Hello students we’re studying the chapter structure of atoms so in this model i will R continue what we were discussing there is the radial probability curves so already we discussed how to calculate the total probability right so for which we took a shell at distance R which is thickness dr and we can calculate the volume of it which is 4 PIRsquare into dr and probability of finding the electron in that small thickness dr it can be defined as DP which is side squared into DV whereas side square is the probability density function and which can be written as 4 pi r square side square into dr so the total probability we learned that I can integrate that from 0 to PDP and it comes to be r1 r2 size square 4pirsquare y a squared dr right so this is what we learned and hear that PR that’s what ever that has been defined in that integral part is what we called as the radial probability distribution function so therefore to calculate the total probability it is integral r1 to r2 PR into dr area where PR is the probability distribution function right this is what we learned earlier continuing this now we will try to draw the total probability versus the R so let’s see that first so if it all I draw the total probability vs. R here that p of R is the probability distribution function VS the R now at the nucleus r is equal to 0 so PR will be 0 so the graph will always start from the origin as R square increases side squared is actually decreasing so there are two functions one is the R squared part and the other one is the side squared part then what would happen the graph looks something like this for one its orbital what is this suggesting that initially size square is decreasing but the r-squared is increasing but as R is increasing size square is decreasing exponentially so initially it will increase because of the R squared and then it decreases because of the side squared so r square is contributing first in the first half of the graph and side square is contributing in the second half of the graph and eventually tends to become 0 now here you could see it is reaching a maximum value and maximum values what we call it as the radius of maximum probability and that is found to be 0.5- 9 Armstrong’s which is exactly the same work bored how calculate and let me a same it as a not now we know that according to bohr’s r is equal to 0.529 n square by z so if Z is constant for every value of n you should be getting a higher value of the radius right so which i can write it as a naught into n square by Z so from the graph it is everything that the probability of finding the electron said nucleus and infinite distance from the nucleus is always zero not let me draw a similar graph for two s so far two s if at all you see I have applauding probability distribution function versus R now this is the graph you will get now here what I would see is that we are getting a radial node here where the probability of finding an electron is 0 now this is the maximum distance are the peak where we have the highest probability and this distance amazingly matches to 4 a knot which is again suggesting from the bohr’s theory that radius will be a knot into n square so it is a second orbit so n square users 4 a knot so the radius of maximum probability of one s will always be less then 2 s so that is what we will get that means the electron into 2S is always found at the larger distance from the nucleus compared to the 1s of orbital know if I like keep drawing this for different orbital’s what do I get so total probability were probably this distribution curve vs r if it is 2s this is what we found and it has one radial Node with maximum radius of maximum probably at a distance similarly if I draw it for 2p i will get no nodes here this is how we will get with certain maximum distance similarly for 3p you will see it is quite similar to that of 2s similarly if at all I keep drawing it for again with the radial node here and if I draw for three D and then you would see this quite matching to that of 1s and 2p similarly if at all I draw it for 4 d you will see the graph varies quite similar to 2s and 3p with one radial node this gives us a pattern so here you would see there is one radial Node forming so this gives us a pattern that the total number of radial nodes will be equal to n minus L minus 1 so therefore to calculate the number of radial Nodes for any particular orbital . we can use this formula that is n minus L minus 1 so from there we can get what is the total number of radial nodes as we go for the next module we will see about the planar nodes or the angular nodes thank you

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