Chapter 15 - Electrons in atoms

In the classical model of an atom, why can't electrons escape from the nucleus, or fall into it?
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- The three spatial quantum numbers act as the polar coordinates for the orbital, labelling it and telling us what shape it is.
> "n" is the radial quantum number, and tells us which shell an electron is in.
> "l" is the angular quantum number, which tells us which orbital an electron is in. (0 = s orbital, 1 = p orbital, 2 = d orbital, 3 = f orbital)
> "m" is also an angular quantum number, and it tells us which direction an orbital is pointing in. If there is a 3p orbital where m=0 and another where m=1, these two orbitals are pointing in opposite directions.

- "s" is the spin quantum number, which measures the time evolution of the wave.
As a general rule, the more maxima and minima that an orbital has (and therefore the more nodes), the shorter the wavelength and the higher the energy.

- For a wave in a one-dimensional box, each allowed wave has (n-1) nodes.
- For a wave on a circle, each allowed wave has l nodes.
- For a wave localised in an atom (ORBITALS), each allowed orbital has a total of (n-1) nodes; l angular nodes and (n-l-1) radial nodes.

This means that an electron in a higher shell will have more energy than one in a lower shell, as "n" will be higher so the number of nodes will be also.
What does the Pauli exclusion principle state?No two electrons in an atom can have the same set of quantum numbers. (In other words, if they occupy the same space (n, l and m are the same), then their spin s must be different. No more than two electrons can occupy any one orbital.) - Antiparallel electrons (with different spins) can have the same m quantum number and they can occupy the same orbital. They will therefore have more repulsion, because they are very close together. - Parallel electrons (with the same spin) must have different m quantum numbers, and so cannot occupy the same orbital. They will therefore have less repulsion, because they cannot be as close together.Which two types of interaction contribute to the energy of electrons in atoms?- Attraction of the nucleus for the electron. (Increases with nuclear charge, but decreases with distance from nucleus, "n".) - Repulsion between electrons in the atom. (Increases with number of electrons present. Generally speaking, increases with "l", because localisation to a smaller area reduces ability to move to minimise repulsion.)What three factors affect the energy of an electron in a particular orbital?- The size and shape of the orbital - The nuclear charge - The number of other electrons presentExplain the order of orbital energies for a H atom / Li2+ ion: 1s < 2s = 2p < 3s = 3p = 3d- H only has one electron, so there is no electron-electron repulsion to consider, just the attraction with the nucleus. - Therefore, electron energy just depends on the distance of the electron from the nucleus; as distance increases, attraction to the nucleus decreases, so energy becomes higher (less stable).Explain the order of orbital energies for a Li atom: 1s < 2s < 2p < 3s < 3p < 3d- Li has three electrons, so electron-electron repulsion needs to be considered. The repulsion will be bigger in orbitals with a larger "l" value (type of orbital), but to a smaller effect than that of the change in distance.Compare the orbital energies in Li(2s) and Na(3s).- The 2s orbital in Li is closer to the nucleus than the 3s orbital in Na, leading to a reduced nuclear attraction in Na. - The nuclear charge for Li is only +3 compared to +11 for Na, leading to increased nuclear attraction in Na. - These two factors approximately cancel, thus the orbital energies are around the same.Explain the order of orbital energies for a Ca atom: 3s < 3p < 4s < 3d < 4p- Calcium has 20 electrons, and because "l" = 2 for d-orbitals, the electron-electron repulsion terms will be large. - This means that the increase in electron-electron repulsion in the d orbital relative to the s orbital is larger than the decrease in electrostatic attraction between the 3rd and 4th shells. - Therefore, although the others increase for regular attraction / repulsion laws, the 4s orbital is lower in energy (more stable) than the 3d orbital.Why do electrons fill the 3d subshell after 4s but before 4p?The increase in electron-electron repulsion between p and d orbitals is larger than the decrease in electrostatic attraction between the 3rd and 4th shells. 3d is therefore higher energy than 4s, but not higher than 4p.Define "ground state" and "Aufbau principle".The ground state is the electronic configuration that gives the lowest overall energy. The Aufbau (building up) principle states that we put each electron into the lowest energy orbital available. This allows us to find the ground state.Which three steps do we take to determine the ground state electronic configuration of an atom?1. Determine the order of the orbital energies. 2. Determine the number of electrons present. 3. Feed the electrons into the lowest energy orbitals available.Why do all first-row transition metals lose the 4d electrons first on ionisation, rather than the 3d electrons?Because of the positive charge on the ion, the attraction for the nucleus is now more significant than the electron-electron repulsion in determining the orders of the 4s and 3d electron energies.How does a scanning proton microprobe function? How can it be used to map the distribution of elements during, for example, the biomineralisation of a growing nettle hair?- A very narrow beam of high-energy protons is scanned across the sample. This beam causes X-rays to be emitted by the core electrons of the atoms present. - Each element has a unique set of core electron energies, and so gives a unique peak in the resulting spectrum, which can be used to identify the elements present at any given point and their concentration. - When a nettle hair is touched, the tip breaks off to leave a sharp point that penetrates the skin and injects a solution of toxins. These toxins can be examined with the microprobe.What affects an atom's ability to form cations and anions?- Ionisation potential (the energy required to remove electrons from an atom to form a cation). - Electron affinity (the energy required to add electrons to an atom to form an anion). - The energy recouped in forming ionic interactions with other ions or solvent molecules. (This is determined by the electrostatic attraction between ions, and depends on their charge and radius.)Predict the ion that K will form.K has the electron configuration 3p(6)4s(1). The 4s electron will be easily lost, but the 3p electron will not, because it is much closer to the nucleus. It will therefore not form a +2 ion, and will only form the +1 ion.Predict the ion that Ca will form.Ca has the configuration 3p(6)4s(2). We can easily remove the 4s electrons, but not the 3p, so Ca cannot form a +3 ion. However, Ca also will not form a +1 ion, because it will lose the second electron easily to gain a noble gas configuration - and the energy required can always be recouped through electrostatic interactions. Ca will therefore only form the +2 ion.Predict the ion that Fe will form. What does this tell us about Fe in biological systems, in comparison to K or Ca?(NOTE: When talking about ionising first-row transition metals, we write 3d before 4s.) Fe has the configuration 3p(6)3d(6)4s(2). The 4s electrons are easily lost, so Fe will form +2 but not +1. Removal of a 3d electron requires about the same amount of energy we can regain from electrostatic interactions, so it can be possible in some cases. We can also sometimes remove a fourth electron, depending on its electrostatic interactions, but this is unlikely due to the increased energy necessary. So Fe will form +2 and +3 ions, and occasionally +4. Because Fe has multiple oxidation states, it is much more reactive than K or Ca. It is therefore always bound to macromolecules in biological systems, unlike K or Ca which are found in free solution.Predict the ion that Sc will form.Sc has the configuration 3p(6)3d(1)4s(2). It will lose the 4s electrons easily, but it will also lose the 3d(1) electron easily, as having a single electron in the 3d orbitals is unstable. It will therefore form a +3 ion.What factors affect atomic/ionic radius?The size of the largest occupied orbital, which in turn depends on the value of "n" and the nuclear charge. Generally, orbitals with a large value for "n" are larger, and ions with a larger positive charge are smaller as the electrons are pulled closer in towards the nucleus.Put the following in order of increasing ionic radius: Na+, K+, Ca2+, Zn2+. Which of these atoms forms the strongest electrostatic interactions in biological systems?- Zn2+ has the largest positive charge, so the electrons are pulled in towards the nucleus. It therefore has a relatively small ionic radius. - Ca2+ has a larger positive charge than Na+, but also has a larger "n" value. These cancel out, so their radii are around the same. - K+ has a larger "n" value than Na+ and a less positive charge than Ca2+, so it is the largest. The order is therefore: Zn2+ < Ca2+ ~ Na+ < K+ Zn2+ forms the strongest interactions, because it has a high charge and small size, so more can be present in one area. It is frequently used in the active sites of enzymes, such as carboxypeptidase.Explain why electrons in atoms occupy discrete orbitals with well-defined shapes and energies.Localisation of electrons around a nucleus leads to specific waves being allowed. These waves have very well-defined shapes, based on the allowed waves on a circle. Each wave also has a well-defined energy, based on the electrostatic attractions and repulsions with the nucleus and other electrons.Explain, briefly, the following ideas or concepts: - Principal quantum number - Pauli exclusion principle - Aufbau principle- The principle quantum number is the radial quantum number, "n". A large value of n indicates a large orbital with the electron having considerable density a long way from the nucleus. - The Pauli exclusion principle states that no two electrons can have the same four quantum numbers. Thus, only two electrons can occupy any one orbital and they must have opposite spins. A further consequence is that electrons with the same spin cannot occupy the same orbital and so have reduced electron-electron repulsion. - The Aufbau principle states that the ground-state electronic configuration of an atom or ion can be obtained by placing each electron sequentially into the lowest energy available orbital.Why does aluminium have a lower first ionisation energy than magnesium?Al's outer electron is in a 3p orbital, while Mg's is in a 3s. This means: - further away from the nucleus, so reduced attraction - increased shielding by 3s.Why does silicon have a lower first ionisation energy than phosphorus?Si's outer electron is from a doubly occupied 3p orbital, while P's is from a singly occupied 3p orbital. The electrons in the doubly-occupied orbital are closer together, so electron-electron repulsion is increased and the electron is more easily lost.