Download From atoms to the periodic table

General Chemistry Dr Andrew Robertson A More Detailed Look at Atoms Warning: Everything you are about to hear is only partly true! At the 9ny size scale of subatomic par9cles, such as electrons and quarks, the laws of physics are unlike anything we know in our daily lives. For this reason, we make imaginary models that explain most of the behaviour of these par9cles. Some models are very simple but have lots of mistakes. Other models are more complex but have fewer mistakes. None of them, however, are exactly right. In science and engineering, we usually use the simplest model that gets us the informa9on we want. For instance, metallurgists oLen imagine metals as being made of hard atoms, while chemists imagine atoms as being made of electrons, protons and neutrons, and physicists imagine protons as being made of quarks. Including quarks into metallurgy or chemistry makes the resul9ng model far more complicated than it needs to be and overcomplicated models take too much effort to be useful. When studying atoms and subatomic par9cles, always remember that there are different models with different good points and bad points. Atoms are Mostly Empty Space In 1911 Ernest Rutherford reported an experiment where he fired 9ny α-­‐par9cles at a gold foil. He wanted to see how many would break through the foil and how many would bounce off. Whilst most of the α-­‐par9cles passed straight through, a 9ny amount were deflected at wildly different angles. This lead to his proposal that the atom consists mostly of empty space with a 9ny, dense core known as the nucleus. The Solar System Problem This is the simple model of an atom that followed Rutherford’s discovery. It was soon shown to be wrong, however, because moving electrical charges lose energy when they change direc9on. This means that the electrons should quickly lose momentum and crash into the nucleus. The problem of why nega9vely charged electrons do not crash into the posi9vely charged nucleus puzzled physicists for years. Despite its problems, the solar system model is easy to imagine and most people s9ll think this is what atoms are like. The Quantum Problem When atoms absorb energy they become excited — the electrons jump to a higher energy level (we can imagine this as the electrons moving further from the nucleus). But atoms only absorb certain amounts of energy known as quanta (singular: quantum). If electrons around the nucleus were like planets around the Sun, atoms should be able to absorb any amount of energy, which means they should be able to move to any distance from the nucleus. The reason for the quan<sa<on of energy levels in atoms was also a difficult problem at the beginning of the 20th century. hν
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Light is made of Wave/Par9cles The beginning of the 20th century brought the idea that light was not just a kind of wave but was also made of par9cles called photons. This was a revolu9onary idea — a par9cle, such as a ball, has a definite posi9on and velocity, whereas waves, such as sound, can fill a whole room at a 9me. Par9cles bounce off each other but waves interfere with each other and produce diffrac<on paCerns — in our daily lives, waves and par9cles are completely different. The concept that certain waves can also be par9cles, and vice versa, is known as wave/par<cle duality. In chemistry, the most important finding was that light is made of photons and the energy of a photon is related to its frequency by a number known as Planck’s constant (h). E = hν = hc/λ where E = energy, h = Planck’s constant, ν = frequency, c = speed of light, λ = wavelength Note that this means that photons with higher frequencies have higher energies and vice versa. Photons and Excita9on/Relaxa9on When an atom or molecule absorbs a photon we say it is excited to an excited state. When it releases that photon, we say it relaxes. The lowest energy level is called the ground state. Low energy photons, like microwave and infra-­‐red photons, cause low-­‐energy changes like rota9on or vibra9on in molecules. excitation
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excited state
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relaxa<on Mid-­‐energy radia9on such as visible and ultra-­‐violet light cause changes in the valence electrons. High energy radia9on, such as X-­‐rays, causes changes in inner shell electrons and gamma rays cause changes in the nucleus. Wave/Par9cle Duality Explains Quan9sa9on In 1924, a physicist called de Broglie proposed that wave/par9cle duality worked both ways and said that all par9cles also have a wave nature. He proposed a rela9onship between the wavelength of a par9cle, its momentum and the Planck constant. => Wavelength of 100eV electron ≈ 10–10 m λ= h/ρ Roughly equal to size of atom. (ρ = momentum) => Wavelength of 40 ms–1 cricket ball ≈ 10–34 m h = 6.63 × 10–34 m2 kg s–1 Much, much smaller than any known par9cle. Because Planck’s constant is so 9ny, only par9cles with a 0ny momentum have a detectable wavelength — in chemistry, that means electrons. In 1926 Erwin Schrodinger developed this idea to produce an equa9on that predicts where electrons will be around a nucleus. The equa9ons shows that electrons can only exist in a space within a stable wave shape. This instantly explained the quan9sa9on of energy levels since stable waves must be standing waves and standing waves can only have half integer values for their wavelengths. In three dimensions, we call these stable wave-­‐shapes orbitals. ^ Schrodinger equa9on: EΨ=HΨ Electron Density In 1927, Heisenberg proved that it is impossible to know both the posi9on and momentum of a quantum par9cle like an electron. It is not difficult, it is fundamentally impossible. This theory is known as Heisenberg’s Uncertainty Principle. In a very simple explana9on, the Uncertainty Principle tells us that we can find out where an electron is or how it is moving. However, the more we know about one of these proper9es, the less we can know about the other. What we can do, however, is find a general area where the electron is most likely to be. We can find a space with a high probability of containing an electron by solving the Schrodinger equa9on in three dimensions to calculate the posi9on of the orbitals. Because orbitals define a space that is likely to contain an electron, we say they have a high electron density. Note that electron density refers to the probability of finding an electron, and is not necessarily an indica9on of how many electrons are in that space. Remember that the Schrodinger equa9on is a wave equa9on. This means that orbitals have phases like waves, i.e. up/down or in/out. We shall see later that orbitals can overlap and interfere like waves and create areas with higher or lower electron density. s-­‐Orbitals When we solve the Schrodinger equa9on in three dimensions, we get a series of orbitals that grow in complexity. The simplest orbitals are called s-­‐orbitals and look like hollow spheres. As we increase the value of energy (EΨ) in our calcula9on, we find that s-­‐orbitals build up around each other like the layers of an onion. They also get more complicated with more layers for each orbital. Note that orbitals are actually fuzzy spaces and we usually think of an occupied orbital as being like an electron cloud. But we oLen represent them as hard shells because it is easier to visualise. p-­‐Orbitals The next set of orbitals have two lobes. They are symmetrical about one axis with a nodal plane (a planar gap) at the nucleus. These orbitals are known as p-­‐orbitals and they come in sets of three, oriented at 90° to each other. The colours here represent different phases. Other nota9ons, in old textbooks for example, represent phases as ‘+’ and ‘–’. It is important to understand that, for orbitals, these signs represent phases and not charges. We can visualise the phases of an orbital by imagining that ‘+’ means expanding and ‘–’ means contrac9ng (if one lobe is expanding, the other will be contrac9ng and vice versa). d-­‐Orbitals The next set of orbitals are known as d-­‐orbitals and each d-­‐orbital has two nodal planes. d-­‐
Orbitals come in sets of five. Beyond the d-­‐orbitals are the f-­‐
orbitals, with three nodal planes. f-­‐Orbitals are buried deep within the atom and so we do not oLen consider them in chemistry. (Orbitals con9nue to grow in complexity aLer the f-­‐orbitals but no atoms have enough electrons to reach these higher orbitals in the ground state.) More Facts about Orbitals   The orbitals are all centred on the nucleus, which means they interpenetrate each other. Orbitals of the same symmetry (s, p, etc) are nested inside each other like Russian dolls.   All atoms have all possible orbitals. However, since orbitals are empty spaces, empty orbitals have no meaning — we only need to consider an orbital when it is occupied by an electron.   Electrons in different orbitals do not strongly interact with each other (e.g. they do not collide), even if their orbitals overlap.   Higher energy orbitals are either larger or have more nodes than lower energy orbitals.   As a simplifica9on, we can imagine that the electrons ‘jump’ between the lobes of one orbital without entering the gap in between. Orbital Energy Diagrams three degenerate orbitals one orbital This diagram shows a very simple way of represen9ng orbitals and the rela9ve poten9al energy required to occupy them with an electron. Each dash represents one orbital. Orbitals with the same poten9al energy requirement, e.g. the three 2p orbitals, are called degenerate orbitals. Note that orbitals do not actually contain any energy themselves. An orbital is not a real ‘thing’ — it is simply a space that we calculate using the Schrodinger equa9on. It is electrons that carry the energy and the ‘energy of an orbital’ is actually the poten9al energy that an electron needs to occupy that orbital. To keep things simple, however, we just refer to orbitals as being high or low energy. Return to the Periodic Table Now we can understand the shape of the periodic table — it is based on which orbitals are filled in an element’s ground state. We can also understand why elements in the same group have similar chemical proper9es — they have similar configura9ons of their valence electron orbitals. In the next few slides, we will see how the proper9es of the elements influence the proper9es of the molecules they form. Ionisa9on Energy Across a Row First ionisa9on energies The first ionisa9on energy of an element is the energy needed to remove a first, outermost, electron and make a +1 ion from one mole of atoms. As we move across a period, we need more energy to remove an electron because the nuclei have a larger posi9ve charge but the size of the electron clouds remains roughly the same. A plot of first ionisa9on energies illustrates general trends of the elements’ hold on their electrons — the large discon9nui9es show where electrons are occupying new principle quantum shells and the small discon9nui9es reveal electrons occupying new subshells. Ionisa9on Energy Down a Group When we go down a group, the ionisa9on energies decrease. Why would this happen when we know that larger nuclei avract electrons more strongly? The decrease in first ionisa9on energy upon descending the group arises because the inner shells of electrons screen the charge from the nucleus, reducing its effect on the outer electrons. This screening effect is very important for understanding many chemical and physical proper9es. Atomic Radii Plots of ionisa9on energies help us to understand why atomic radii get smaller going from leL to right across a row but larger going from top to bovom. More posi9ve nuclei pull the electrons closer going from leL to right along a period. However, more electron shells screen the charge of the nucleus when going from top to bovom. Ionic Radii In many aspects of chemistry, biology and materials science, the size of ions is also important. This diagram shows the rela9ve sizes of s-­‐block (and group 3A) ca9ons and p-­‐
block anions. Note that, since the ca9ons have no valence electrons, they are smaller than their parent atoms. p-­‐block anions are larger than their parent atoms because the extra electrons cause the valence electrons to repel each other more strongly. The general trends along periods and down groups remain the same. (Electron Affini9es) Electron affinity is the stability gained when a free, gas phase atom acquires an extra electron. This stability is measured as a release of energy and more nega9ve values represent greater stability. The trends of electron affinity are complicated by the details of orbitals being filled. Some of the elements appear to have an electron affinity of zero on this chart but the value is actually just very small. Electron affinity is generally used for studies of atoms and elements but not molecules. It explains certain chemical and physical proper9es of the elements.