 The next thing is what in these two equation if you observe the net force of attraction which is nothing but this electrostatic force this is the net force net force of attraction provides the necessary centripetal force. Now suppose if you have some other electron present here right why it is true for one electron system that we are going to understand now now suppose if you have some other electron present in the inertial then this electron this electron we have some repulsion this electron this electron again we have some repulsion right this electron this nucleus some attraction this two some extraction so net force we have to calculate in all these right that is why 1 2 3 4 and we have some different different like all these electrostatic force we have okay and that is why since there are different types of forces acting in all the direction so it is very difficult to calculate the net force right that is why this model is true only for one electron system okay so all these net force we have to calculate here and that net force should be equals to the centripetal force okay that is why the calculation is very difficult and complex that is why this Bohr's model is valid only for one electron system the system which has only one electron. Now you see these two equation what are the unknowns we have mass of electron we know right n value is the number of orbit h value we know pi we know k value we know it is the Coulomb's law constant again z is the atomic number that also we know so if you see these two equations there are only two unknowns that is velocity and radius okay so now we can solve these two equations and we can find out the expression for velocity and radius okay so from this equation you see now we are trying to solve these two equation that is it you can also solve this on your own okay now you see first of all what is the velocity from this expression from equation one vn is equals to n h by 2 pi into 1 divided by Me into Rn okay now this velocity and this expression you see this square and this Rn gets cancelled right so if you find out Rn from this equation Rn is equals to Rn is equals to will go this side and this whole thing will come this side right that will be k ze square divided by Me into 1 by vn square this is what we get now this vn we can substitute here so what we get you see k ze square Me vn square if you substitute you will get okay we will substitute vn so we will get what this is 1 by vn square so what I will write here 1 divided by vn is this so that will be n h divided by 2 pi Me Rn right this is whole square of it this is vn now when you solve this you will get this Rn is equals to k ze square divided by Me into 4 pi square Me square Rn square divided by n square h square so this Rn and this square gets cancelled Me and this square gets cancelled so Rn is equals to the expression for Rn is equals to n square h square divided by 4 pi square Me k ze square k ze square further if you rearrange this we will get Rn is equals to h square divided by 4 pi square Me k e square this whole thing into n square by z okay now all these are constant we know the value of all these constant term so in CGS system if I write in CGS system this expression becomes h value is 6.626 into 10 to the power minus 27 Erg second the value of pi we know mass of electron is 9.1 10 to the power minus 28 gram electron charge on electron 1.6 10 to the power minus 19 coulomb k value is the coulomb's law constant is 1 in CGS right or in SI it is 9 into 10 to the power 9 Newton meter square per coulomb square okay all these value when you substitute here the Rn expression you get here is this the value for Rn or the expression for Rn is 0.5 to 9 n square by z this is the formula for radius in nth orbit the unit of this is extra 0.5 to 9 n square by z okay similarly Rn we can substitute here and we can find out the vn formula which is what again vn is equals to we can write nh by 2 pi into 1 by m e into Rn okay so when you substitute all the value here we will get vn is equals to 2.188 into 10 to the power 8 z by n centimeter per second this is the formula for velocity means what in nth orbit the electron that radius of this will be this and the velocity of the electron will be this in centimeter per second okay if you have to find out this in meter this you can easily convert into meter one angstrom this relation you should know one angstrom is equals to minus 10 meter which further you can convert into centimeter which is nothing but 10 to the power minus 8 centimeter okay sometimes the radius is given in nanometer so one nanometer is 10 to the power minus 9 meter all these relation you should know conversion is important in this chapter you should know all these relations okay so far we have discussed about the radius and velocity of an electron present in nth orbit okay this is again important the formula is this formula is not that much important hardly you will get some questions on to this but this relation you should know this constant this constant n square by z z by n all this relation you should know okay now now we are going to calculate since the electron is moving in nth orbit this electron must have some kinetic energy and potential energy so what is the kinetic energy of the electron kinetic energy is equals to half m e vn square half m e vn square you see what is m v square m e vn square is this right m e vn square we are substituting from equation 2 what we are doing this m e vn square we are substituting from equation 2 so what is kinetic energy then the kinetic energy is equals to half into k ze square divided by rn this is the expression for kinetic energy right you can also substitute vn from here to here and then mass you can substitute you will get the expression but we are going to establish some relation here that is why I have taken this expression now potential energy we already know this formula k q and q 2 by r so in this radius rn the potential energy of the electron with the help of the formula what we can write minus k ze square by rn right potential energy is negative right because what we assume at infinite distance the energy of an electron is 0 this is an assumption basically and if you are taking the electron from infinite to any orbit this much work like if you are if you have to place electron from this point to this point you have to do some work on to that ok this work is you know associated or you know or you know or stored this work whatever work is done this work is stored into the electron and that is why we are taking this as negative ok another thing the electron here has some negative energy total energy if you calculate here the total energy will be what the total energy will be the sum of kinetic energy and potential energy so now when you solve this the total energy is equals to you will get or before this one relation is what kinetic and potential energy in relation if you see if you see this expression here the kinetic energy k e is equals to k e is equals to minus 2 into potential energy see here this term is same so when I multiply this by minus half into p e half into p p have minus half into p this is the relation of kinetic energy and potential energy we have ok from these two expression we can draw this conclusion kinetic energy is equals to minus half of p now you see the total energy of the electron is what in this orbit the sum of kinetic energy plus the sum of potential energy so now when you add these two will get what the total energy is equals to the total energy is equals to minus half of p e and that is equals to k e minus half of p e and that is equals to k e is it minus half of p e if you solve this you will get positive sign here and you will get negative sign here ok when you substitute k e is equals to minus half of p e here will get minus so suppose p is x right p is x so kinetic energy is minus x by 2 plus x minus x by 2 plus x is x by 2 only half of p e and minus of k e now when you see this expression the total energy is negative because you see potential energy is negative and p e is equals to plus of potential energy minus half of potential energy means this term is negative kinetic energy is positive and minus of k e is negative means what the total energy is negative now what is the significance of total energy is negative that is what I said when you have to do some work from this distance to this distance electron you have to place over here then the work that is done is stored here as a potential energy and that is why this is negative so now in this orbit if the electron has total negative energy and you are providing some energy to take this electron out then only this is the positive energy and we have we already have negative energy present over here the positive negative cancel it out so at the moment these two energy cancel out completely the electron becomes free from the nucleus and it can come out from the orbit ok so that is the thing we have so this is the meaning of the total energy which is negative here right now since we have all these kinetic energy relation potential energy relation so we can also write down the expression for total energy so total energy expression when you substitute all the values of constant when you substitute all the constant value that will be total energy is equals to minus of 2.18 into 10 to the power 18 z square by n square joule per atom unit is important here right this is the expression in another unit minus 13.6 z square by n square electron volt per atom and the another value is ok so the next value we have minus 13 12 z square by n square kilo joule per mole these are the units we have kilo joule per mole so you have to keep this in mind this one is very important ok in terms of electron volt this is the three different expression expression is actually same but in different units we have different different values we are getting here ok so this is the formula we have you do not have to you know memorize the derivation derivation is not required formula you have to keep in mind you have to memorize the formula formula based question only you will see so what all things you have to memorize first of all the radius is this ok unit is angstrom velocity is this right this is the conversion we have kinetic energy is this it is not required kinetic energy is minus half of potential energy this we must remember total energy is negative total energy is equals to plus half of p and minus half of k ok one conversion we have when you have to convert joule and electron volt ok so one joule we can write 6.2419 into 10 to the power 18 electron volt this is the conversion we have one joule is equals to 6.2419 into 10 to the power 18 electron volt one electron volt if you have to convert this into joule just you multiply this by the charge on electron 10 to the power minus 19 joule ok this conversion you must remember ok so the point is here the question you will get based on this formula only ok so now first of all you see the formula is this that I told you that you have to memorize another thing what you can conclude that the radius in any orbit is directly proportional to n square by z this you must remember velocity is directly proportional to z by n this is the second time you should second thing you should remember total energy is directly proportional to z square by n square this three things also you have to keep in mind which is nothing but we will get from this expression only sometimes or most of the questions were like you have to find out the radius ratio in different orbits for different atoms ok so when you have to find out the radius ratio so when you take the radio in r1 and r2 this is the constant term right so this will get cancelled only that is why this relation is important ok most of the question you will get with respect to this ok now another thing one last thing we are going to understand here is for hydrogen atom for hydrogen atom the z value is 1 correct so r1 if I calculate radius of first orbit that will be 0.529 1 square by 1 n is 1 z is also 1 so r1 is equals to r1 is equals to 0.529 angstrom this we also call it as the radius of first bore orbit the radius of radius of first bore orbit ok since it is for hydrogen atom so instead of r1 we also write it as rh 0.529 angstrom ok this rh is 0.529 so this we can also substitute here and the expression we can write if you have to find out the ratio the expression becomes rn is equals to rh n square pi z ok now how do we use this formula suppose you have to find out the radius of Li 2 plus i n Li 2 plus i n in the orbit in the orbit for which the radius of hydrogen atom is given that is 53 nanometer suppose if this is given ok means the question the meaning of the question is what we will have an orbit for hydrogen atom in which the radius is 53 nanometer right so this orbit can be 1 2 3 4 and so on n we do not know correct so whatever the value of n we have for the same value of n what is the radius of Li 2 plus i n that is the question so now this we can do this question we can do in two different way actually the first is what the question you understood the question is we have to find out we have to find out n first and then for that particular value of n we have to find out the radius of Li 2 plus n we do not know so this we can do it in two way one formula that I have given you already the radius of the atom n is equals to rh n square by z ok I will do one change here it is he plus suppose we have he plus helium plus ok so this rh is given now for helium plus you see for he plus the electron present in first orbit the configuration is 1 s 1 electron present in first orbit itself so when you use this formula we can put directly rh is equals to 53 nanometer n is equals to 1 z for helium is 2 so when you substitute you will get r is equals to 53 into 1 square by 2 which is approximately 27 nanometer this is one way ok method one now method 2 is what suppose rh is equals to 0.529 n square by z and the radius we have to find out that is rh e plus for this n again the formula is 0.529 n square by z ok so we will equate n because we do not know n value so what is n square here rh is given 53 into 0.529 divided by z is 0.529 divided by z is 0.529 divided by z is 1 sorry 0.529 into 53 into 1 divided by 0.529 of this n square we will substitute here so this becomes what 0.529 into z value for helium is 2 and n square is this 53 divided by 0.529 so again you see when you solve this when you solve this the answer will be of approximately 27 nanometer so any way you can solve right any way you can solve you will get the same answer the question is what the orbit in which the hydrogen radius radius for hydrogen atom is 53 nanometer for the same value of n for the same orbit what is the radius for h e plus i n so like this we can solve either you can use this formula directly or from this find out n substitute there you will get the answer ok now one thing is important like energy in nth orbit is minus 13.6 n square by z right suppose I am assuming hydrogen atom suppose I am assuming hydrogen atom so for hydrogen atom you see the energy formula is 13.6 n square by z z square sorry energy is minus 13.6 n square by z square so energy in first orbit what is the answer e 1 is equals to minus 13.6 electron volt this is electron volt only similarly when you calculate for energy in the second orbit n value will be n value will be 2 right so that will be minus 13.6 into 2 e square that will be minus 54.4 electron volt oh sorry that is what I was thinking this is not n square by z square this is z square by n square I am sorry this is z square by n square energy formula is this z square by n square ok so when you substitute n is equals to 2 you will get this by 4 it means it is it is minus 3.4 electron volt similarly when you calculate for this e 3 minus 13.6 by 9 so that will be minus 1.5 electron volt. So now you see the energy in first orbit e 1 is minimum here you see it is increasing and it is increasing right if you see all this value the order of energy is e 1 is minimum then we have e 2 then we have e 3 and so on it goes e 4 e 5 means what when we go away from the nucleus the energy increases right and we assume what at infinite distance the total energy of an electron is 0 at this point it is the energy of an electron is maximum and it is free from the attraction pull of the nucleus ok. So this is it for Bohr atomic model we have discussed all the formula you must have you know we will see there are many questions based on energy radius velocity and all those in the books you can solve those questions thank you.