 Good morning friends, today we are going to understand the Bohr's atomic model ok. We have already seen so far what is the particle nature, what is the wave nature and the various other models which we have discarded since they are not standing or they are not you know found to be true for various other investigations ok. So, today in this session we are going to understand about this model what is Bohr's model, but before that one small thing we have to understand that what is absorption spectrum ok. So, so far we have we have you know discussed already that the wave the particle or electromagnetic radiations has both wave nature and particle nature and we have discussed photoelectric effect in detail in the last session ok. Today we are going to understand what is absorption spectrum ok. We will discuss this absorption spectrum and then we will see the Bohr's atomic model. Absorption spectrum is suppose we have a light source right and then here we have a prism and then we have some atom or suppose hydrogen atom we have here. This is hydrogen atom and this side we have a screen you can take any atom over here that is not a constraint it is prism and it is source of white light ok. So, what happens here from this source white lights comes and it strikes at prism right. When it comes out from this prism it it is splits into 7 different color that we know already 7 different color ok. It is it is splits into 7 different color and falls on the atom which we are taking this side ok hydrogen atom ok. So, 7 different colors means we have 7 different wavelength ok that is the meaning we have. Now, when this light comes out to this hydrogen atom and we get this light here on the screen. So, what we observe there are few wavelengths which are missing here we only get few wavelengths here 2 or 3 all 7 wavelengths are not present here suppose it is lambda 1 this is lambda 3 this is lambda 5. So, few wavelengths 2 4 6 7 were missing here right. So, what is the conclusion of this particular experiment what is the meaning here why few wavelengths are missing here right. So, first of all this wavelengths like we have we have you know a definite wavelengths present and this spectrum or this spectrum is not continuous is not continuous few wavelengths are missing ok that is why it is not continuous ok. So, this wavelength is formed by the absorption of few wavelengths by this hydrogen atom and hence we are calling it as absorption spectrum this one absorption spectrum ok. Since few wavelengths has been absorbed now what is the meaning of this why all wavelengths was not absorbed why few wavelengths are only absorbed sorry absorbed. Now, the thing is of what we conclude from this whenever electrons whenever electrons receives energy from any other external source suppose any light we have. So, what it does electrons suppose if it is present here it receives energy from the light source and then it jumps to the higher energy level comes over here right. So, this means within an atom there are energy levels present energy level present ok and electron absorb only those energy corresponding to that the energy level is present within an atom partial exchange of energy is not possible ok suppose if I take an example of this suppose the 10 joule of energy we have here and here we have 30 joule this is suppose 50 joule and here we have 100 joule of energy means for electron to be in this energy level it must has it must have 100 joule of energy similarly here 50 30 and 10 correct. Now, suppose you are providing energy of 30 joule here right if you are providing energy of 30 joule. So, in this state electron already has some energy that is 30 joule and 30 joule more you are providing. So, this 30 and this 30 become 60. So, 60 joule of energy level is not present in this atom we have just taken and an arbitrary value to make you understand right. So, this 30 plus this 30 become 60 60 joule of energy level is not present within this atom that is why this particular wavelength right which gives 30 joule of energy to this electron is completely reflected by the electron it would not get absorbed ok. So, 30 joule goes over here and 30 joule reflects back correct, but if the electron has or the wavelength has 20 joule of energy this 20 becomes 30 plus 20 becomes 50 and then the electron jumps to the higher energy level which has 50 joule of energy correct. So, this means what within an atom there are energy level present and electron absorb only those wavelengths or only those radiations or wavelengths corresponding to that the energy level is present within an atom partial exchange of energy is not possible 30 joule of energy if you are giving in it cannot take 20 joule out of it and it reflect 20 joule of energy because this energy is the energy associated with one photon or quantum ok one photon or one quantum ok. So, either the whole energy of one photon or a quantum get absorbed or whole will get released partial exchange is not possible ok. So, very important there are other spectrum also emission spectrum we have right different types of spectrum we have line spectrum band spectrum based on the you know the classification is based on origin and you know the nature of the or you know the thickness of the spectrum we have based on that there are different different types of spectrum not very much important for you know exam point of view. But why absorption we are discussing because with this experiment only we have come to this conclusion that within an atom there are energy levels present ok. Now, we have already discussed about particle nature now we come to know that within an atom energy levels were present ok. So, on the basis of all these conclusion or result boards given his own atomic model that we call it as board atomic model ok. Now, we are going to understand what is the postulates of board atomic model and that the you know calculation associated with it ok. So, first of all the constraint we have here in board atomic model that this is true or valid only for only for one electron system one electron system means what the species has only one electron present in it. For example, hydrogen has one electron H e plus has one electron L i 2 plus has one electron. So, this board model is applicable only for one electron system more than one electron the you know the model is not valid why that also we will discuss later in this ok. So, the main postulates the main postulates of board atomic model first point infinite energy levels present within an atom within an atom K L M N or 1 2 3 4 and so on. So, there are infinite energy level present within an atom ok. Now, second postulate is out of infinite energy levels electron revolves only in those orbit in which in which its angular momentum in which its angular momentum is integral multiple multiple of H by 2 pi integral multiple of H by 2 pi this H by 2 pi we also represent by this symbol sorry this H by 2 pi ok. Third point is the electrostatic force of attraction provides necessary centripetal force provides the necessary centripetal force. Electron revolves in a circular path called orbit electron revolves in a circular path called orbit. If electron absorbs energy absorbs energy it jumps to the higher energy level higher energy level and the sixth point is and the sixth point is if electrons electron loses energy energy it comes back to the lower energy level these are the postulates of boards model out of infinite energy levels right there are infinite energy level present within an atom named as K L M N or 1 2 3 4 and out of infinite energy levels electron revolves only in those orbit in which its angular momentum is angular integral multiple of H by 2 pi electrostatic force of attraction provides the necessary centripetal force to the electron electron revolves in a circular path called orbit ok. So, out of these 5 6 you know postulates the second one and the third one is the most important we are going to derive an expression for radius and velocity with respect to these 2 postulates only ok. So, now you see here ok. So, these 2 postulates are important here 2 and 3 now right now you see what is angular momentum angular momentum from the point 2 we are going to write is m v r ok. So, first of all suppose we are assuming nth orbit right nth orbit nucleus we have here and suppose the electron we have here. So, in this nth orbit the velocity of the electron is suppose v n this radius is r n this is electron and the mass of the electron is m e mass of the electron is m e right. So, now the angular momentum of this electron we write it as mass m e v n r n m v r is the angular momentum m v r m e is the mass of electron v n is the velocity in nth orbit r n is the radius of this orbit ok is equals to the integral multiple of h by 2 pi n h by 2 pi nth orbit we have ok. This is equation 1 now the third postulates we have electrostatic force of attraction provides the necessary centripetal force ok. So, electrostatic force of attraction is what k q 1 q 2 by r is where you must remember this if the 2 charge present at a distance q 1 q 2 at a distance r from each other then the electrostatic force between the 2 charge is k q 1 q 2 by r square this is electrostatic force of attraction and one more thing the potential energy is minus k q 1 q 2 by r this 2 formula we are going to use here minus k q 1 q 2 by r ok all these things you will study in physics in electrostatic. Now suppose if this electron has charge e then the charge on the nucleus will be z into e because e is the electron and this z is the atomic number what is z? z is the atomic number. So, charge is what? Number of proton into the charge on one proton which is nothing but equal to the charge on one electron ok. Now you see we have 2 charge this one is positive in the nucleus which is q e is this and it is negative the electron we have. So, we have electrostatic force of attraction between 2. So, according to this formula we can write k q 1 q 2 z e into e by r square which is the radius square is equals to the centripetal force of attraction. Centripetal force of attraction is mass m v n square by r n centripetal force is required for an object to move in a circular path ok and this centripetal force is given by this is centripetal force and this is always equals to m v square by r right. So, mass is m e v is v n radius is r n ok you must know the net force is equals to mass into acceleration. So, v square by r if you check the unit or dimension of it it is the unit of acceleration itself what is v square by r you see v square by r the unit is what v is the velocity. So, meter per second square r is the distance so meter. So, unit is meter per second square. So, this is the unit of acceleration right. So, this v square by r is nothing but the acceleration in circular motion m v square by r that is why we did force of attraction which is along this radius towards the center this force provides the centripetal force to this electron. So, that it can move into the circular path that is the two equation we have ok.