CH 2.6-2.12 Flashcards
Principal quantum number
The quantum number relating to the SIZE & ENERGY of an ORBITAL
- n
- shell
- has integer values: 1, 2, 3, …
As n increases, the orbital becomes ____ & the electron spends more time _____ from the nucleus
larger; farther
An increase in n = _____ energy, because the electron is ______ tightly bound to the nucleus, & the energy is _____ negative
higher; less; less
orbital angular momentum quantum number
Quantum # relating to the SHAPE of an atomic ORBITAL
- Integral value from 0 -> n-1
- L
- subshell
- l = 0 is s
- l = 1 is p
- l = 2 is d
- l = 3 is f
Magnetic quantum number
Quantum # relating to the ORIENTATION (direction) of an atomic ORBITAL in space relative to the other orbitals in the atom
- m sub l
- orbitals of subshell
- Integral values between +L and -L, including 0
Nodes
- aka nodal surfaces
- an area of an orbital having 0 electron probability
The number of nodes increases as _____ increases
n
For s orbitals, the number of nodes is given by
n-1
Function for s orbital
positive everywhere in 3D space
- when the see orbital function is evaluated at any point in space, its results are a positive #
Function for p sub z orbital
has a positive sign in all regions of space in which z is positive & negative sign for when z is negative
- similar to sine wave with alternating positive and negative phases
The d orbitals first occur in level
n = 3
5 d orbitals
dxz, dyz, dxy, d(x^-y^2), d(z^2)
- x,y,z are subscripts
dxy orbital
centered in the xy plane
- lie between the axes
d(x^2-y^2)
- centered in the xy plane
- lies along the x and y axes
d(z^2)
two lobes along z axis & a belt centered in the xy plane
The f orbitals occur in level
n = 4
All orbitals with the same value of n have the ______
same energy
Degenerate
A group of orbitals with the same energy
Summary of the Hydrogen Atom
- In the quantum (wave) mechanical model, the electron is viewed as a standing wave. This representation leads to a series of wave functions (orbitals) that describe the possible energies and spatial distributions available to the electron
- In agreement with the Heisenberg uncertainty principle, the model cannot specify the detailed electron motions. Instead, the square of the wave function represents the probability distribution of the electron in that orbital. This allows us to picture orbitals in terms of probability distributions, or electron density maps.
- The size of an orbital is arbitrarily defined as the surface that contains 90% of the total electron probability.
- The hydrogen atom has many types of orbitals. In the ground state, the single electron resides in the orbital. The electron can be excited to higher-energy orbitals if energy is put into the atom.
Electron spin
a quantum # representing 1 of 2 possible values for the electron spin; either +1/2 (spin up) or -1/2 (spin down)
-ms
- developed by Samuel Goudsmit & George Uhlenbeck
- connected with Pauli’s postulate
- Magnetic field induced by the moving electric charge of the electron as it spins
- spins are opposite regardless of orientation
Pauli Exclusion Principle
In a given atom no two electrons can have the same set of 4 quantum numbers (n, l, ml, ms)
- since ms has only 2 values, an orbital can only hold 2 electrons & they have opposite spins
- If there are 2 electrons in an orbital ONE MUST MAVE +1/2 spin and the OTHER MUST HAVE -1/2 SPIN
Fraunhofer
- widened wavelength rainbow spectrum
- Saw blank & black spaces btwn colors (they weren’t continuous)
Visible light characteristics
- White light contains all wavelengths (when passed through a prism, the different wavelengths are separated
Line spectrum
- aka hydrogen emission spectrum
- Light from an electrical discharge through gaseous element doesn’t contain all wavelengths
- Spectrum is discontinuous (big gaps)
Continuous spectrum
occurs when white light is passed through a prism
Balmer-Rydberg Equation
1/lambda = R (1/(n1^2) - 1/(n2^2))
- (n1
Neils Bohr (1913)
- proposed model of an atom w/ discrete (quantum) states
- Explained how atoms emit light quanta & their stability
- Combined postulates of Planck & Einstein
Postulates of Bohr’s theory
- Each atom has a # of discrete energy levels (orbits) (stationary states) that exist w/out emitting/absorbing EM radiations
- As the orbital radius decreases, so does the energy of the electron
- An electron may move from one energy level (orbit) to another, but in so doing, monochromatic radiation is EMITTED (TO LOWER ENERGY) or ABSORBED (TO HIGHER ENERGY)
- an electron “revolves” in a circular orbit about the nucleus & its motion is STILL governed by the ordinary laws of mechanics & electrostatics, with the restriction that its ANGULAR MOMENTUM IS QUANTIZED & CONSERVED
Angular momentum equation
angular momentum = m x v x r = nh/(2pi)
- m = mass of electron
- v = velocity of electron
- r = radius of orbit
- n = energy levels
- h = Planck’s constant
Energy of states of electrons equation
- A/ n^2
- A = constant
- n = quantum #
Bohr equation
E = -2.178 x 10^-18 J (Z^2/n^2)
- n = integer
- z = nuclear charge
What trend occurs as you go up in energy levels
Distance between the orbitals decrease
Radius of Bohr Hydrogen orbit equation
r = n^2 (5.29 x 10^-11 m)
Any one-electron atom radius equation
r = (n^2 x a0)/Z
Ionization energy
The energy required to remove the electron from an atom
- each ionization energy is removing 1 highest-energy electron
- express in kJ per mole of atoms (or ions)
Change in energy of ionization of an atom equation
delta E = -AZ^2 (1/(nf^2) - 1/(ni^2))
- delta E > 0 means energy is absorbed
- delta E < 0 means energy is emitted
The change in energy for one atom of hydrogen
- 2.178 x 10^-18 J
- Ionization for 1 mol = 2.178x10^-18 J x 6.022x10^23= 13.12 x 10^5 J mol^-1
As energy is brought closer to the nucleus, energy is _______ the system –> ______ atomic stability –> energy becomes more ______ relative to the free electron
released from; increased; negative
As energy is brought closer to the nucleus, energy is _______ the system –> ______ atomic stability –> energy becomes more ______ relative to the free electron
released from; increased; negative
Limitations of Bohr model
- only explains hydrogen
- neither accounts for intensities nor the fine structure of the spectral lines for hydrogen
- couldn’t explain binding of atoms
- unexplained quantum jumps (not good physics)
evidence for wave-nature of light
- diffraction & interference
- optical microscopes
- EM wave
evidence for particle-nature of light
- photoelectric effect
- compton effect
- black body effect
- photons
- convert light to electric current
Compton Effect
X-ray scattering by e- in atoms- photons have momentum
Number of photons is = to
energy density (square of EM field strength)
What is the wave aspect of matter
radiation (light)
as momentum increases, wavelength gets _____
shorter
as momentum decreases, wavelength gets ______
longer
heavy particles of matter are mainly _____-like
particle
extremely light particles of matter are mainly _____-like
wave
Particles in order from most particle-like to wave-like
proton, electron, photon
does the wave nature of a particle have a visibility threshold
yes,
the wave nature of a particle will only show up when the scale p is comparable (or smaller) with the size of h
wave nature of electrons
- matter waves
- electron microscope
- discrete (quantum) states of confined systems, such as atoms
particle nature of electrons
- electric current
- photon-electron collisions
parts of a wavefunction
ψ = R(r) Y(φ, θ)
- R(r) = radial part, gives you range of position
- Y(φ, θ) angular part, gives you shape of
What does the radial part of a wave function give you
- the principal quantum number (circumference), n
- the orbital angular momentum quantum number, l (max # determined by n-1)
What does the angular part of a wave function give you
- the orbital angular momentum quantum number, l
- the magnetic quantum number, m sub l (determined by +-l)
An orbital (wavefunction) is completely characterized by..
quantum numbers n, l, & m sub l
- defines orbit of electron
- solves Bohr model
- consistent w/spectrum lines & Bohr model
What is special about the orbitals of the H-atom
all orbitals of the same value of n have the same energy
equation for # of orbitals
n^2
ψ
value of the amplitude of the electron wave at any position in space
ψ^2
corresponds to the probability of finding the electron at any point in space
- probability density
Electron density map
the more time the electron visits a particular point, the darker the negative becomes
Radial probability distribution grap
plots the total probability of finding an electron in each spherical shell vs the distance from the nucleus`
size of 1s orbital
radius of the sphere that encloses 90% of the total electron probability
The larger the # of radial nodes in an orbital, the _____ the energy of the orbital
higher
of radial nodes =
n - l - 1
of planar (angular) nodes increases with ______
l
total # of nodes =
(radial + angular) = n - 1
orbital
- a wavefunction defined by quantum number n, l, & m sub l
- a region of space ‘occupied’ by an electron
- have energies, shapes, & specific orientations in space
d orbitals
- clover shaped
- ## important for metals
f orbitals
- not involved in bonding in any compounds
____ are said to be isoelectronic with the H-atom
Ions
The attractive Coulomb force is much bigger due to the higher _____ charge of the nuclei
Z+, (more protons)
Increasing Z charge has what trend
atomic orbitals contract & come closer to the nucleus
What is the effect of the Z^2 term
to increase the energy level spacing
What is a flaw of the schrodinger equation
fails if atom has > 1 atom
What fields does an electron have
an intrinsic magnetic field that interacts with its orbital magnetic field
Dirac
- tried to solve Schrodinger’s equation
- extended wave mechanics to include special relativity & an extra coordinate– time
- yielded a new QN- an intrinsic angular momentum of the electron (ELECTRON SPIN)
greater nuclear charge _____ sublevel energy
lowers
Orbital approximation
- make a polyelectronic atom like a 1e- atom
- assumes every electron to be on its own experiencing an eff nuc charge
- then the orbitals for the electrons take the form of those in H but their energy & sizes are modified by simply using eff nuc charge
electrons in the same level lead to a _____ lower Zeff
slightly
Electrons in an inner level lead to a _____ lower Zeff
much
Electrons in _____ energy levels shield the outer electrons very effectively
inner
Penetration
- to get close to the nucleus
- energy does down when it gets closer to the nucleus; also ^ negative
- arises from angular nodes in wave function
- occurs when electron gets excited
screening/shielding
to block the view of other electrons of the nucleus
Penetration _____ nuclear attraction & ____ shielding
increases; decreases
higher electron energy =
- easy to remove electron
- farther from nucleus
splitting
- caused by penetration & its effect on shielding
order of sublevel energies
s < p < d < f
order of effective nuclear charge in a polyelectronic atom
zeff (s) > zeff (p) > zeff (d)
Energies of atomic orbitals are affected by
- nuclear charge
- shielding by other electrons
A higher nuclear charge
- increases nucleus-electron interactions
- lowers sublevel energy
Shielding by other electrons _____ the full nuclear charge to an eff nuclear charge
reduces
orbital shape affects what energy
sublevel energy
Effective nuclear charge
lower than actual nuclear charge
- increases toward nucleus (ns > np > nd > nf)
- Zeff = Z - S
- Z = protons
- S = electrons shielding, # core electrons
General energies of subshells of the same principal QN
s < p < d < f
electron-electron repulsion
- removes degeneracy
- electrons less tightly bound to the nucleus
Quantum Wave Mechanics of the Atom explains…
electron configuration of the atoms
Aufbau rule
- aka building up principle
- determines electron config
- electrons are always placed in the lowest energy sublevel available
1. within a shell (n) the filling order is s>p>d>f
2. within a subshell (l), lowest energy arrangement has the highest # of unpaired spin (Hund’s)
3. The (n+1)s orbitals always fill before the nd orbitals
4. after lanthanum, the 4f orbitals are filled
5. after actinium, the 5f orbitals are filled
core electrons
electrons that are in filled, inner shells & not involved in chem rxn
Maximizing the # of parallel spins- the exchange interaction
- each electron pair w/ parallel spins leads to a lowering of the electronic energy of the atom
p subshell orbitals
3 orbitals w/ same energy
d subshell orbitals
5 orbitals w/same energy
f subshell orbitals
7 orbitals w/same energy
Hund’s rule
when orbitals of equal energy are available, the lowest energy electron config has the max # of unpaired electrons w/parallel spins
- parallel spin config of lower energy for degenerate orbitals
- every orbital has to occupy one electron first before doubling up
Elements in the same group of the PT….
- have the same outer electron config
- exhibit similar chemical behavior
- therefore… similar outer electron configs correlate w/similar chem behavior
- are isoelectronic w/respect to # of valence electrons
Ground state of Chromium
[Ar] 4s1 3d5
- because of 2 half-filled subshells
Ground state of Copper
[Ar] 4s1 3d10
- because of half-filled subshell & a filled subshell
filled subshells and # electrons
s: 2 e-
p: 6 e-
d: 10 e-
f: 14 e-
Isoelectronic
atoms/ions that have identical #’s & electorn configs
cation
positive ion formed by removing electrons from atoms
anion
negative ion formed by adding electrons to atoms
removal of electrons from transition metals
remove ns electrons & then (n-1)d electrons
paramagnetic
- attracted to a magnet
- atoms (or ions) w/unpaired electorns
diamagnetic
- repelled by a magnet
- atoms (or ions) w/out unpaired electrons
Elements in the same row…
- show regular trends in their properties due to the continuing increase in # of valence electrons until a shell is filled
atomic radii
- Half the distance btwn nearest atoms in element
- for nonmetallic atoms; estimated form their covalent solids (elements/compounds) since they don’t form diatomic molecules
- for metallic atoms; calculating half of distance btwn metal atoms in solid metal crystals\
- for ions;interatomic distance in ionic crystals
Valence electrons
- major role in periodic properties of atoms
- simultaneously attracted to + nucleus & - electrons
as shielding increases, effective nuclear charge…
decreases
Trends across a period
- # protons increase
- # core electrons stays same
- valences drawn closer to nucleus
- Zeff increases
- atomic & ionic radius decreases
- Ionization energy increase
Trends down a group
- atomic & ionic radius increases
- ionization energy decrease
Ions and their relative sizes
- cation smaller than neutral atom (cores exposed, zeff incr, remaining e more tightly bounded)
- anion bigger than neutral atom (increase e-e repulsion, no change of zeff)
a larger atom has ___ potential energy
lower
ionization energy levels in order
l1 < l2 < l3
- removing an electron from a positive ion is more difficult than removing it form a neutral atom
Metals
- form cations
- have smaller # of electrons in valence shells
- low ionization energies
- s, d, f , and some p block
metallic character
- related to atomic radius & ionization energy
- increases to left of period & down
nonmetal
- larger numbers of electrons in valence shells
- form anions
- all in p-block
