Chapter 5!!!! Electronic Structure of Atoms and Ions Flashcards
- Atomic Orbital - explain
- Quantum Numbers and their allowed values
- Define Orbital Radial Probability Distribution
- What does angular node mean? Where would it be located?
- What does radial node mean? Where would it be located?
- How do you determine the quantum number/name of an orbital, how would you draw it on a cartesian coordinate system + phases and nodes
- in your head, what do orbital 3D diagrams/cross sectional/radial probability distributions look like?
- how do you calculate energy/draw energy level diagrams for one electron atoms and ions??
What does coulomb’s law describe??
PE of attraction between two charges
coulomb’s law
V(r) [proportionate to squiggly unfinished infinity] (q1*q2)/r
where V(r) = potential energy
q1 = charge of particle one
q2 = charge of particle 2
r = distance between two particles
in atomic units (ex -1 for electron)
lowest PE similarly charged particles??
lowest pe long distances large r, forces are repulsive
lowest pe oppositely charged particles??
short distances (small r)
what terms does the schrodinger equation include???
term rep KE, PE, and depends on 3 coordinates, as the electron is moving in 3D space
Spherical polar coordinates??
(r, 0 with line through horizontally, o with line through vertically)
image a coordinate plane with x,y flat on the ground @ 90 degrees between, z goes straight up 90 to x and y
r is the distance between point (electron etc) and the origin
0 with horizontal is the angle between r and z
o line verticle angle between projection of r onto the xy plane, and x
How do you write the wave-function for one electron species???
using spherical polar, and as a product of two parts;
R(r) and Y(0,o)
R(r) depends only on r and describes the size of the orbital, imagining origin is the nucleus
Y(0,o) depends on angles 0 and o and describes shape and orientation of the orbital
n principle quantum number
describes the size of the orbital - gives how many subshells in an atom
can only be whole numbers above 0; 1,2,3,4 etc.
can only be 1 value of n for each system
swirly l quantum number
indicates s, p, or d subshell;
l=0=s, l=1=p, l=2=d etc
can be any integer value between 0 and n - 1, ex if n = 4, l = 0,1,2,3
number of l values indicates how many subshells there will be, n values of l, so n also indicates how many subshells
also called the angular momentum quantum number
m swirly l quantum number
magnetic quantum number
takes on all integer (whole) values between and including -l and l
ex if l = 2, ml can be -2,-1,0,1,2
indicates number of orbitals and orientation within a subshell, ex if there are 2 m values there will be 2 orbitals from 1s to 2p
l values and their associated subshells
0 - subshell s
1 - subshell p
2- subshell d
3 - subshell f
n = 2, what are l and ml and what do they mean??
n = 2,
l =0, 1
if l = 1, ml can equal -1, 0, or 1
l = 1 indicates subshell p, and 3 ml values so 2px, 2py, 2pz - 3 orbitals
if l = 0, ml can only be 0
l = 0 indicates subshell s, so just 2s
4 total orbitals in n = 2
radial nodes!!
at radial coordinates, on r, like layers of the onion
number of radial coordinates = (n-1) - l
what gives total nodes
n - 1
angular nodes! <3
in the angular coordinates, like slices of the onion
total number is given by l
little summary of what n l and ml mean
n gives number of subshells, also refers to size of electron shell, 1 the smallest and so on
l determines which subshell; 0 means s, 1 means p, 2 means d, 3 means f
ml gives number of orbitals within a subshell specified by l
how many orbitals in the n shell?
n^2 orbitals total in n shell
how many orbitals for each value of l?
2l + 1 orbitals, each orbital has a unique ml value
what is the probability of finding an orbital at particular location?
proportional to psi (wavefunction)^2 and zero at a node
where does phase of the wave function change??
what does that mean??
over every node, switches sign
what equation gives radial probability distribution for s shell?
what is that equation based on??
4(pi)r^2*R^2
only based on r (RADIAL) r^2 would give max probability at the nucleus which isnt possible, so you need to multiply r by the total sa of a sphere
what do you multiply to find full probability of 3D atoms?
radial probability distribution x angular probability distribution
s orbitals!!!!
l = 0 therefore no angular notes
probability distribution varies with r only, spherical!!!
STILL RADIAL NODES you can have l = 0 with n = 4 and more, in that case there would be 3 radial nodes
remember n determines number of shells, if I have 1s only 1 shell, no radial nodes; 2s 2 shells so 1 radial node between shells; 3s, 3 shells, 2 radial nodes (1 between each shell)
1s vs 3s how does where you’re most likely to find an electron change???
3s more likely to find the electron further from the nucleus compared to 1s BUT you could still find it close, even closer than 1s electron just not super probable
does probability ever reach 0 to the right of the graph??
technically no, it extends to infinity but the it would be considered to be removed from the nucleus
how do trends in probability decay relate to different species, increase in Z
as the nucleus grows more positively charged ex H vs Li^2+, for comprehension only considering s subshell, probability is more noticibly greater closer to the nucleus (higher peak and closer to nucleus) and the probability decays faster because electrons are more attracted to the positively charged nucleus
how do you figure out what dimensions etc to draw your 3D model to???/ what do scientists do
s orbital
find the value of r for which 90% of the area of the radial prob distribution lies under, s orbital can be drawn to that r value
how would you draw a cross sectional diagram of an s orbital??
1 plane, either z x or zy or yx, nice little circle with nodes represented by dotted lines, arrow pointing to outside of circle with [r subscript 90%], LABEL PHASES, switch positive to minus or minus to positive every node
p orbitals!!!
there are 3 p orbitals , px, py, and pz
l = 1, therefore ml can be -1, 0, 1
ALSO l = 1 so 1 angular node
- number of radial nodes determined by (n - 1) - 1
^^ that means for each value of p, 2p, 3p 3 orbitals of each
they look like peanuts!!!
what equations represent p orbitals?
psi(px) ~ xR(r)
psi(py) ~ yR(r)
psi(pz) ~ zR(r)
R(r) = an exponentially decreasing function of r
x, y, and z represent distances along corresponding cartesian coordinates of the atom
where does the angular node occur for p orbitals???
there are 3 p orbitals, px py and pz.
px, for example, lies right across the x axis (kebabed by x). py kebabed by y, pz kebabed by z
the nodes occur for each when _ letter = 0, therefore at the plane of the other two (like the kebab was sliced in half at _ = 0
radial probability/radial nodes for p orbitals???
same as s, greater n value more likely electrons will be further but they can still be close!!
where would radial nodes be for p orbitals, how do you draw that?
imagine a cross section of a peanut, looks like an hour glass, each radial node would be like you cut the peanut with a circular cookie cutter nicely centered, remember to write phase changes too!!!
d orbitals!!!
d orbital when l = 2
2 angular nodes
therefrom ml can be -2, -1, 0, 1, 2
5 different d orbitals!!! these can be dxy, yz, xz, x^2y-y^2, z^2
for xy, yz, xz, the two angular nodes are coming up from the axis in the description, so it looks like theyre 4 ballons all tied together and each balloon condined to in a quarter of the _ _ axis in the discription - xy is zero where y equals 0 which is xz plane, and where x = 0 so yz plane
for x^2 - y^2 looks kinda that same, like 4 ballons, except angular nodes occur where the 45 degree mark would sort of be, extending up from the xy plane (where x^2 =. y^2)
the z^2 one is WIERD doesn’t look like 4 balloons, but rather like one big donut laying flat along xy plane but skewered by axis there is a donut hole. on either side of this donut, skewered only by z axis.
how to draw d orbitals
dxy show x and y axis with the 4 dew drops settled nicely each quarter
dxz show x z axis, dewdrops nicely nestled
dyz same, nestley dewdrops with z and y axis
x^2 y^2 - xy axis and 4 dewdrops but theyre skewered by the axis
dz^2 - z axis and either x or y, along z axis just two dew drops skewered by axis, +
on x or y axis on either side of the dew drops two circles (this is the cross section of the donuts
shell structure of an atom, explained!
all orbitals w same n value have maximum probability distributions about the same distance from the atom, leading to believe layered structures like onions!, greatest n in the valence shell, and define how an element/atom reacts with it’s environment
what describes the energy of an electron??
the function En = -2.18 x 10^-18 J x (Z^2/n^2)
energy depends on n only!! so electron in 2s 2p 2d all have the same energy
degeneracy
multiple states with the same energy
what does E = 0 correspond to
electron seperated at infinite distance from the nucleus, so ionized from an atom!!!
what makes the energy of the state increase
Z decreases (which is atomic charge) or n increases
what would an energy level diagram look like for an atom??
ground state energy, 1s, low down then biiiiig jump between that and n = 2, then littler jumps between all the others until almost immeasurable!
is the energy in an electron positive or negative??
negative due to coiulombic attraction, values depend on n and Z
