Describe an atom

Atoms consist of a positively charged nucleus surrounded by negatively charged electrons. The nucleus is formed of positively charged protons and neutral neutrons.

Describe what determines an element

Elements are determined by their atomic number (Z) ie the number of protons they have in their nucleus.

Define atomic mass (A)

The number of protons + the number of neutrons

Describe isotopes

Isotopes are atoms of an element with the same number of protons but a different number of neutrons

State the mass of an electron relative to that of protons and neutrons

1/1836

Describe an electron

Early experiments showed electrons behaving as particles, with mass m and momentum p. They also have kinetic energy and a property called spin

State the equation relating momentum and mass

p = mv

p is momentum

m is mass

v is velocity

State the equation for kinetic energy

KE = 1/2mv^{2} m is the mass v is the velocity

Describe spin in an electron

Spin refers to the presence of a magnetic moment. For an electron the values spin can take are opposite, not parallel: ±1/2, or described as up and down

State De Broglie's wavelength relationship

λ = h/p

λ is wavelength

h is planck's constant

p is momentum mv (which demonstrates wave particle duality)

Give light's fundamental properties and state the equation linking them

Wavelength (λ) frequency (f) and velocity (c)

λ x f = c

Give the equation for the energy of a photon, ie packet of light energy

E = hf

Describe the Rutherford model and why it has been superseded.

There was said to be a central massive nucleus orbited by electrons. Spectroscopy showed that only certain orbits were "allowed" which formed the basis for the Bohr model

Describe ᴪ (psi)

ᴪ represents wavefunction, which is a mathematical function describing the behaviour of an electron; it consists of a radial component and an angular component and describes the behaviour of an e- in an orbital. It refers to the amplitude of an electron

Describe what the Schrödinger equation is used for

The SE describes the behaviour of electrons in atoms, by treating them as waves. Ie, the SE is a wave equation

Describe solutions of the SE

Solutions of the SE are ᴪ (wavefunctions) which describe possible states for an electron.

Describe quantisation

Quantisation results directly from boundary conditions, which means only solutions and energies are possible

Describe ᴪ^{2}

ᴪ^{2} refers to the probability of an electron being at a certain point, ie the electron density at a certain point.

State the three quantum numbers that can describe the 3D hydrogen orbital/ atom

n, l and m_{l}

Define the lowest energy state

Lowest energy state is the ground state, and has the lowest value of the quantum number

State the name given to higher energy states

Excited states

Give the equation for wavenumber in which it is split into its radial and angular parts

ᴪ = R(r).Y(𝜃,ɸ)

r = radius

𝜃 (theta) = colatitude/angle defining orientation

ɸ (phi) = azimuth

Describe the radial wave function, R(r)

The radial wave function changes with distance from the nucleus - depends only on the radial distance between the nucleus and the electron. It depends on quantum numbers n and l, and contains no information on direction or orientation.

Describe the angular wave function, Y(𝜃,ɸ)

The angular wave function changes corresponding to different shapes - depends on direction or orientation but not distance, and on the quantum numbers l and ml. The angles 𝜃 and ɸ define a orientation with respect to a coordinate system.

Describe n; the principle quantum number

n describes the size of the orbital and can take any integral value from 1 to ∞. For species with just one electron (eg hydrogen atoms), the energy of the orbital depends on n but not l and ml. For any given n, energy order is s < p < d

Describe l; the angular momentum quantum number

l describes the shape of any orbital. It can take any integral value from 0 to n-1.

State which orbital has l=0

s orbital

State which orbital has l=1

p orbital

State which orbital has l=2

d orbital

State which orbital has l=3

f orbital

Describe m_{l}, the magnetic quantum number

m_{l} is the orbital orientation quantum number. It can take any integer value from -l to +l. This means there are several different orbitals per value of l

State the name given to sets of orbitals with the same value of n

A shell

State the name given to sets of orbitals within a shell for which l is the same

A sub shell

Define a node

An area of zero electron density

State the number of nodes per orbital

n-1

State the number of angular nodes per orbital

l

State the number of radial nodes per orbital

n - l - 1

Describe the change in energy as n increases

As n increases, energy increases.

Describe hydrogen orbitals with the same value of n

Eg 2s, 2p both have n = 2, so they have the same energy. In other words, they are degenerate.

Describe the value of wavenumber (R(r)) for s orbitals

There is a non zero value of 𝜓 at the nucleus (ie when r = 0) as s orbitals are spherical

Describe a radial node

A spherical surface where the sign of 𝜓 changes from positive to negative.

Describe the value of wavenumber (R(r)) for p orbitals

𝜓 = 0 at the nucleus (ie when r = 0) as there is a node in the centre of the orbital.

State the 3 rules which describe how orbitals are filled by electrons

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- The Pauli exclusion principle
- The Aufbau Principle
- Hund's rule

Describe the Pauli Exclusion principle

m_{s} (a fourth quantum number) is associated with the electron and its spin. m_{s} = ±1/2

The Pauli exclusion principle says that no two electrons in the same atom can be described by the same quantum numbers. Each orbital is defined by 3 quantum numbers, so each orbital can contain two electrons.

These two electrons are called 'spin paired' or have opposite spins.

Describe the Aufbau principle

Electrons fill the lowest energy orbitals available

Describe Hund's rule

For a set of degenerate orbitals (ie those that have the same energy), electrons will start by filling the orbitals with one electron with spins aligned or parallel, before pairing up in individual orbitals.

This is because electrons that are further apart minimise inter-electron repulsions, and when singly occupied, the atom is more stable. Spin parallel is more stable than spin paired.

State the quantum numbers that orbital energy depends on for atoms other than hydrogen

n and l

State and explain the ordering of orbital energies

ns < np < nd

This ordering is due to the different penetrating ability of the different types of orbitals and the different effective nuclear charges felt by the electrons in those orbitals.

Describe penetrating ability

Penetrating ability describes the proximity to which an e^{- }can approach the nucleus.

Penetrating power: s > p > d

Describe the trend in ionisation energies

IE increases across a period as there is an increase in effective nuclear charge (Z_{eff}).

Define Z

Z is the atomic number, ie the number of protons

Give Slater's rules which can be used to estimate Z_{eff}

Z_{eff }= Z - S, where S is the shielding constant.

For s and p outer electrons, the contributions to the shielding constant S from other electrons in the atom are

- Zero for any electrons with a higher n
- 0.35 from any electron with the same n
- 0.85 from every electron with n one less than the chosen electron
- 1.00 from every electron with lower values of n

Describe the trend in successive ionisation energies.

Successive ionisation energies will increase because Z_{eff} increases as electrons are removed.

Define 1st electron affinity

The energy required to add an electron to a neutral element

Describe three general trends in atomic radii

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- Radii decrease across a period because of an increase in Z
_{eff}
- Radii increase down a group because the electrons are further away from the nucleus
- Increasing the distance from the nucleus outweighs the effective nuclear charge for radii down a group

_{eff}Define ionic bonding

Electrons are transferred between atoms to cations and anions

Define diamagnetic

Electrons are paired

Define paramagnetic

Electrons are unpaired

Describe molecular orbital theory

The underlying assumption is that the two or more nuclei are placed at an equilibrium distance and electrons are added to molecular orbitals in much the same way as electrons are added to atomic orbitals in atoms. Pauli exclusion principle, Hund's rule and the Aufbau principle all apply.

Describe the representation of the wavefunctions for the molecular orbitals.

Wavefunctions for the molecular orbitals are represented as combinations of the wavefunctions for the individual atomic orbitals.

When the individual atomic orbitals are in phase, the bonding orbital

ψ_{b = }ψ_{HA} + ψ_{HB} displays constructive interference.

When the individual atomic orbitals are out of phase, the antibonding orbital

ψ_{a} = ψ_{HA} - ψ_{HB} _{ }displays destructive interference.

Describe a bonding orbital for a molecule

The overlap is positive and electron density between the nuclei is increased

Describe an antibonding orbital for a molecule

The overlap is negative and the electron density between the nuclei is decreased.

Antibonding orbitals are usually denoted by *

Note that a nodal plane occurs in antibonding orbitals, which is perpendicular to the internuclear axis

Describe how we can consider electron density (ie probability) in molecular orbital theory

We need to consider (ψ_{a} + ψ_{b})^{2} or (ψ_{a} - ψ_{b})^{2}

Give the relationship between the number of molecular orbitals and the number of atomic orbitals

The number of molecular orbitals = the number of atomic orbitals

Show how molecular orbital diagrams can be formed

ΔE_{1} indicates the extent to which the bonding orbital is lowered in energy

ΔE_{2} indicates the extent to which the antibonding orbital is raised.

In general, ΔE_{2} > ΔE_{1 }by a small amount

Describe how bond order can be determined from a molecular orbital diagram

Bond order = ½(N_{b} - N_{a})

N_{b} is the number of electrons in bonding orbitals

N_{a }is the number of electrons in antibonding orbitals

Describe the shape of a σ orbital

σ orbitals are cylindrically symmetric about the internuclear axis.

Describe the difference between atomic orbitals and molecular orbitals

Atomic orbitals are labelled s, p, d ...

These are analogous to molecular orbitals labelled σ, π, δ ...

Describe the relationship between atomic orbitals and molecular orbitals relating to the number of nodal planes

Any nodal plane present in atomic orbitals will be present in molecular orbitals. All antibonding orbitals have an additional nodal plane between the nuclei and perpendicular to the internuclear axis

Describe π bonds

π bonds are analogous to p orbitals and have a nodal plane along the internuclear axis. They exhibit less strong bonding than σ_{p}

Describe the graphical representation of an s orbital, ψ plotted against r

The plot has a non zero value at the nucleus. Nodes are shown by crossing or touching the x axis

Describe the graphical representation of a p orbital, ψ plotted against r

The plot has a value of 0 at the nucleus. Nodes are shown by crossing or touching the x axis

Describe how to sketch a radial distribution function

As the distribution represents probability, there can be no negative values