Atoms Flashcards
Conditions to solving the Schrodinger equation
Normalised – that is the sum of the probabilities over
all points must equal 1 i.e. the electron must be somewhere
- Continuous function - That is the nature of all energy waves.
- Single valued function i.e. each set of points only gives one probability - There is no uncertainty (here).
- Finite function - The electron is definitely somewhere.
Polar coordinate system
r = radial coordinate. θ and φ = angular coordinates
- φ is the angle between the x and y axes (latitude).
- θ is the angle between the xy plane and the z axis (longitude).
- r tells us about the size of the orbital.
- θ and φ tell us about shape of the orbital.
The solutions to the schronginer equation depend on either
r to produce a radial wave function R(r).
- θ and φ to an angular function Θ(θ), Φ(φ).
- The total wave function is the product of the two parts.
What three quantum numbers are produced by the schrodinger equation
Radial wave function, R(r):
the principle quantum number, n. A positive integer - Angular function Θ(θ), Φ(φ):
-
where 1 ≤ n ≤ ∞
the angular momentum quantum number, l, defines the to (n-1).
-
shape of the orbital and has allowed integer values from 0
the magnetic quantum number, ml, gives information +l and -l.
What is the energy of an orbital
energy of initial state (0) - energy of nucleus + electron in orbital
What does energy depend on for helium?
the attraction between electron 1 and the nucleus. the attraction between electron 2 and the nucleus. the repulsion between the two electrons.
Describe the differences from hydrogenic atoms
If wave equation is solved exactly, it would generate wave functions essentially the same as for H atom
Differeing nuclear charge will affect radial component
Angular component would remain the same
Orbitals on differing angular momentum but of the same shell aren’t degenerate
Describe electrons effectively screen other electrons from nucleus
- Attraction between an electron and the nucleus is a stabilising force.
- Repulsion between the electrons is destabilising but by a much smaller extent
Describe penetration
The 2s and 2p orbitals penetrate the 1s orbital to different extents based on their shape (angular momentum).
- The 2s orbital is more penetrating than the 2p. The 2s orbital is less shielded (screened) than the 2p orbital
- At higher atomic numbers the energy differences between these orbitals becomes smaller.
- Electrons generally prefer to be in the lowest available energy level .
Describe Aufbau principle
Lowest energy orbitals are filled first and are then filled in order of increasing energy
Describe Pauli Exclusion Principle
No two electrons have exactlyy the same set of four quantum numbers so electrons in degenerate orbitals where n, l and ml are the same but have different ms
Describe Hund’s Rule of Maximum Multiplicity
‘Electrons fill degenerate orbitals preserving the maximum number of unpaired, parallel electrons.’
- This minimises coulombic interactions (electrons as far apart as possible).
- Degenerate orbitals are filled singly before spin pairing.
Maximum stabilising exchange energy results from parallel electron spins called correlation energy
Describe valence electrons
Electrons occupying the outer shell and the other electrons are called core electrons
Describe accidental degeneracy
3d orbitals sometimes fall below the 4s in energy
Describe ionisation energy
The ease with which an electron can be removed depends on the energy of the orbital i.e. the effects of penetration and shielding and also on the effect of pairing electron spins.
X(g) → X+(g) + e-
ΔH is always positive
