Quantum Mechanics Flashcards
what does the schrodinger equation explain
how particles (electrons) behave
what is the quantum object characterised by
a wave function
whats the probability that a particle will hope to a different place given by
a quantity called the action
explain wave function duality
-objects bigger than a molecule have a negligible wavelength
-an electron is tiny so its wavelength is around the size of an atom
-electrons are viewed as particles+waves
how would you describe electrons in terms of waves in an atom
they’re circular standing waves surrounding the nucleus
what is an objects wavelength inversely proportional to
its mass
how do you calculate the energy of a photon
=planks constant x frequency
=h x f
explain what the wave function is
-a probability amplitude
-the square of the magnitude of the wave function describes the probability of an electron existing in an exact location
explain an electron is terms of quantum mechanics
a cloud of probability density
summarise the main info about schrodinger equation
-applies the quantum systems
-describes the systems 3-dimensional wave function
-calculates the wave function of a system
-the info it contains is probabilistic (Heisenberg uncertainty principle)
what does the Schrodinger equation tell us
where/how the particle is inside the walls
what is assumed for a particle in a 1D box
a potential V(x)=infinity, everywhere except in between x=0 and x=a, where V(x)=0
what does it mean when V(x)=infinity
a mathematical way of saying the particle is definitely not there
what does P(x) when V(x)=infintity
P(x)=0
the probability density function equals zero
what 3 quantum numbers are acceptable wave functions numbered by
n=principle quantum number
l=orbital angular momentum quantum number
MI=magnetic orbital quantum numbers
what does n describe
size +energy of that orbital
what does l describe
shape of the orbital
what does MI describe
orientation of the orbital
list the relationship between between these 3 quantum numbers
N=1,2,3
L=0…n-1 e.g. when n=3, l=0,1,2
MI= -l…l e.g. when l=1, MI=-1,0,1
what is the wave function for an electron called
an orbital
describe the quantum numbers of a degenerate orbital
-the same energy, n
-different l and MI
for the h atom describe the orbitals
all n^2 orbitals for a given value of n are degenerate
what does the radial part (r)determine
the spatial extent of the wavefunction
how do you calculate how many nodes an atomic orbital has
=n-1
what does the radial distribution function give
the probability of finding the electron in spherical shell of thickness at distance r
what does the angular part of an orbital determine
the shape of the orbital
what does ref equal at the nucleus
0
what is an orbital a product of
=radial part x angular part
what the angular part of an s orbital
-they have no angular dependance
-they’re spherically symmetric
compare the radial part of 2s in comparison to 2p
radial part of 2s is more highly curved(1 radial node)than radial part of 2p(no radial nodes) so 2s has more radial kinetic energy so the e- has more energy moving in and out of the nucleus
compare the angular part of 2s in comparison to 2p
angular part of 2s(no angular node) is less curved than angular part of 2p(1 angular node), 2p has more angular kinetic energy so the energy is used moving around the nucleus
what is an atomic orbitals nodes made up of
radial +angular nodes
list how many +what type of nodes a 1s,2s,2p,3s,3p atomic orbitals have
1s=0 nodes
2s=1 node(radial)
2p=1 node(angular)
3s=2 nodes(both radial)
3p=2 nodes(1 radial+1 angular)
what is angular momentum quantised by
magnitude+length of vector
why is the wavefunction higher closer to the nucleus
-as the electron is attracted to a more positive nucleus
-so there’s a contraction of orbitals
-so the electrons now have lower energy so it’s a more stable system
why does the SE only give approximate solutions for atoms with more than 1 molecule
as the electrons interact with each other making it too complicated
whats the relationship between angular momentum,l and magnetic dipole moment, u
they’re always anti-parallel to each other
what type of spin do particles have
-integer spin
-half-integer spin
what’s an electrons spin quantum number
s=1/2
what’s the magnetic spin quantum number(ms) for an electron
-s…+s
what values are magnetic spin quantum numbers restricted to
2s+1
what’s another word for spin-up
alpha
what’s another word for spin-down
beta
define Zeff
the effective nuclear charge, the net positive charge pulling these electrons towards the nucleus
why does the 2s orbital penetrate the 1s2 orbital
because the 2s orbital with its inner radial node has a inner peak of electron density that partially penetrates the shielding of the 1s2 electrons
why is Zeff lower for 2p than the 2s orbital
as the 2p orbital doesn’t have an inner radial node so doesn’t have an inner peak of electron density+so has greater shielding from 1s2 electrons
why is the 2s orbital lower in energy than the 2p orbital
as it has a higher Zeff so a stronger attraction
what is shielding
when inner electrons partially shield outer electrons from full Z
what’s penetration
when an e- in an outer orbital has a significant probability of being found inside an inner orbital
what type of orbitals are 2s+2p for any 1 electron ion
degenerate
what happens to atomic radius and down a group and across a group
-increases down a group
-decreases across a period
why does atomic radius increase down a group
-n increases by 1
-so the number of completely filled shells increases
-these shield the nuclear charge
why does atomic radius decrease across a period
-increasing nuclear charge
-so electrons are attracted more strongly
-atom is more compact
define first ionisation energy
energy required to remove 1 electron from the neutral atom in the gas phase
what happens to ionisation energy down a group and across a period
-increases down a group
-decreases across a period
why does ionisation energy decrease down a group
-completed inner shells of electrons shield
-valence electron is attracted less to the nucleus
why does ionisation energy increase across a period
-increasing nuclear charge
-electrons are bound more strongly
which elements don’t follow the average trend for ionisation energies
Li
B
O
why odes Li not follow the ionisation energy trend
as there’s an e- in the 2s orbital, which is well shielded by the completed (1s)^2 shell
why does B not follow the average ionisation trend
it’s the first time the 2p is occupied, p electrons are less strongly bound than s electrons
why does O not follow the average ionisation trend
as its the first time any of the 2p orbitals are doubly occupied, e-e repulsion is higher for an electron in a doubly occupied orbital, lowering the binding energy
what does HOMO stand for
highest occupied molecular orbital
what does LOMO stand for
lowest unoccupied molecular orbital
what does UV absorption occur from
excitation of an electron from filled to empty orbital
what’s a destructive wave
when a positive+ negative wave cancel each other out so the resultant becomes zero
what happens when you combine separate atoms in a molecule
constructive interference
what happens when constructive interference occurs
-overlap of wave functions
-results in increase in value of wavefunction
-increase in electron density
describe an antibonding combination
-positive+negative wave functions added together results in close to zero wave function
-destructive interference results in low probability of finding the electron
-no electron density in the region between the nucleus
how are molecular orbitals built up
by adding or subtracting atomic orbitals
describe the electrons in bonding MO
-high probability of being close to both nuclei, build-up of density between the nuclei
-internuclear density +nuclei attract each other, stabilising
-density pulls nuclei together, bonding
-more stable in separate atoms
describe electrons in the anti bonding MO
-zero probability of being close to both nuclei, depletion of density between the nuclei
-nuclei pulled apart by density outside the internuclear region
-node means that electrons have high kinetic energy which is destabilising
-less stable than in separated atoms
what do molecular orbital diagrams
connection between shape, energy and phase
how do you calculate bond order
(number or e- in bonding MOs- number of e- in anti bonding MOs)/2
how are sigma-bonding MOs formed
from overlapping s-orbitals or from p-orbitals oriented along the bond axis
how are pi-bonding MOs formed
from overlapping p-orbitals oriented perpendicular to bond axis
why is oxygen paramagnetic
due to unpaired oxygen
why is N2 diamagnetic
there are no unpaired electrons
what’s the relationship between electronegativity of an atom +its orbital energies
the more electronegative an atom, the lower its orbital energies
