Atomic Structure part 24

追加: 2026-05-15

[00:00:00]now today we will do the calculation of wavelength by d broglie's formula all right calculation of wavelength by d broglie's formula when a potential difference v is applied across to it means i mean to say suppose an electron is there electron beam is there we are applying a potential difference that is v let us say v we are applying so the energy acquired by the electron is nothing but e into capital v energy acquired by the electron isn't it electron beam is there we are applying a potential difference we are applying a potential difference across it so the energy that which is occurred by the electron is nothing but small e into capital b now definitely when it when it gains some energy when it acquires some energy the electron starts moving of course it is moving but it starts moving with an increase of acceleration it is of course moving no doubt about it but it is moving with an increased acceleration but it is moving so that is it changes into energy which is nothing but known as kinetic energy we can say that because energy possessed by body in motion is known as kinetic energy all right again i repeat an electron beam is there you are applying a potential difference across it so it gains some energy electron gains of energy and that energy with the help of that energy it uh accelerates the electron accelerates and it moves so the energy possibly body in motion is what half mv square we can say that kinetic energy now we have to find the wavelength of that particular but you can say electron beam you have to find out so what you need to do now see here that is e v now this v is potential potential difference e is the electron the charge on the electron m stands for the mass of the electron v is the velocity of the electron we can select so small v let me write small v is equal to 2 e into capital t by m correct see that 2 e into capital v by m root over we got it okay now next is we have seen it lambda is equal to h by mv small v lambda is equal to h minus mv that means 1 by v so here we can write that is h by that is m v so v is nothing but this one is equal to this here one by v is there minute here this v is equal to root power of t two e into capital v by m see here v is equal to but here what is that h by m v that means one by v mind it alright so what but it will be reciprocal of it so it is nothing but that is m by 2 e into capital v is right that is m by 2 e into capital v we can say that so now if you simplify it what will happen this root m and here also root m into root n so 1 root n it gets cancelled so what you what you will be getting root over of 2 m e into capital v mind if this v is your potential this v is your potential this v and this v was small v was the velocity correct listen so now h the value is constant six point six to six and ten to the power minus thirty four joules again m the mass of the electron which is nine point one into ten to the power minus thirty one kg e is the charge in electron which is one point six zero two into ten to the power minus nineteen coulomb and he is the potential difference which is only varying now when you will put this value the value of h the value of m the value of e then ultimately what you will be getting is that lambda is equal to 1.226 into 10 to the power minus 19 by root over of capital v mind it uh that is let me write it a big one so that you otherwise you'll think it has small v it is not small v it's capital v okay again i write 1.226 into 10 to the power minus 19 by root over of capital v that is potential i'm saying you potential when you put the value of h m and e when you put it you will be getting this as lambda is equal to this much what meter definitely is my unit that is nothing but meter one point two two six and ten to the power minus sin so this is the wavelength calculated by d broke d broccoli we can say so it is also said to be as d broglie's wavelength got it now we have got miracles upon it we will do it later on that particular one now coming to that is the next principle now de broglies we have finished up now one more was there you know it that is hissenberg's uncertainty principle we can say that his inbox uncertainty principle what i said he's in burbs uncertainty [Music] principle on it his involves uncertainty principle very very important now what do you mean by this particular why it is uncertainty listen very carefully the concept we are going to change after this now see when a car is moving on a road when a bus is moving on a road all right when the planet is moving in an orbit they are having a particular trajectory means path they are moving on their own path got it so when this objects are moving on their path we are able to know the position of that particular object we are able to know the path of that particular object from the part we can also calculate that is nothing but velocity we can and as a result we can calculate the momentum mass and velocity we can say we can calculate the momentum that means we can know the position like suppose a bus is moving now we can say see the bus is moving so we can we can identify the position as well as we can identify the path on which path it is moving yes we can see the path or not because it's moving on the road so in this way we can know the path from where from which we can calculate the velocity yes from the speedometer we can't calculate the velocity here we can calculate the velocity as a result we can calculate the momentum that is mass into velocity that means for macroscopic object we can calculate the momentum as well as the position alright but suppose when an electron is moving now how you know the electron is moving what you have to do is that you have to take an atom you have to observe it under an electron microscope how will you observe it that is you you take an atom is will an atom be visible no you have to take a particular ah what you can say element clear that you will observe it under a microscope then you will see the atoms electrons protons whatever it is you will be seeing the subatomic particles now how will you see will you see in a dark room no suppose you identify the position of an if you identify an electron suppose an atom is there all right let us say that pictorial pictorial representation i am showing you this is the nucleus you can say atom is there electron i have mark it here that is a when the light will fall upon it listen carefully when the light will fall upon it the light is having sufficient energy to change the position of the electron because electron will gain that energy when the light will turn upon it electron will gain that energy and by gaining that energy what will happen is that electron will change its position it will occur the energy just now i said you it will acquire the energy and will change its position immediately you will say will not use the light and how you see it how will you see then electron protons you don't have to observe it under microscope microscope when you are observing it light is required whichever light it is sunlight white light whatever it is light is required and that light when it will fall upon the sub atomic particles what will happen is that the subatomic particles is going to gain that energy and immediately the electron will change its position from here it may come back it may come to this particular position we can say that let us say b so do you think the position here and the position here is the same the path which is is the same we can say that no it's not the same because angular velocity is changing so momentum is going to change angular velocity changes because angular velocity here and angular velocity here is it the same no so momentum is going to change so can you calculate the position as well as the momentum of a sub atomic particle like electrons simultaneously like in case of microscopic object we are able to calculate it i told you also an example but in case of microscopic object like electrons protons and all these things the sub atomic particles can are we able to calculate the position as well as the momentum because when you mark a particular position of an electron you mark it but this is the position when the right falls upon it we see that particular electron there but as soon as the light falls upon it the electron changes its position because you said why because electron is of negligible mass the light is having sufficient amount of energy the light is having that sufficient amount of energy to change the position of the electron from one place to another place it is having so you cannot calculate the position and momentum simultaneously you cannot suppose you would say here i'm being calculated okay when the light will fall upon here you'll mark the position b and then the light is going to fall upon here then definitely electron will again change the position to see or somewhere else it will move it is going to jump from one shell to another cell by gaining energy it is going to jump it will change its position so you cannot say what you can say the position of an electron now by this what we come to know you know nilbor what is said that in the first shell there is two electrons in the second shell there is eight electrons in the third shell there is eighteen electrons give us a formula two n square so nilbor actually did was not able to experimentally find it out this one he assumed this particular one and he gave us a formula again i repeat neil bohr did not give us this particular formula on the basis of experimental verification it was his completely an assumption because when the light is going to fall upon it the position of the electron is going to change it will jump from the first shell to the second or third shell you can say that then how can you say that in the first shell that two electrons are being present in the second shell eight electrons are being present in the third shell maximum 18 electrons can be present how can you say that we cannot say with certainty can we say certainty now no because the sub atomic particles are so lighter 9.1 in 10 to the power minus 31 kg there is a mass of an electron the mass of proton is 1.672 in 10 to the power minus 27 kg this is so lighter we can say that so when the light is going to fall upon it it will gain energy and it will jump from its position of course protons is there inside the nucleus we have nothing to do we have to do with the electrons only all right so hence what we find is that with certainty we cannot say that the first cell contains two the second shell eight the third cell eighteen saying maximum capacity we cannot say with certainty but i am using the word certainty we cannot say so hence this principle is called as isenberg's uncertainty principle because we cannot say with certainty we cannot identify the position as well as momentum of an electron simultaneously we cannot say we will not be able to predict it suppose a right is moving if you allow a torch light to fall upon the rat if you focus the dot straight up on the right you will see that a rat changes its position yes it changes position why because out of fear it changes position because somebody is coming to catch hold of it it is not that the torch light is falling upon it due to which it changes in position no not at all correct not at all suppose you are moving on the road when the light falls upon it will the question does the position of that object changes the microscopic object like bus or suppose you are only driving when the light is falling upon it does is your position changing no not at all isn't it so hence what you find is that or suppose you are standing is the when the light falls upon it is your portion changing no not at all so in this way for macroscopic object it is not true got it so it is only true for microscopic object hence again i say his inbox uncertainty principle has nothing to do with the objects which we did in our day-to-day life i'll prove it also this particular thing it has nothing to do with those objects which you deal with the day-to-day life and the sub atomic particle which we are talking about with certainty we cannot say the position as well as the momentum of an electron simultaneously mind it simultaneously we cannot say suppose we we can calculate the velocity of momentum of a but the electron will not be at a when you are calculating the momentum the electron will be at b suppose you are calculating at b the position that electron will not be at b when the light falls upon it will be at c somewhere so the momentum and the position you cannot calculate simultaneously but for microscopic of the present we can calculate no problem we can do it clear so understood so hence this principle is said that he's in berg's uncertainty principle and the definition is also said that what is the definition hisenberg uncertainty principle according to heisenberg we cannot simultaneously determine the position as well as the momentum of a subatomic particle like electrons because again i repeat according to hissenbergs we cannot determine simultaneously the position or it is impossible to determine the position or as well as the momentum of an electron not a of a subatomic particle like electron simultaneously we are not able to determine it all right so based upon this he gave us a mathematical relationship his work what is that he gave us is that delta x delta x is the uncertainty in position into delta p delta p is uncertainty in momentum is greater than or equal to h by 4 pi 4 pi h by 4 pi is a constant all right he found it out experimentally this one the delta x into delta p delta p is what m into delta we can simplify this one delta x again uncertainty in position delta p is n into delta v is greater than or equal to h by 4 pi we can say that okay so delta v is uncertainty velocity we can say that uncertainty in velocity now one thing you need to remember here that when i say we cannot determine the uncertain position means what suppose if an electron is in the x axis if in the electron is in the x axis we cannot determine the position of an electron when the light falls upon it in the x axis because it will change its position because of that understood i said that is it's important to understand that uncertainty uncertainty principle it is uh to the position and momentum along the same axis along the same axis uncertainty in position the momentum all right what i said if an electron is in the x-axis you'll see when the light falls upon it will not remain in that particular axis it will change its path it will change its axis clear the same axis we are talking to you so in this way hissing bugs arrive to this particular principle that is known as hezenberg's unstudied principle and based upon that he gave us this particular formula understood now so hence what i said you that he challenged as a result the board's atomic model for that reason i said in the beginning that this is very important we will be coming we will be arriving up after reading this particular what you can say principle will be arriving to a new concept a new concept will be arriving all right beginning before that also i said okay so what is that what more how can we prove it this particular thing that is it is it's applied only to microscopic object not microscopic we'll see it later thank you