Atomic Orbitals I s, p, d and f orbitals I Shapes of Orbitals I Quantum Chemistry I Hydrogen Atom

hello everyone welcome to chemison complete chemistry so in our previous video we had seen the basic structure of an atom and its subatomic particles that is the electron proton and neutron we also saw that charges and we also learned what do we mean by atomic number and atomic mass number so have you ever thought of what would be a home of an electron or in an atom around the nucleus what would be the probability of finding an electron or where would you find an electron so the correct answer is atomic orbitals what are atomic orbitals atomic orbitals are the region around the nucleus in the three-dimensional space where you would find or you would have the maximum probability of finding an electron why i'm using the word probability because we cannot see the atom and we are not exactly how sure that the electron will be present around the nucleus so we make use of quantum mechanics and the quantum chemistry concepts to understand uh the atomic orbital and the position or probability of an electron into that orbital so let us now understand the different types of atomic orbitals that is the s orbital you can see it is a very fundamental orbital which is spherical in shape and the entire region of s orbital will have one phase so the next set of orbitals is the p orbitals we have three p orbitals that is p x p y and p z the basic shape of the p orbital is the dumbbell shape as you can see here there are three of them p x which is oriented along x direction p y which is oriented along y direction and p z which is oriented along z direction so a very important point to be noted is that the both the two lobes of p orbitals are of different phase that is one is let's say positive phase then the other one will be negative or the other way round if one is negative another will be positive so both the lobes of p orbital are of opposite phase so the next set of orbiters is the d orbitals so there are total of five d orbitals that is d y z d x y d x z d z square and d x square minus y square so the first three d orbitals are the d orbitals in which the lobes of the d orbitals are oriented in between the axis whereas the last two orbitals that you can see that is d x square minus y square and the z square are the two d orbitals which are oriented along the axis so let us see the shapes of the d orbitals so here you can see this is the divisor orbital which is oriented in between y and the or z axis the d x y which is oriented in between x and y axis d x z which is oriented in between the x x axis and the z axis whereas this is the dz square orbital which is oriented along the z axis and this is the x square minus y square which is oriented along x y direction so in this way the orbitals d x y d y z and d x z are the three orbitals which are oriented in between the axis whereas d z square and d x square minus y square are the two orbitals which are oriented along the axis the next set of orbitals is the f orbital and there are a total of seven f orbitals that is f y d x square minus y square f z x square minus y square f y z square f z cube f x z square f x y z and f x x square minus three y square you can see all the seven f orbitals have different shapes so how do we get the names of these uh whether it is a d orbital we have dx square minus y square dz square dx y yz or xz or all these f orbitals how do you get the names of these orbitals so we get the names of these orbitals from orbital symmetry and the group theory the concept of group theory orbital theory and a little bit of quantum mechanics involved in it and then we get the names of these orbitals so now the question is why these orbitals are let's say an s orbital is spherical or a p orbital is dumbbell shape or a d orbital is double dumbbell or an f orbital has different shapes why it is this spherical or dumbbell shape or white cannot be of any other shape like cone shape or a cubicle or any other shape so the correct answer comes from the quantum mechanics so this equation which you can see is nothing but a schrodinger wave equation for a very simple hydrogen atom so hydrogen atom is a two body problem uh as it comprises over the nucleus and the single electron which revolves around the nucleus so this is a basic schrodinger wave equation for a hydrogen atom you need not be afraid or scat scared by looking at this big equation we will be dealing this in much detail in the quantum chemistry so this is the schrodinger wave equation so what we do is we first use the mathematical concepts and we try to solve this uh hydrogen atom uh the schrodinger wave equation of this hydrogen atom and after solving we get something called as a plot of radial distribution function uh and we get these plots or these curves for all the different orbitals like 1s 2p 2s 3d 3p and 3s so what would do we interpret from this graphs or curves so here you can see the same plots have given again that is for 1s this is the radial distribution plot and from this we interpret that an s orbital will be spherical in shape similarly a 2s orbital will look something like this from this plot and then there is this 3s so 1 is 2s3s these are the radial distribution plots that we get by by solving the schrodinger wave equation for hydrogen atom and this is how we get the shapes of the orbitals and let's say if we apply this uh hydrogen wave equation for all the different types of orbitals and accordingly you can see all these contour plots what do you mean by contour plot control plot is a three dimensional plot generally on paper we plot a two dimensional plot that is x axis and y axis or y or z or x or z but when we take all the three dimensions together that is x y and z axis and when we plot anything on a three dimensional axis then that plot is called as a contour plot and here you can see based on the different uh quantum numbers we have plotted all these different shapes of orbitals you can get by solving this hydrogen schrodinger wave equation [Music] so in this way we come to know that how beautifully we can make use of mathematics in quantum mechanics and we come to know the different shapes of the orbitals and thank you so much

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Length: 7min 55sec (475 seconds)

Published: Tue Jul 28 2020