WEBVTT 00:13.929 --> 00:21.240 hello good morning so today is the second day of this course so in the last class 00:21.240 --> 00:29.250 if you remember we talked about the symmetry aspects of different objects and different 00:29.250 --> 00:36.870 molecules i showed you quite a number of structures of different objects as well as certain molecules 00:36.870 --> 00:45.620 and we discussed about the symmetry aspects of those and we we say that ok some molecules 00:45.620 --> 00:51.430 are most symmetric than others and ultimately we also showed that there is a something called 00:51.430 --> 00:57.579 symmetry element and symmetry operation which is like symmetry operation is the we know 00:57.579 --> 01:05.640 a movement of a body by which you you know end up having an indistinguishable structures 01:05.640 --> 01:14.350 and today what we are going to do we want to find out about the symmetry elements 01:14.350 --> 01:18.640 and symmetry operations in bit more detail ok 01:18.640 --> 01:31.290 so what are the symmetry elements and symmetry operations that a molecule can have ok so 01:31.290 --> 01:42.060 one can have five different symmetry elements and we can generate several symmetry operations 01:42.060 --> 01:48.630 out of those elements ok will look at that in create a detail so lets look at one by 01:48.630 --> 01:56.409 one so as you can see on the screen that you can have an element called identity 01:56.409 --> 02:05.159 another element called proper axis of rotation and you can have mirror planes you can 02:05.159 --> 02:12.200 have center of symmetry and you can have improper axis of rotation so now lets look at one by 02:12.200 --> 02:21.150 one what is what first lets look at identity you know the element of identity so what is 02:21.150 --> 02:27.230 it so before going going to the details of this identity operation and all these things 02:27.230 --> 02:38.409 let us also see what this identity of operation is denoted as identity operation this is denoted 02:38.409 --> 02:44.419 as e ok 02:44.419 --> 02:51.639 now what is this identity operation before going into the molecular structure i will 02:51.639 --> 03:04.419 give you very simple you know representation of this identity operation a suppose the 03:04.419 --> 03:14.260 person is you know looking at a particular direction then he can take several turns so 03:14.260 --> 03:17.909 one can take a complete right turn that is by ninety degree so if i take a right turn 03:17.909 --> 03:23.829 i will be looking at this direction and then if i take another right turn then i will look 03:23.829 --> 03:29.549 at the back that is towards the board and then two more right turns i will come here 03:29.549 --> 03:42.359 so there is a very nice story about you know army so in army what we have is 03:42.359 --> 03:50.769 a commander will tell you to take a particular position they call it take a phase so what 03:50.769 --> 03:56.839 commander will take right face left face so you move by you know rotate by in ninety degree 03:56.839 --> 04:02.689 either on the right side or left side so there is another turn that is by hundred and eighty 04:02.689 --> 04:09.129 degree you actually taken an above turn this is called an above turn now the commander 04:09.129 --> 04:16.799 says take an above turn and then he takes one more above turn now some time in the drill 04:16.799 --> 04:23.370 the veterans the aged person who has retired from army they come and take part in the 04:23.370 --> 04:29.250 drill so one of the veteran he was taken part in the drill and then when he heard the 04:29.250 --> 04:38.720 above turn command he starts turning around by one eighty degree while taking this turn 04:38.720 --> 04:44.800 he realizes that he is old enough and is very difficult for him to take turn a proper way 04:44.800 --> 04:47.220 he twisting is like and all these things 04:47.220 --> 04:55.150 and he knew that the in a commander will ask him to turn around again so he as to took 04:55.150 --> 05:01.850 take two above turns so he realizes that while ultimately i will be looking at the 05:01.850 --> 05:10.000 commander at the end after taking two above turns so if i do nothing then also i am having 05:10.000 --> 05:21.729 the same position so this idea of do nothing is actually an identity operation so if you 05:21.729 --> 05:33.349 look at this picture here the person is looking at us and then he takes keeps on taking 05:33.349 --> 05:38.370 turns from here to here to here and then here to here and then here to here and then 05:38.370 --> 05:46.090 here so ultimately there is no change in the position of the person so now if i do not 05:46.090 --> 05:57.319 go through all these intermediate states and if i come from this state to this state directly 05:57.319 --> 06:03.139 the symmetry operation that we have performed is an identity operation ok so essentially 06:03.139 --> 06:08.759 you can figure out identity operation means you do nothing you keep an object as such 06:08.759 --> 06:14.719 in his position you get obviously the identical structure because you are not done anything 06:14.719 --> 06:21.629 so this identity operation is also called do nothing operation ok and this is the easiest 06:21.629 --> 06:29.969 thing and no matter what any objects in this universe will have at least one symmetry element 06:29.969 --> 06:35.580 in it and that is this identity element ok so anyone can do an identity operation on 06:35.580 --> 06:43.180 any object and get an identical structure here is identical not only indistinguishable 06:43.180 --> 06:48.189 ok so that is about identical operation e 06:48.189 --> 06:58.460 next we talk about rotational symmetry elements ok this is also called proper axis 06:58.460 --> 07:08.529 of rotation why this called proper we will talk about this you know in during this 07:08.529 --> 07:16.740 course but less for the being just call it as an proper axis of rotation so in the 07:16.740 --> 07:23.189 last class i showed you an example of rotating at equilateral triangle by hundred and twenty 07:23.189 --> 07:35.330 degree and getting back in distinguishable structures so that particular you know axis 07:35.330 --> 07:43.949 is called axis of proper rotation ok and this axis of proper rotation this symmetry 07:43.949 --> 07:58.560 element is designated by the this c n c subscript n now in that particular example that i give 07:58.560 --> 08:04.580 you in the last class we had an hundred and twenty degree rotation about that particular 08:04.580 --> 08:18.639 axis which is perpendicular to that triangle so what is this n ok so you can see that for 08:18.639 --> 08:26.740 c n n is equals to two we have an hundred and eighty degree rotation if i have an hundred 08:26.740 --> 08:33.460 and twenty degree rotation and we can get an in distinguishable object then the you 08:33.460 --> 08:40.570 know order of this rotation this n here that is written in this c n is called order 08:40.570 --> 08:47.310 of rotation ok so for an hundred and twenty degree rotation you have an order because 08:47.310 --> 08:54.920 to three similarly for an ninety degree rotation you can have an order four so you can easily 08:54.920 --> 09:05.949 figure out that if you have say an object like a square a perfect square 09:05.949 --> 09:13.029 you can imagine an axis through this point and this axis is perpendicular this plane 09:13.029 --> 09:19.029 of the board then for every ninety degree rotation you get an indistinguishable structure 09:19.029 --> 09:25.680 because this if i mark one two three four now we can easily do because you have already 09:25.680 --> 09:31.839 seen it for the triangular case you have another square because square is not going to be changes 09:31.839 --> 09:34.300 to a triangle right square will remain a square 09:34.300 --> 09:41.279 so when you give a ninety degree rotation so one will come here two will go here three 09:41.279 --> 09:49.550 will go here and four will go here so ultimately what you have is this one two three four until 09:49.550 --> 09:53.850 and unless you have this numbers you have an indistinguishable structure that is a square 09:53.850 --> 10:07.040 and this is done by a rotation by ninety degree ok so this axis this c n here is known as 10:07.040 --> 10:18.050 c four and four comes from from this relation where your n is equals to is equal to three 10:18.050 --> 10:30.870 hundred and sixty degree by the angle of rotation angle of rotation right so three hundred here 10:30.870 --> 10:40.339 it is this rotation is bout ninety degree so the angle will be three sixty degree by 10:40.339 --> 10:49.959 ninety degree is equal to four so i have an axis c four so you know in that way if i have 10:49.959 --> 10:57.519 a rotation of sixty degree thirty degree i can find out what is the order of rotation 10:57.519 --> 11:05.519 and the name of the particular rotational symmetry that is c ten c eight c six whatever 11:05.519 --> 11:10.620 ok for a sixty degree rotation for example it will be c six because three sixty degree 11:10.620 --> 11:15.410 by sixty degree right so it will be six c six 11:15.410 --> 11:25.040 now you can see that you are i can vary the you know value of n i can go from say like 11:25.040 --> 11:32.690 c three four five six so i have not written there c one why not because c one will mean 11:32.690 --> 11:50.790 what c one will mean from this particular relation it will mean that n for c one n equals 11:50.790 --> 11:58.050 to one so nj equals to one means i must have a situation why this angle of rotation this 11:58.050 --> 12:04.459 equals to three hundred and sixty degrees this is exactly the case what we described 12:04.459 --> 12:09.459 just sometimes back when you are discussing about the identity operation right so that's 12:09.459 --> 12:16.089 why c one is not mentioned anywhere because c one and e are the same ok so we have seen 12:16.089 --> 12:22.150 that ok n can be like two three four five six seven eight depending on the structure 12:22.150 --> 12:29.370 of the object or structure of the molecule in particular so like for benzene i have so 12:29.370 --> 12:40.870 c six right so benzene structure is like this so this position of the carbon atoms and associated 12:40.870 --> 12:52.940 hydrazine's and if assume equal distribution of the 12:52.940 --> 13:00.880 then i can have an equivalent or indistinguishable structure for every six degree rotation about 13:00.880 --> 13:07.470 the axis which passes through this one right so every sixty degree i can have the indistinguishable 13:07.470 --> 13:16.800 structure and we can have for this one and axis c six and this particular is axis is 13:16.800 --> 13:19.250 c six right 13:19.250 --> 13:30.500 now in that way i can go increasing increasing so can i have something which is c infinity 13:30.500 --> 13:44.829 that's a question right so from this expression it looks like yes i can have what is the 13:44.829 --> 13:51.329 what what is the solution that means here i have to have n equals to infinity right 13:51.329 --> 14:00.500 so if i equate this one to be infinity what do i have here i have extremely large number 14:00.500 --> 14:11.480 right almost like an infinity so in that case what i have i have a situation like an object 14:11.480 --> 14:18.899 or a molecule which as an axis about which i can give any turn by any amount of angle 14:18.899 --> 14:26.519 and i can get an indistinguishable structure you need an example right so here is one example 14:26.519 --> 14:40.670 for you carbon dioxide now look at the axis if i have an axis passing through all these 14:40.670 --> 14:46.750 atoms right this is the linear molecule carbon dioxide is a linear molecule and if have an 14:46.750 --> 14:55.540 axis passing through this linear molecule you know through all the atoms then you see 14:55.540 --> 15:01.300 about this axis all around this is highly symmetric right so doesn't matter whatever 15:01.300 --> 15:09.029 be the you know angle by which i rotate it gives an indistinguishable structure so in 15:09.029 --> 15:18.690 a sense i can give an infinite you know amount of rotation before it comes back to 15:18.690 --> 15:26.410 its original you know configuration got it so because i can give this infinite degrees 15:26.410 --> 15:36.800 of rotation about this axis and get indistinguishable structure this axis is known as c infinity 15:36.800 --> 15:39.240 ok 15:39.240 --> 15:47.500 now we say that this operation is called rotation and you know really you should 15:47.500 --> 15:53.300 say its a proper rotation why it is proper because if i really can have axis that will 15:53.300 --> 15:59.899 change this you know molecular configuration from one to another indistinguishable one 15:59.899 --> 16:05.519 ok so there can be really an axis there so there mean that means there will be something 16:05.519 --> 16:12.050 which is not like this that is not a proper rather improper ok we will come to that it 16:12.050 --> 16:20.339 is there and we will come to that now lets see some more example of this rotation 16:20.339 --> 16:27.529 so as i said that we can have c two c three c four and so on so here is an example which 16:27.529 --> 16:34.459 shows you the two fold rotation ok and the axis about which this two fold rotation is 16:34.459 --> 16:42.100 you know taken place is called two fold axis of rotation so here we have a molecule h two 16:42.100 --> 16:58.140 o ok so to you know of i have an axis which bisects the angle h o h then we can rotate 16:58.140 --> 17:05.780 the molecule about that axis right it is given here ok so this is that axis about which you 17:05.780 --> 17:14.760 can turn them so you see we get an indistinguishable structure by a rotation of hundred and twenty 17:14.760 --> 17:21.500 degree and another rotation by the hundred and twenty degree will end of having the same 17:21.500 --> 17:28.800 structure back ok so this is an example of c two ok 17:28.800 --> 17:34.300 now lets come to three fold axis of rotation which we have already looked at in terms of 17:34.300 --> 17:41.820 ammonia this is another example which is boron trifluoride so here you can see that 17:41.820 --> 17:49.150 one fluorine is mutt by a different colour then other fluorine so that you can actually 17:49.150 --> 17:57.770 distinguish them ok so now by hundred and twenty degree rotation you get an indistinguishable 17:57.770 --> 18:02.870 structure but you know you can actually distinguish till because you have colored one of them 18:02.870 --> 18:09.900 separately but in a you know its chemistry is not going to change because b f three is 18:09.900 --> 18:18.670 still b f three there ok so you can give more rotation and you can change the positions 18:18.670 --> 18:25.020 of the fluorine atoms but they remain indistinguishable though because of the colour you can distinguish 18:25.020 --> 18:31.850 them here at least on the pen and paper now we have been talking about only one particular 18:31.850 --> 18:38.830 axis will about which i can have a proper axis of rotation now its not necessary 18:38.830 --> 18:44.810 that in a particular molecule we have only one type of axis of rotation ok so here is 18:44.810 --> 18:54.530 one example while we talk about trigonal planar molecule ok so say this is boron trifluoride 18:54.530 --> 19:03.360 ok so all the you know atoms are in the same plane so its a trigonal planar now in the 19:03.360 --> 19:09.550 in the last page we have seen that there is an c three axis right about which you can 19:09.550 --> 19:14.690 have one twenty degree rotation and you can get the identical structure but is 19:14.690 --> 19:24.330 that all no here you see that i can imagine and axis which right here which passes through 19:24.330 --> 19:33.140 one fluorine and one boron that you know particular axis you can have an hundred 19:33.140 --> 19:41.710 and twenty degree rotation about that particular axis so you can get an indistinguishable structure 19:41.710 --> 19:49.520 so you have three boron fluoride bond right so this0 is one and this is two and this is 19:49.520 --> 19:57.190 three so you can have the same type of axis same type of c two axis through each of this 19:57.190 --> 20:05.650 boron fluoride bonds so you can essentially have three c two axis for this molecule and 20:05.650 --> 20:10.300 you can have one c three axis ok 20:10.300 --> 20:18.510 now will also see that this c three is an element now when you operate this c three 20:18.510 --> 20:24.290 consecutively you can get indistinguishable structures so you can have c three followed 20:24.290 --> 20:30.660 by another c three and then another three and you can keep going unless you get an identical 20:30.660 --> 20:40.750 structure so so if you you know do two successive c threes then you have something 20:40.750 --> 20:47.490 called c three square we will talk about this things much later and similarly you add one 20:47.490 --> 20:57.450 more c three into this and you can have c three three which again is nothing but the 20:57.450 --> 21:05.440 identity operation right we have already discus that so in this particular case what we 21:05.440 --> 21:15.030 learnt is that a molecule may have more then you know one type of proper axis of rotation 21:15.030 --> 21:20.920 and here particularly we see that if the molecule as c three as well as c two and its also you 21:20.920 --> 21:27.080 know not necessary that this c three and c two that is two different you know axis 21:27.080 --> 21:34.020 of symmetry they will be coinciding ok so they can have they can be that you know 21:34.020 --> 21:41.740 different plane and different directions ok or you can have the you know two different 21:41.740 --> 21:49.050 axis in the same you know coinciding together ok 21:49.050 --> 21:53.620 so before going to the next one let me also clarify the last point that i made that is 21:53.620 --> 22:00.810 in the case of b f three we saw that c three and c two they are not coinciding but 22:00.810 --> 22:09.910 inside an molecules you can have you know more than one more than one proper axis 22:09.910 --> 22:17.370 of symmetry coinciding together ok so for example you can have lets take this particular 22:17.370 --> 22:23.590 molecule benzine here ok so you have seen that there is an axis about which we can give 22:23.590 --> 22:33.480 a sixty degree rotation and you can have a c six axis now for every c six turn this 22:33.480 --> 22:39.340 hydrogen goes here this hydrogen goes here so you gave a give a sixty degree movement 22:39.340 --> 22:48.820 here now if if you want you can have an axis here and you can rotate in such a way this 22:48.820 --> 22:54.570 h comes here that is i can have an hundred and eighty degree rotation right so this hundred 22:54.570 --> 22:59.510 and eighty degree rotation about this axis without going through this so directly you 22:59.510 --> 23:06.420 rotate and bring it here do not stop here so this is a c two axis right so c two and 23:06.420 --> 23:14.920 c six they are about the same axis ok so which is different from b three but again here this 23:14.920 --> 23:23.620 is not all we can have many other rotational axis for example what we can see here that 23:23.620 --> 23:34.770 is about this you have c six axis you have c two axis ok and you can come from here to 23:34.770 --> 23:44.070 here directly and then from here to here and here to here by hundred and twenty degree 23:44.070 --> 23:51.630 rotation so there by you have c three axis so all this c six c two c three they 23:51.630 --> 23:58.600 you know coincide on each other ok they are about the same physical axis if you can imagine 23:58.600 --> 23:59.740 one here 23:59.740 --> 24:11.230 but there are other axis like if you connect this hydrogen to this hydrogen you find a 24:11.230 --> 24:18.390 symmetry axis here about which if you give a rotation of hundred and eighty degrees we 24:18.390 --> 24:23.840 will find an i will you know identical structure because this will come here and this will 24:23.840 --> 24:32.980 go here so it is just a flipping so similarly this will do the same job this will also do 24:32.980 --> 24:43.150 the same job ok and if i can imagine an axis like this this will also do the same job ok 24:43.150 --> 24:51.100 so i can have six different c two axis which are lying on the plane of the molecule not 24:51.100 --> 24:57.970 coinciding with this six c six or c three or c two and this c two is different than 24:57.970 --> 25:10.930 the c two that i just showed you ok now lets move on to the next symmetry element which 25:10.930 --> 25:19.360 is known as a plane of symmetry ok so what is this plane of symmetry operation ok 25:19.360 --> 25:26.800 so you imagine any object or any space if you take this x y z coordinate and you 25:26.800 --> 25:34.180 you know reflect it about a plane and if you get an identical structure that is having 25:34.180 --> 25:44.890 coordinate minus x minus y minus z ok then you get equivalent and you get rather 25:44.890 --> 25:55.790 indistinguishable structure by this reflection so you are doing a reflection about a plane 25:55.790 --> 26:02.200 and you are getting indistinguishable structure and this plane is a is asymmetric plane ok 26:02.200 --> 26:08.640 and this symmetry operation is called plane of symmetry ok or also sometime called 26:08.640 --> 26:11.320 reflection operation ok 26:11.320 --> 26:20.690 now this reflection operation is or the mirror planes they are denoted by a symbol 26:20.690 --> 26:27.870 sigma ok so all the plane of symmetry are denoted by the symbol sigma now there can 26:27.870 --> 26:36.000 be a different type of sigmas so you can see that we have something special called sigma 26:36.000 --> 26:49.750 h sigma subscript h so sigma h is a mirror plane which is perpendicular to the principle 26:49.750 --> 26:59.990 axis of rotation ok now you also have something called sigma v sigma v is also mirror plane 26:59.990 --> 27:07.540 but this particular mirror plane as a as a particular characteristics which says 27:07.540 --> 27:14.710 that this particular mirror plane will contain principle axis of rotation there is another 27:14.710 --> 27:23.330 type of mirror plane which is known as sigma d so sigma d is mirror plane that bisects 27:23.330 --> 27:31.730 the dihedral angle made by the principle axis of rotation and two adjacent c two axis 27:31.730 --> 27:37.310 here one notice this two is actually a subscript ok so this mirror plane bisects 27:37.310 --> 27:42.580 a dihedral angle made by the principle axis of a rotation and two adjacent c two axis 27:42.580 --> 27:47.030 which are perpendicular to the principle rotation axis 27:47.030 --> 27:54.580 so you can see that whatever be the name sigma v sigma d or sigma h their functions are same 27:54.580 --> 28:06.090 ok so this subscripts v d and h just are used to sefer separate different you know 28:06.090 --> 28:13.080 planes of symmetries but their jobs are same ok so in the following class we will 28:13.080 --> 28:20.530 talk about more about this mirror planes and we will sight some examples and 28:20.530 --> 28:24.740 go to the other kind of symmetry elements and symmetry operations ok so see you again 28:24.740 --> 28:25.740 in the next class 28:25.740 --> 28:26.310 thank you very much