Why do atoms form molecules? The quantum physics of chemical bonds explained

think about this the visible universe consists mostly of less than 100 naturally occurring elements yet there's an immense diversity and complexity reflected in not only the myriad of substances that can be found in the universe but also substances that can be found within your own body how is it that we can have a near boundless number of chemical substances with only about 100 relatively simple building blocks called atoms to work with this is because the naturally occurring atoms are rarely found alone they're mostly found in combinations with other atoms through the process of chemical bonding the combinations of chemicals and materials that can be built with these various combinations is so vast that it can give rise not only to the variety of phenomena that we can observe in the universe but also the complexity required to create life fuel for energy that we need consciousness that we enjoy and every other macro scale process that affects us why is the universe not full of just 100 different types of atoms floating around in a sea of dull monotony lucky as these atoms bond together to form rich chemicals that have properties fundamentally different than the atoms comprising them why does this happen the answer to this important question lies in understanding the role that energy plays in the formation of molecules and its roots and where else but quantum mechanics that explanation is coming up right now some of the most important chemicals to us like the air we breathe consists not of individual atoms but molecules oxygen for example is not found in the air as individual oxygen atoms but it's o2 are two oxygen atoms bound together nitrogen is also found as n2 two nitrogen ions bound together water without which we could not survive is h2o two atoms of hydrogen combined with one oxygen atom why are atoms prevalent mostly as molecules the key to understanding why atoms link together is energy all natural systems tend to adopt a state of lowest energy the marble at the top of a hill has high potential energy due to gravity if given the opportunity it will roll naturally to the bottom of the hill where it will have a lower potential energy this is the same reason a river flows in one direction from high ground to low ground so how does energy play a role in the formation of molecules let's look at the simplest form hydrogen which consists of only one proton and one electron it is found on earth usually not as individual atoms of hydrogen but in pairs h2 or hydrogen gas by understanding the role of quantum mechanics in the formation of the hydrogen gas molecule we can begin to understand why other atoms also form molecules in order to adopt a lower energy state a hydrogen atom consists of just one electron and one proton as we saw in an earlier video the electron forms a cloud around the nucleus the shape of this cloud is determined by the schrodinger equation which contains a wave function the wave function of the hydrogen atom simply put represents the probabilities of the possible results if we were to measure its properties the hydrogen atom by itself will be in its lowest energy state called the ground state but when a second hydrogen atom is introduced into the system some interesting things begin to happen not much happens if the atoms are very far apart both atoms are in their respective ground state but as they come closer to each other a few things happen at the same time first the electrons since they're both negatively charged repel each other but the electron of hydrogen atom 1 also starts to get affected by the positive charge of the proton in hydrogen atom 2. similarly the electron of atom 2 starts to get attracted to the proton of atom1 so the electrons of each of the two atoms tend to get pulled slightly to the other one's proton and if they get close enough the cloud begins to spread to the space between the two atoms now if the atoms get too close then the protons begin to repel each other and push each other apart so there's a sweet spot distance that the two protons prefer to be in such that the electrons are happier being shared and the protons are not too repelled to each other you might ask why do these two atoms get attracted in the first place because shouldn't the electron clouds be repelling each other and not allow them to get anywhere near each other this is an excellent question what you have to understand is the repulsion of the electrons is not the only interaction taking place here there are a multitude of interactions happening and what happens to the entire system is determined by the total energy of the system to calculate the lowest energy of this two atom system or molecule of hydrogen we have to take into account the following the kinetic energy of each atom the potential energy between the two protons the potential energy between two electrons and the potential energy between each electron and each proton the sum of the possible outcomes of kinetic and potential energy of this entire system in quantum mechanics is referred to as the hamiltonian represented by capital h the hamiltonian of our two atom hydrogen system looks something like this when you do all the calculations to be clear the hamiltonian is an operator corresponding to the energy of the system and once you plug it into the time independent schrodinger equation written here you can solve to get possible values for energy now as you might imagine this is not a trivial equation to solve but it can be represented for simplicity by the following graph and as we move from right to left you can see what happens to the energy when the two atoms go from being far apart to being closer together the dip in the graph represents the lowest energy state of the two atom system if the distance between the protons gets any smaller than that the energy goes up significantly and if the distance gets larger it also goes up although not as steeply so the two atoms find a natural sweet spot such that they're both happier being at a lower energy state together than when they were further apart by themselves it turns out that the energy of this two atom system is less than the energy of two separate one atom systems this is the reason if a bunch of hydrogen atoms are near each other they will naturally combine to form a molecule of h2 rather than float around by themselves this sharing of electrons by two atoms of hydrogen is called a covalent bond and similarly covalent bonds formed by other atoms work analogously now if you took high school chemistry you will know that not all atoms form bonds with atoms of their own kind nor with just any other atom one of the most remarkable things about chemical bonding of atoms is that all the substances that you see all around you comprised of molecules is due to the remarkable stability of atoms that have or share seemingly magical numbers of electrons 2 10 18 36 54 or 86 electrons in so-called shells around the nucleus of atoms and all this is due to the fact that certain combinations of atoms that contain these numbers of electrons tend to have the lowest potential energy if you look at the periodic table you will see that these numbers correspond to the number of electrons contained in the six naturally occurring noble gases these are inert elements meaning they do not react to form bonds with other atoms under standard conditions that's because they already contain the number of electrons needed to form highly stable shells around the nucleus other elements strive to contain a full set of electrons in their outer shell called the valence shell any element with an unfilled outer shell has a much higher chemical potential energy than these noble gases so for example if you look at the halogen elements right next to the noble gases fluorine chlorine etc they are only one electron away from being highly stable so they are desperate to attract one electron from any atom that wants to get rid of one of their electrons also if you look at the alkali metals on the far left side of the table these are elements that have one too many electrons so they are desperate to get rid of one electron thus when these alkali metals get together with the halogen compounds guess what happens they form very strong bonds and the resulting compounds have so much lower energy that the excess energy is released in the form of heat in an exothermic reaction in fact one very important compound results from this type of reaction it's when sodium bonds with chlorine to form sodium chloride or ordinary table salt so atoms can either shear electrons with one or more other atoms resulting in covalent bonds or they can give away or take on electrons from other atoms resulting in ionic bonds there are other types of bonds as well but these are the only two we're discussing today you might ask why are these numbers i talked about earlier such magical numbers chemists will say well these are the numbers that allow atoms to fill their electron shells or in other words all atoms strive to form what's called a full valance set of electrons and this attractive force of atoms to share electrons in order to form a full valence shell is balanced by the repulsive forces of their electron clouds and protons but what is the underlying reason why should 10 electrons have lower energy than 6 electrons for example or why is the number 18 more special than some arbitrary number like 16 the answer lies as many phenomena do again in quantum mechanics it all has to do with potential energy of multi-atom systems there are two concepts in quantum mechanics that are important in determining the energy of these systems the first is the schrodinger equation as i pointed out in our example of energy related to the hydrogen molecule the second is the pauli exclusion principle this principle basically states that no two fermions an electron is a fermion can occupy the same quantum state for our purposes this means that in a molecule two electrons that are in the same orbital must have opposite spins these two principles taken together can reproduce those exact sequence of numbers that i called magical and solving the equations will show that these are the precise numbers that result in the lowest potential energy of chemical systems so for example if we wanted to look at water h2o consisting of two hydrogen atoms and one oxygen atom a wave function can be written for this structure energy can be calculated by solving the equations and bond lengths can be determined that result in the lowest potential energy but precise calculations can get very mathematically complex so approximations called morse potential represented by the equation below is usually used plugging in the numbers a graphical representation of morse potential for the o h bond in water can be shown as the following here u naught is the bond energy and r naught is a bond length that can be read from tables like the one below so as usual it all comes down to quantum mechanics but what i want to impart to you is that the quantum mechanics behind these phenomena only allow you to see how nature behaves it does not explain why nature is the way that it is it only shows you how nature works the question of why things are the way they are is what i think the most interesting question and there may be some underlying reason for example that lies in string theory or some other theory of everything and that's what i hope the next generation of scientists will keep pursuing now if you are such a scientist whether professional or hobbyist who wants to pursue profound ideas like this in greater depth consider signing up for brilliant today's sponsor it's a problem-solving website and app that allows you to go deeper and further into the world of science including physics than any video or article ever can brilliant allows you to master science subjects by what i think is the best way to learn and that is solving problems and working on challenges one of the best classes in quantum mechanics is offered at brilliant called quantum objects this course explores experiments that seem to defy classical physics by interpreting these experiments you'll learn about the revolutionary ideas of quantum theory one by one eventually leading to the schrodinger equation this would be very helpful if you want to pursue the details of some of the concepts i discussed in this video head on over to brilliant.org forward slash arvinash right now to sign up for free and the first 200 visitors will even get 20 off their subscription check it out i think you'll be impressed i'd like to thank my generous supporters on patreon and youtube if you like my videos consider joining them and leave a question below because i try to answer all of them i will see you in the next video my friend [Music] you

Channel: Arvin Ash

Views: 709,839

Keywords: why do atoms combine to form molecules, hamiltonian mechanics, quantum mechanics of atoms, quantum mechanics of hydrogen atom, quantum mechanics of molecular structures, potential energy of molecules, energy level of molecular orbital, kinetic energy of molecules, morse potential, morse potential energy diagram, schrodinger equation, covalent bonds explained, covalent and ionic bonds, valence electrons, valence bond theory, chemical bonds explained

Id: azI-_S6g8C8

Length: 13min 24sec (804 seconds)

Published: Sat Aug 29 2020