Atomic structure

Inside the atom: particles, mass, charge and the numbers that describe them

An atom is mostly empty space. Almost all of its mass is concentrated in a very small, dense nucleus at the centre, which contains protons and neutrons; the rest of the atom is the empty space through which the electrons move, arranged in shells around the nucleus. If an atom were scaled up to the size of a football stadium, the nucleus would be about the size of a pea on the centre spot, yet it would still carry more than 99.9% of the mass of the atom.

Protons and neutrons have almost exactly the same mass, and each is about 1840 times heavier than an electron, so nearly all the mass of an atom sits in its nucleus. The charge is just as unevenly distributed: a proton carries one unit of positive charge, an electron carries one unit of negative charge, and a neutron carries no charge at all. In a neutral atom the number of protons equals the number of electrons, so the positive and negative charges cancel and the atom as a whole has no charge. The electrons are held inside the atom by the electrostatic attraction between the negative electrons and the positive nucleus.

Two numbers describe every atom. The atomic number (or proton number), symbol Z, is the number of protons in the nucleus, and it identifies the element: every carbon atom has Z = 6. The mass number (or nucleon number), symbol A, is the total number of protons and neutrons, so the number of neutrons is A - Z. A chlorine atom with A = 35 and Z = 17 therefore has 17 protons, 35 - 17 = 18 neutrons and 17 electrons. For an ion only the electron count changes: an ion with a charge of n+ has lost n electrons and has Z - n electrons, while an ion with a charge of n- has gained n electrons and has Z + n electrons. A 56Fe3+ ion has 26 protons, 30 neutrons and 26 - 3 = 23 electrons; the mass number is untouched by the charge, because only electrons have been gained or lost.

Because the force on a moving particle in an electric field depends on its charge, a beam containing protons, neutrons and electrons all travelling at the same velocity is split into three. Protons are deflected towards the negative plate, and electrons are deflected towards the positive plate, in the opposite direction. Neutrons are not deflected at all, because they carry no charge. The electron beam is deflected far more than the proton beam: a proton has the same size of charge as an electron but about 1840 times the mass, so its charge-to-mass ratio is much smaller and the field bends its path much less.

• Neutrons = mass number A - atomic number Z.
• Electrons in a neutral atom = Z; in an ion of charge n+ they are Z - n, and in an ion of charge n- they are Z + n.
• Almost all the mass and all of the positive charge of an atom are in the nucleus; the electrons occupy the empty space around it.
• The deflection of a particle in an electric field depends on its charge-to-mass ratio, which is why electrons are bent far more than protons.

Isotopes: the same element with a different mass

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. They therefore have the same atomic number but different mass numbers. The symbol for an isotope carries the mass (nucleon) number at the top left and the atomic (proton) number at the bottom left of the element symbol, so the two isotopes of chlorine are written with 35 above 17 and 37 above 17 in front of Cl, and on a single line as Cl-35 and Cl-37. Chlorine-35 has 17 protons and 18 neutrons, and chlorine-37 has 17 protons and 20 neutrons.

Isotopes of an element have identical chemical properties, because chemistry is controlled entirely by the number and arrangement of the electrons, and isotopes of the same element have exactly the same number of electrons in exactly the same configuration. Chlorine-35 and chlorine-37 both form chloride ions, both form hydrogen chloride, and both bleach litmus in the same way. The extra neutrons in chlorine-37 sit in the nucleus and take no part in bonding.

Their physical properties differ wherever mass matters: the two isotopes have different masses, and a sample enriched in the heavier isotope has a greater density. Heavy water, D2O, is made from deuterium, the isotope of hydrogen with one proton and one neutron, and it is denser than ordinary water and boils at a slightly higher temperature. Because mass is practically the only difference, isotopes can be separated by physical methods that depend on mass, such as the gaseous diffusion or gas centrifugation of uranium hexafluoride, which separates uranium-235 from uranium-238.

The relative atomic mass you find on the Periodic Table is the weighted mean of the masses of the isotopes, so it is rarely a whole number. Copper, for example, has a relative atomic mass of 63.5 because it is a mixture of Cu-63 and Cu-65, and chlorine has 35.5 because it is roughly three parts Cl-35 to one part Cl-37. The mass number, by contrast, is always a whole number, because it counts particles in one particular atom.

• Isotopes: same number of protons and the same number of electrons, different number of neutrons.
• Identical chemical properties, because the electrons are arranged identically.
• Different mass and density, because the masses of the atoms differ.
• Relative atomic mass is the weighted mean of the isotope masses, so it is usually not a whole number, unlike the mass number.

Atomic radius and ionic radius

Atomic radius decreases across a period from left to right. In Period 3 the radius falls steadily from sodium to chlorine, because the nuclear charge rises from +11 to +17 while the outer electrons stay in the same shell. The inner shells shield the outer electrons by the same amount in each element, so the steady increase in nuclear charge pulls the same shell in more tightly and the atom gets smaller.

Down a group the atomic radius increases. Each element down the group has one more occupied shell than the element above it, so the outer electrons begin further from the nucleus. The extra inner shells also shield the outer electrons from the nuclear charge more effectively. Both effects weaken the pull of the nucleus on the outer electron, and they outweigh the increase in nuclear charge, so the atom gets larger as you go down a group.

A cation is smaller than the atom it came from, because electrons have been removed from the outer shell while the nuclear charge is unchanged, so the same positive charge is now pulling in fewer electrons. A sodium atom is about 186 pm across and a sodium ion only about 102 pm. An anion is larger than its atom, because extra electrons have been added into the outer shell and the increased electron-electron repulsion spreads them out: a chlorine atom is about 99 pm across and a chloride ion about 181 pm.

Ions that contain the same number of electrons, called isoelectronic ions, can be compared directly. N3-, O2-, F-, Na+, Mg2+ and Al3+ all have 10 electrons in the same arrangement, but the nuclear charge increases from +7 to +13 across the series. The same ten electrons are pulled in more strongly as the charge rises, so the ionic radius falls along the series N3- > O2- > F- > Na+ > Mg2+ > Al3+. Down a group the ionic radius increases for the same reason the atomic radius does: an extra shell has been added, and the extra shielding outweighs the extra protons.

Shells, sub-shells and orbitals

The electrons in an atom are arranged in shells, each labelled by a number called the principal quantum number, n. The shell with n = 1 lies closest to the nucleus and is lowest in energy, and the energy of a shell increases as n increases, so the 3s sub-shell is higher in energy than the 2s sub-shell. A shell is not a simple ring of electrons: each shell contains one or more sub-shells, and each sub-shell contains one or more orbitals.

An orbital is a region of space around the nucleus that can hold a maximum of two electrons with opposite spins. The type of sub-shell decides how many orbitals it contains. An s sub-shell contains one orbital and holds two electrons, a p sub-shell contains three orbitals and holds six electrons, and a d sub-shell contains five orbitals and holds ten electrons. Watch the wording here: it is the p sub-shell that holds six electrons, spread over three separate p orbitals, and each single p orbital still holds only two.

The sub-shells fill in order of increasing energy, which for the elements up to krypton gives the sequence 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p. Notice that 4s lies below 3d in energy, so 4s is filled first even though it belongs to the fourth shell. The reason is shielding: the 3d sub-shell is screened from the nucleus by the electrons already present in 3s and 3p, which raises the energy of 3d above that of 4s. The ground state of an atom is the arrangement of its electrons that has the lowest possible energy, and every configuration you write for this course is a ground state configuration.

Electronic configurations of atoms and ions, and electrons in boxes

To write the electronic configuration of an atom, fill the sub-shells in order of increasing energy, 1s 2s 2p 3s 3p 4s 3d 4p, and put in as many electrons as the atom has. Sodium has 11 electrons, so its configuration is 1s2 2s2 2p6 3s1, which shows 2 electrons in the first shell, 8 in the second and 1 in the third. Iron has 26 electrons and its full electronic configuration is 1s2 2s2 2p6 3s2 3p6 3d6 4s2, while the shorthand electronic configuration replaces the first 18 electrons with the symbol of the noble gas that has the same arrangement, giving [Ar] 3d6 4s2.

Electrons in boxes notation shows the arrangement orbital by orbital. Each box is one orbital, and inside a sub-shell the boxes are filled singly first, with all the single electrons given parallel spins, before any box receives a second electron. Iron in boxes is [Ar] followed by five boxes for 3d holding 1, 1, 1, 1 and 2 electrons, and one box for 4s holding a pair. The arrangement with single electrons in separate orbitals is preferred because electrons repel one another and keep as far apart as possible, which lowers the energy of the atom.

Two elements in the first row of the transition elements do not follow the simple filling pattern, because a half-filled or completely filled d sub-shell is lower in energy. Chromium is [Ar] 3d5 4s1 and copper is [Ar] 3d10 4s1, not the [Ar] 3d4 4s2 and [Ar] 3d9 4s2 that the filling order alone would suggest. Spreading the six or eleven outer electrons out this way reduces inter-electron repulsion between electrons in the same orbital, so the half-filled and completely filled arrangements are the ground states.

For an ion, add or remove electrons where the energy change is smallest. When a transition element forms a positive ion the 4s electrons are lost first, even though 4s was filled first, because once the 3d orbitals are occupied the 3d sub-shell lies lower in energy than 4s. So iron is [Ar] 3d6 4s2, Fe2+ is [Ar] 3d6 and Fe3+ is [Ar] 3d5. For a negative ion such as O2- or Cl-, add the extra electrons to the next available orbital in the usual filling order: chlorine is [Ne] 3s2 3p5 and the chloride ion is [Ne] 3s2 3p6.

• Fill in the order 1s 2s 2p 3s 3p 4s 3d 4p and check that the electrons add up to the atomic number.
• Shorthand configuration replaces the inner electrons with the previous noble gas in square brackets: [Ar] 3d6 4s2 for iron.
• Chromium is [Ar] 3d5 4s1 and copper is [Ar] 3d10 4s1, because a half-filled or filled d sub-shell has a lower energy.
• When a transition element is ionised, the 4s electrons are removed before the 3d electrons.

The shapes of s and p orbitals, and free radicals

An s orbital is spherical. The chance of finding the electron is the same in every direction at a given distance from the nucleus, so an s orbital is drawn as a sphere with the nucleus at its centre, and every shell has exactly one s orbital: 1s, 2s and 3s. A 2s orbital is not just a bigger 1s orbital: it also has an inner region of electron density, so it is drawn as a smaller sphere inside a larger one, with a radial node between them.

A p orbital is dumbbell shaped: two lobes on opposite sides of the nucleus, with a node at the nucleus where the electron density is zero. Each p sub-shell contains three p orbitals, which lie at 90 degrees to one another and are usually labelled px, py and pz after the axis each one lies along. When you sketch a p orbital, show the two lobes of equal size on opposite sides of the nucleus and make it clear that the nucleus sits at the gap between them, not inside a lobe.

The shape of an orbital matters because bonding happens where orbitals overlap, and the direction of the lobes of a p orbital is what gives molecules such as water and ammonia their three-dimensional shapes. It also explains the difference between a sigma bond, formed by end-on overlap, and a pi bond, formed by the sideways overlap of two p orbitals above and below the line joining the nuclei.

A free radical is a species with one or more unpaired electrons. A chlorine atom, Cl, is a free radical, and it is produced in the first step of the reaction between chlorine and methane when ultraviolet light splits a Cl2 molecule into two chlorine atoms: Cl2 -> 2Cl. The unpaired electron makes a free radical extremely reactive, because pairing that electron with another one in an orbital lowers the energy of the species, so the radical will attack almost anything that can supply an electron. In electrons in boxes notation a free radical is shown by a box containing a single arrow, for example the 3p sub-shell of a chlorine atom has one box with a single unpaired electron.

• An s orbital is spherical; a p orbital is dumbbell shaped with a node at the nucleus.
• A p sub-shell holds three orbitals at 90 degrees to one another; a d sub-shell holds five.
• A free radical is a species with one or more unpaired electrons, which makes it very reactive, for example a chlorine atom Cl.

Ionisation energy: definition, factors and trends

The first ionisation energy of an element is the energy required to remove one electron from each atom in one mole of gaseous atoms to form one mole of gaseous 1+ ions: Na(g) -> Na+(g) + e-. The word gaseous matters, because the definition is about isolated, well-separated atoms, and so does the word one mole, because the energy is quoted per mole. The second ionisation energy removes the second electron from a gaseous 1+ ion, Na+(g) -> Na2+(g) + e-, and the third from a gaseous 2+ ion, Mg2+(g) -> Mg3+(g) + e-. Successive ionisation energies are measured in kJ mol-1.

Ionisation energy is the energy needed to overcome the attraction between the nucleus and the outer electron, so anything that strengthens that attraction raises the ionisation energy. Three factors decide the size of the attraction. Nuclear charge: the more protons in the nucleus, the more strongly the outer electron is pulled. Distance from the nucleus, described by the atomic or ionic radius: the further away the electron is, the weaker the attraction. Shielding by inner shells and inner sub-shells: the inner electrons repel the outer electron and screen it from part of the nuclear charge, so the outer electron only feels an effective attraction, which is smaller than the true nuclear charge. A fourth factor matters when two electrons share an orbital: spin-pair repulsion, the repulsion between the two electrons of a pair, which raises the energy of one of them and makes it easier to remove.

Across a period the first ionisation energy generally increases, and down a group it decreases. In Period 3 the values are 496 (Na), 738 (Mg), 577 (Al), 786 (Si), 1012 (P), 1000 (S), 1251 (Cl) and 1521 (Ar) kJ mol-1. Moving from left to right, the nuclear charge increases by one proton for each element while the outer electron remains in the same shell, so shielding is roughly constant and the atomic radius falls, and the outer electron is held more strongly, so more energy is needed to remove it. Going down a group the outer electron moves into a shell with a larger principal quantum number, so it starts further from the nucleus, and the extra inner shells shield it from the nuclear charge; both effects weaken the attraction and together they outweigh the extra protons, so the value falls from 520 kJ mol-1 for lithium to 496 for sodium and 419 for potassium.

The trend is not perfect, and the two dips have different causes. Aluminium (577) is lower than magnesium (738) because the extra electron in aluminium is the first electron in a 3p orbital. A 3p orbital is higher in energy than the filled 3s orbital below it and is shielded by the 3s electrons, so it is easier to remove than the 3s electron of magnesium. Sulphur (1000) is lower than phosphorus (1012) for a different reason: phosphorus has a 3p3 arrangement with one electron in each p orbital, while sulphur has a 3p4 arrangement containing one pair, and the spin-pair repulsion between the two electrons in that pair makes one of them easier to remove.

Successive ionisation energies: reading the structure of the atom from the data

The second ionisation energy removes an electron from a gaseous 1+ ion, the third from a gaseous 2+ ion, and so on, so the tenth ionisation energy of an element is the energy needed to remove one electron from each ion in one mole of gaseous 9+ ions. Successive ionisation energies always increase, because every electron is removed from an ion that is already positive. With fewer electrons left to share the nuclear charge there is less electron-electron repulsion, and the remaining electrons are held more strongly, so each removal costs more energy than the one before.

The size of the jump between consecutive values tells you which shell the electron came from. While electrons are being removed from the same shell the values rise steadily, but the first electron removed from a shell closer to the nucleus produces a large jump, typically a factor of five or more. For sodium the first ionisation energy is 496 kJ mol-1 and the next eight values climb steadily to about 29 000 kJ mol-1, but the tenth is above 141 000 kJ mol-1. The first electron comes from the 3s sub-shell, whereas the tenth comes from the 1s sub-shell, which is much closer to the nucleus and much more strongly held.

This is how ionisation energy data reveal an electronic configuration. The element with successive ionisation energies of 738, 1451, 7733, 10540 and 13630 kJ mol-1 has a big jump between the second and third values, because 7733 / 1451 is about 5.3 while the earlier step is only about 2.0. Only two electrons are therefore being removed from the outer shell, and the third electron comes from a shell nearer the nucleus. An element with two outer electrons is in Group 2 of the Periodic Table, and these values are those of magnesium, whose full configuration 1s2 2s2 2p6 3s2 confirms it.

The rule to remember is that the number of electrons removed before the first big jump is the number of electrons in the outer shell, which for a main-group element is the group number. Sketching a graph of the logarithm of the ionisation energy against the number of electrons removed makes the pattern obvious, because the values on each completed shell fall on a straight line and the change of shell shows as a break in the line. A transition element shows a jump after the 4s electrons have been removed and then a further break when the 3d electrons are finished, so the same method works for the d block.