we

have charges so we have the nucleus so I have three atoms here and this is the nucleus with one proton this one has

two protons this one has three protons and so when we're thinking about this this uh law here basically what it's

saying is that the energy in the system of these charged particles is going to depend on the charges of the

charged particles and the distance between those charged particles so there's a few things to note here

uh first uh when we have like charges uh the potential energy is going to be

positive and when we're thinking about potential energy in the atom it's very much like potential energy gravitational

potential potential energy when we're thinking about gravitational fields right so I standing on the ground right

now I have a low gravitational potential energy because I am close to the ground I'm uh closer to the Center of the Earth

as compared to like if I was flying in an airplane right so the farther I get away from the

earth the higher my gravitational potential energy so as the distance between me and the Earth increases so

does my potential energy and so the default position or the natural position for me to be in is low potential energy

so if I jump out of the airplane I'm going to be falling to the ground lowering my potential energy increasing

my kinetic energy and uh so on so it's very similar to what we uh see in the atom so when the particles are

absolutely charged they like to be close together but if they are negatively charged or I'm sorry if they are if they

have the same charge then they're not really going to be liking to be close together so what does that mean how does

it how does this law like apply to that so here let's assume we have like charges okay so if we have I'm going to

use different color so if we have two plus charges two positive charges it could be two negative charges too but

if we have two of the same charge then we know that like charges repel they don't really want to be close to

each other so let's assume let's imagine for a moment that we're trying to bring them closer together

so first we notice that these two multiply together if I have a positive charge multiplied by a positive charge

then that's going to make the potential energy positive the uh nature wants to have low

potential energy and that goes the same for anything in the atom so the atom itself is trying to reach the lowest

potential energy possible and so when you have two like charges that are close to each other

um if you lower the distance here if R being the distance between the charges gets smaller right what happens to this

whole thing right if R gets smaller then this whole thing gets larger and therefore the potential energy becomes

more positive so higher potential energy that is not a good system it's not a good uh

um position to be in they don't want we don't want high potential energy so you can understand that when we bring the

two like charges closer together that's raising the potential energy right that is not what uh the system wants the

system wants to go to low potential energy so what are the charges charged particles going to want to do they're

going to want to repel and get away from each other right so getting away from each other lowers the possible the

potential energy so if we make the distance between the light charges lar larger then this gets larger the

denominator gets larger that means this whole thing gets smaller and potential energy goes down so like charges want to

repel they want to remove away from each other in order to lower the potential energy because potential energy is

positive and we want that less and less positive okay same thing for negative charges okay okay well what about

opposite charges right so if I have one of these let me use a different color let's use blue

so what happens when I have a negative charge with a positive charge so we're

multiplying those charges together if I have a negative multiplied by a positive that's going to make the potential

energy negative so now the potential energy is negative so now

what happens with regard to distance so if I decrease the distance between the two

charges if I make them come closer together what happens now same thing happens

right so this gets smaller that means that this whole thing gets larger but now instead of being a larger positive

value It's a larger negative value which means more negative potential energy means lower potential energy so they

want to get closer together that if they if if opposites get closer together that's going to lower the

potential energy and it's going to be uh more they're going to be more happy a more happy system if you want to put it

that way all right so this explains why Opposites Attract they're tracting in order to lower the potential energy so

if we bring those charges apart if we try to separate them and increase the distance

R here gets larger right so when R being a denominator the distance between the the charge particles gets larger then

this whole number here this ratio gets smaller and we end up with a smaller negative number so in this case it's

becoming less negative so another way you could put it is larger potential energy less negative potential energy is

a larger potential energy that is not a favorable system that's not a favorable situation to be in so separating those

absolutely charged particles increases potential energy so they want to be charged they want to be attracted to

each other they want to become closer together and that's going to lower potential energy and again

we want to lower the potential energy or the system or the atom is looking to lower potential energy

okay so with that out of the way if we now fully understand the equation we can now apply it to atoms with various

amounts of electrons so here we have a basic atom this is your hydrogen because we only have one

proton so we have a hydrogen atom in here with the one electron so here the electron and the proton we have one the

nucleus is positive so we the nucleus is one charge right we can think of that as q1

or in this case we could say Q2 is the positive nucleus and q1 is the negative electron and so here we would expect an

attractive Force so an attraction or uh between those two and so being as close as the electron can to the nucleus would

be the lowest possible energy so this explains the outbound principle in the electronic configurations like electrons

want to be in the lowest energy states possible they that means they want to be as close to the nucleus as possible so

lower energy states are closer to the nucleus than farther away as you get farther away energy the potential energy

increases um so that why because the electrons and the protons the nucleus is positive so

they want to be attracted to each other they want to decrease that distance so again negative times positive gives you

negative uh uh uh potential energy um so electrons want to be close to the

positive nucleus so what happens when we put another electron into into the orbit here so

here we have two protons right um so here we have helium

with two protons so the other thing we want to look at is now we have like charges here so we have

two electrons they're in the same orbital they're at the same energy level and so once these two electrons going to

want to do they're going to want to repel each other and so having those two light charges in the same orbital that's

going to if we if we keep them together that's going to raise potential energy so what are these electrons going to

want to do they're going to want to repel each other and move farther farther apart right

so this uh repelling force between the two electrons is going to counteract to some degree the attractive force of the

protons in the nucleus that are attracted to the electrons so not only are the two electrons attracted to the

positive nucleus therefore that they're going to want to come closer to the nucleus in order to lower the potential

energy but the two light charges are going to want to repel in order to also lower that potential energy so there's

some give and take here that there so the repelling force it has to counteract in some degree the positive attractive

force in the nucleus and in that we call that shielding or um

uh the affected nuclear charge so there's some shielding going on here with the repelling Force here

and so these two electrons because they are repelling each other that's going to counteract some of the attractive force

of the nucleus and so these two electrons are not going to quite feel the exact uh strength or the total uh

pulling force of the uh of the nucleus because of the repelling force of the electrons so there is some shielding

going on here so these electrons are kind of shielding each other from from the the attractive force of the nucleus

and so here I also want to point out the fact that we have two protons in this nucleus so

this nucleus has a total of a two plus charge so not only does the uh signs of the charges matter

but the size of the charge itself so larger charges are going to either have a stronger repelling force or a stronger

attractive Force if they're opposite so if they're the same they're going to have a stronger repellent Force if

they're opposite charged they're going to have a stronger attractive Force so here we have a larger nucleus so that

larger nucleus with more protons and it is going to have a stronger attractive force and therefore the potential energy

is going to be greater or less depending on the charges so here we have two protons versus one

so if they're oppositely a Charged then having a larger charge is going to affect and make a larger negative

potential energy okay so this is going to have a greater effect on the uh the pulling of the

electrons so and so we can see here also in this one so this would be lithium with three protons so

we have lithium here and so here you can see uh we have this energy level number one n equals one and now we're adding a

second energy level so energy level number two and now we have electrons in the energy level here and so if we're

looking at this electron here this electron is farther from the nucleus so it's not going to feel have

as much of a pull so because these two electrons are occupying the lower energy this electron has nowhere else to go

except for just to go to the next Higher One which would be your 2s orbital okay and so here this electron is farther

away so it's going to have a higher potential energy but it's as low as it can get so higher potential energy

because it's farther away increasing R okay um

but at the same time you can see that these two electrons are on the inside both of these electrons are going to

have a repelling force on this so you can see this as a two negative so our negative charge will be two

right and then we have a negative charge here right so we have two negative one negative so you can see that these

charges in this in the middle here on the inside are going to have a stronger effect on this electron here on the

outside so that these two electrons have a repelling force on this one therefore it these two are counteracting the

pulling force of the three protons and this nucleus on that electron so there's some counteracting there and so because

of this we call this shielding right these two electrons are shielding the the positive effect of the three protons

on this one if these two electrons were taken away and only that electron was there then the three protons would be

able to have a full effect on that electron without any repulsion or repelling force due to these but because

you have these two electrons there you've got those charges so since there are like charges those

like charges do not want to be close together they are repelling the uh the lower to lower the potential energy they

want to be farther apart but in order to be farther apart um you got to increase the distance but

at the same time you have that attractive force in the nucleus that attractive force is wanting to

attract so this electron also wants to be attracted to the proton and being close together lowers potential energy

so there's that sorry about that so there's that counteracting force and

so because of that counteracting force and all these different attractive and uh repelling forces there's there's got

to be an ultimate balance between these and that's what referred to shielding so increasing the protons in the nucleus

increases the attractive force between the two charges the oppositely charged particles

in this case the nucleus and the electron therefore that's going to decrease the uh or I decrease the

potential energy make it more negative so uh so that's going to allow the

electrons to become closer uh be attracted more strongly but again adding electrons to it will also add a

repulsive force and so in order to lower potential energy they're going to want to get farther apart so understanding

what's going on in the atom with regard to Coulomb's law helps us in the end to understand what's going on with the

periodic trends and so um this is really the background and

understanding of of periodic trends as far as why does the uh the effective nuclear charge change when you go in a

certain way when you go across why does it uh across the periodic table left to right why does

um why does the ionization energy change the way it does why does the size of the atom change the way it does it all comes

back to Coulomb's law so understanding what's going on here will actually explain everything with regard to

periodic trends which I will be talking about in future videos thanks for joining me if you liked this video If

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