Atomic Structure Flashcards
Topic 1, Lectures 1-4 - Ben Ward
Chemical reactivity is determined by:
The movement of electrons between atoms.
Thomson (1898)
Plum pudding model: mainly positive with areas of negative electrons embedded within.
Rutherford (1909)
Electrons are arranged equidistant from the nucleus with spherical orbits
Rutherford weaknesses
Suggests all electrons are equal, makes it difficult to explain atomic emission spectra.
Electron excitation
Heat/light energy is supplied to an atom, causing them to move from a ground to an excited state. This state is less stable, so electrons don’t remain there long, and when they return to lower energy states, they emit electromagnetic radiation - typically a photon of visible or UV light.
Photon Energy
The energy of the emitted photon is calculated using the difference between the energy of the two levels.
Atomic Emission Spectrum
The emitted light is dispersed into a spectrum using a prism or diffraction grating. Spectrum is discrete and unique to each element.
Energy Gaps
Fixed and unique to each element - the larger the energy gap between two levels, the higher the energy of the emitted photon.
Example: Hydrogen emission spectra
When hydrogen atoms are excited, the emitted light can be divided into specific series: Lyman (transitions to n=1 are in the UV region), Balmer (n=2 in the visible light region), Paschen (n=3 infrared region).
Photon energy equation
E = hv = hc/λ
Photon energy relevance to AE
shows the link between the energy of a photon and its frequency.
Bohr (1913)
Similarly structured to Rutherford, however, electrons are at different distances to the nucleus and exist in quantised (discrete) orbits. Electrons closer to the nucleus are more tightly bound and therefore are more stable and have lower energy. E- can absorb energy and be excited or relaxed to different energy levels; this produces AE spectra.
Bohr’s atom weaknesses
- Atomic spectra measured in a magnetic field are different to those measured outside
- Works for hydrogen but less so with heavy atoms
- Doesn’t explain the periodic properties of the periodic table
De Broglie’s relationship
Relates pure particle to pure wave properties using Einstein’s E = mc^2 (particles) and Planck’s E = hc/λ (waves); finding that if those two statements are correct, then h/λ = mc = p (momentum)
Heisenberg uncertainty principle
States that though with particles we can determine position and momentum exactly, this isn’t possible for wave/particles.
Observed electron behaviour
When observing an electron in the classical sense, lightwaves reflect off the surface of the electron and reach the eye. These light waves add energy to the electron and change its momentum; therefore, observed electrons inherently behave differently.
Implications of wave particle duality for atoms
An electron in orbit must have a definitive position and an exactly defined path; therefore, if electrons do not have an exact position or path, they cannot exist in orbits.
Orbitals
A region of space within which an electron resides, although the exact location is unknown. The orbital represents a stationary wavefunction: the probability of finding an electron within a certain region.
Wave mechanics of electron orbits
Electron orbit circumference should be an integral multiple of its wavelength to ensure that the wave meets in phase after completing one full circle. If it were out of phase, the wave would cancel itself out.
Schrodinger’s equation
Describes how the quantum state of a physical system changes over time—how the wavefunction changes and therefore where electrons could be found. Shows how energy from movement and attraction impacts the wavefunction.
Wavefunction Ψ
The most important component of Schrodinger’s equation. If the electron is defined by SE, then the wavefunction is the amplitude of that equation at a given value of (x,y,z).
Probability density Ψ^2
Ψ^2(x,y,z) is the probability of finding an electron at (x,y,z).
Implications of Schrodinger’s equation
Describes electron behaviour, predicts location, helps to determine where energy levels are.
Principle quantum number (n)
Determines the size of an orbital, distance from the nucleus, and therefore the energy
Angular momentum number (l)
Determines the shape of an orbital, all orbitals with the same l value will have the same shape. Only the hydrogen atom energy levels are unaffected by the value of l.
Why are H energy levels unaffected by l?
The attractive forces between the proton and electron are spherically symmetrical; this means that regardless of the value of l, all orbitals with the same n value experience the same potential from the nucleus. H atoms also do not experience electron-electron interactions; therefore energy is determined solely by distance from the nucleus.
Magnetic quantum number (ml)
Determines the orientation of the orbital rlative to Cartesian axes.
Naming orbitals
As the quantum numbers describe solutions to Schrodinger’s equation for hydrogen, they also provide probability distributions and energy states. Orbitals are therefore named after the quantum numbers that describe them.
Radial wavefunction (R)
The function of the distance of an electron from the nucleus. The radial aspect refers to how the probability changes as you move further away from the nucleus. relates to n and l.
Radial distribution functions
shows how likely an electron is to be found at specific distances from the nucleus. The maximum point shows the most probable distance. RDF = probability of electron x number of locations at said distance.
Radial nodes
points at which probability is 0; they appear in higher energy levels. For n, the number of radial nodes is n-l-1.
Consequences of RDF
- The area of maximum probability increases with increasing n but is independent of l.
- There is a small probability of finding the electron a very long way from the nucleus; hard to accurately define orbital size.
- Nodes exist in further out energy levels
Angular wavefunction (Y)
Dependent only on the l and ml numbers, it describes how the probability varies with angular direction around the shape of the orbital. Determines the shape and orientation of an orbital.
Link between l and ml
For every value of l, ml can take any integer between -l and l. e.g. when l = 1 there are 3 possible values of ml and therefore 3 possible orbital shapes.
Weaknesses of Shrodinger’s equation
Potential energy (V) includes nucleus-electron attraction and electron-electron repulsion, which is 0 for H atoms. For atoms with >1 electron, the probability distribution must be determined before the potential energy - making the equation impossible to solve
Mitigating SE weakness
H atom orbital wavefunctions can be used for many-electron atoms. Orbitals ar the same shape as the hydrogen atom. HOWEVER, o energies are dependent on both n and l.
Orbital energies many-electrons
Electrons in orbitals with a larger n have higher energy as they have a probability distribution further away from the nucleus and are therefore less tightly bound.
Shielding effect
Electrons closer to the nucleus prevent the outer electrons from feeling the full nuclear charge that they would if they were isolated. These electrons therefore have a lower effective nuclear charge and higher energy than expected.
Why are orbital energies s < p < d < f?
When superimposing 2s and 2p RDFs, it is seen that the residual maximum of 2s is closer to the nucleus; therefore, 2s electrons on the whole have greater nuclear charge and lower energy levels.
How Z affects orbital energies (3d, 4s)
As Z increases, the more penetrating 4s orbitals will experience greater nuclear charge and lower energy. 3d orbitals are closer to the nucleus and will also have lower energy. In K and Ca, 4s orbitals are more penetrating than 3d orbitals and have lower energy as a result. From Sc onwards, vice versa.
Filling orbitals
Electrons fill orbitals starting from those with the lowest energies. With some exceptions, the 4s subshell tends to fill before the 3d.
Aufbau principle
In the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy level before occupying higher-energy levels
Spin quantum number (ms)
Describes the intrinsic spin (angular momentum) of an electron and has two possible values: 1/2 (spin up, or -1/2 (spin down)
Pauli exclusion principle
No two electrons in any given system can have identical values for all four quantum numbers.
Hund’s rule
Electrons will occupy degenerate orbitals (of the same energy) singly and with parallel spins before pairing up. Makes for the most stable state.
