137B- spectroscopy Flashcards
what is wavenumber
equation for speed of a wave (constant)
c= vλ
what are the trends in wavenumber, frequency, wavelength and energy of the EM spectrum
wavenumber- increases
frequency- increases
wavelength- decreases
energy- increases
Where is the visible light spectrum in terms of wavelength and what are the rough measurements
400-700 nm
how are speed and time related
inversely related
how are λ and v related. If λ increases what happens to v
inversely- λ increases v decreases
Inversely related
As I increases B gets smaller
Ek doubles
What type of EM waves are needed to move an electron up and down rotational levels, vibrational levels, and electron levels
rotational- microwaves (low E) small gaps ΔE
Vibrational- infrared
electron levels- Visible/ UV
difference between absoption vs emission spectra
emission- shows the colours emitted
absorption- shows the colours absorbed
Which part of the EM spectrum does rotational spectroscopy relate to
high microwave to low infrared
E= 1/2mv^2 is the equation for KE. What is the new equation for finding the KE of a rotating molecule
v is the velocity, but in this equation this is subbed for r2 ω2
the gymnast goes faster when they go off the bar into a tuck. Its mass and energy is fixed. Using this analogy, how does the radius of a rotating molecule change the angular velocity
when radius gets smaller the angular velocity increases as long as E and mass stay constant
equation for the total rotational energy (inertia) of a molecule (for molecule with several different atoms all different distances from the centre of mass due to different bond lengths)
sum of mass x radius squared
if a molecule has 3 axis of rotation x,y and z, how many different moments of inertia will it have
3
if the molecule rotates in any of these directions the co-ordinates of each atom changes
1 moment of inertia is in 1 direction only
How many moments of inertia do diatomic molecule have
2
to have a moment of inertia the coordinates of each atom need to change when it is rotated
In a and b the co-ordiantes change, but rotating down the H-Cl bond (c) the co-ordinates don’t change so we can cancel out that moment of inertia
How many moments of inertia do diatomic molecule have
2
to have a moment of inertia the coordinates of each atom need to change when it is rotated
In a and b the co-ordiantes change, but rotating down the H-Cl bond (c) the co-ordinates don’t change so we can cancel out that moment of inertia
if one atom is more heavy than the other where would the centre of mass be
for a diatomic molecules, because the centre of mass might not lie equally between the two atoms, we use µ instead of m in I=mr2. µ is the reduced mass. What is the equation for µ using the masses of each individual atoms
this gives an average mass to put into the equation for inertia
What is the one assumption in rotational spectroscopy with equations such as this used for diatomic molecules
rigid motor model the bond length of the molecule stays the same no matter how fast it is rotating/ bond length can stretch with increasing speed
hint means that reduced mass needs to be in kg not kgmol-1
what are the units in the inertia equation
what are forbidden transitions
where there is zero probability of a transition from one energy state to another. Selection rules tell you which transitions are allowed and which ones arnt
in rotational spectroscopy, selection rules tell you which transitions are allowed and which ones arnt. What is a gross selection rule vs specific
gross- wether that molecule will even absorb that type of radiation
specific- if the molecule does accept the radiation, this tells you what transitions are allowed /which levels you can jump between
What are the gross and specific selection rules for rotational spectroscopy/ for a molecule to interact with microwave radiation
e.g can’t go from 1 to 5
Would CO2 and H2O have a rotational spectra
selection rule for rotational spectra- must have dipole
CO2 wouldn’t as it doesn’t have a permanent dipole but H2O does
which of these will have a rotational spectra
specific selection rule for rotational spectroscopy is the electrons can only go from one energy level above or below
equation for the energy of any rotational level in a molecule
what is B
the rotational constant
the rotational constant B can be in J, wavenumber (cm-1) or Hz, how does the bottom equation change depending on what unit you want it in
not squared in Hz, not squared and c added in cm-1
What happens to B if bond length decreases (radius gets smaller)
B gets bigger as r is on the bottom
What happens to B if reduced mass decreases
B gets bigger (is on the top of the equation so they change in opposite directions)
Which one of these molecules will have a rotational spectra using gross selection rules
CO and HCl
-hetronuclear diatomics
-permenant dipole
what is the equation for the energy of an energy level using B
As B gets bigger what happens to the energy levels
they get further apart
Why is the next energy level up from J always J+1
selection rules says can only go up one level at a time
What is the equation for any ΔE of any energy gap in a molecule (the energy of the photon the gap needs to absorb)
J+1 is the top level
B is rotational constant
what does ΔE (energy gaps) only depend on
bond length and molecular mass
What is the absolute energy, ΔE, and ΔΔE of J=5
absolute= 30B
ΔE = 10B (energy gap)
ΔΔE= 2B (difference between added B each time)
What is always the gaps between the peaks
2B
Why are all the gaps evenly spaced
2B- the difference between each one is constant
If the difference between all consecutive values is 3.84, what is B
How would you convert B from cm-1 to “real energy units”
h x c x v (wavenumber)
What happens to B/ the spacing between spectra lines when the mass of the molecule increases [in example 12C becomes 13C or 16O becomes 18O]
mass increases= smaller rotational constant spacing gets smaller with heavier molecules
-reduced mass gets bigger
What are the small lines [pointed out on the diagram] due to
low levels of 13C isotope in the spectra (these smaller lines are closer together than the other ones for 12C )
Which mass change [due to isotopes] will have the greatest effect on how much B changes
Cl 35 to 37 or
H 1 to 2
larger effect when changing the mass of smaller elements
H 1 to 2
We assume in the equation that bond length doesn’t change no matter how fast the molecule is rotating. In the real world, when bond length increases
r gets longer, B gets smaller, gaps don’t become constant any more and start to get closer together
Why does a transition graph have this shape (low, high, low intensities)
Absorption is related to number of molecules in that rotational state which can be promoted to the next state by absorbing a photon
What 2 factors does the intensity depend on (how the peaks are spread out high to low)
occupancy- how many molecules are in each rotational state to begin with.
(no going to absorb many photons If lots of molecules in one transition state [test tube diagram])
-this occupancy is dependant on temp
Molecules will occupy a range of energy levels depending on the thermal energy available
degeneration- Levels with the exact same energy within a molecule
A molecule may have more than one transition that gives rise to the same photon energy being absorbed
Which diagram has the highest temperature
getting higher in temp/ at higher temp more molecules can occupy higher rotational energy levels
How does this prove that the peaks will have different intensities
going from 1–>2 the intensity will be 4
2–>3 will be 2 and so on.
Intensity gets less and less as wavenumber increases as there are less molecules occupying higher energy rotational levels
why would there be a peak of higher intensity at electrons jumping from 1s to 2p than 1s to 2s
the electron could go into any of the 3 orbitals. More pathways for your molecule to get into higher energy
how does the population of energy levels change when ΔE increases or decreases
ΔE smaller- more distribution as molecules needs less energy to climb up levels
ΔE bigger- almost all molecules might be in lower energy state
what equation gives the ratio of molecules in the upper vs lower energy levels [Boltzman distribution equation]
what equation gives the ratio of molecules in the upper vs lower energy levels [Boltzman distribution equation]
how much energy there is in each degree of kelvin
When putting E into the equation what do you have to do to it
What do the numerical answers mean in writing
0.13- about 10% molecules are in higher state compared to the lower
0.995- about 99% molecules are in higher state compared to lower
what does this mean
for each J energy level, that level has 2J+1 other degenerate levels
define all the terms in this equation
n upper/ n lower= ratio number molecules in upper and lower energy levels
g upper/lower= degeneracy of upper/lower levels
E= energy difference between 2 levels
Kb= Boltzmann constant
T= temp in K
What is the ratio of g upper/ g lower of this energy diagram
J=0 2J+1 = 1
J=1 2J+1 = 2J+1 or (3)
What is this equation modified when working out anything relative to ground level (one of the levels is the ground state) J=0
Infrared photons are shorter/longer wavelength than microwave
shorter
define simple harmonic motion
as a system moves from equilibrium there is a restoring force pulling it back
what is hookes law
k= constant [specific for each individual bond]
the further you push the molecule back the bigger the restoring force
what does the value of K tell you about the strength of a chemical bond
higher K= stronger bond
this is the equation for the frequency of a wave in simple harmonic motion/ define all the terms.
v= fundamental frequency (vibrations unit time [s])
k= force constant
µ= reduced mass
what is the equation for µ
this equation is given
how can we turn this equation into showing the energy in the vibration of the bonds not the fundamental frequency (v)
(e.g C=O is 1700 wavenumbers, and using this we can calculate what that is as an energy)
C=O is supposed to be at 1700nm [this is v], but this can change from molecule to molecule. Why is that
µ can’t change it is constant so K must change to change v
meaning the strength of the bond can change from molecule to molecule because K changes (K is related to bond strength, the higher K the stronger bond)
is bond strength positive/ negative for stretching
is bond strength positive/negative for compression
positive for stretching
negative for compression
What do these graphs on the left describe
this is to do with bond stretching and displacement of x
𝚿0 is the lowest energy level. The spike at 0 tells you you are most likely to find x to be 0 (the molecule is at equilibrium/ no stretching)
𝚿1= is next lowest E, it has some stretching and peak tells you what x (displacement from equilibrium is)
it makes sense that the peaks of 𝚿3 is the furthest away from 0, as the molecules can be stretched further apart
-think as where the biggest peak is where the two atoms are
what is the equation for energy of vibration quantum levels (in rotational this was E= BJ (J+1)
What is different between vibrational and rotational spectroscopy (rotational is E= BJ(J+1))
- rotational lines starts off close together and get more spaced out, these ones are all equally spaced
- No degeneracy in vibrational levels (each rotational level has a degeneracy of 2J+1)
vibrational levels are always equally spaced and separated by what
ΔE between levels is always = 0.5 hv
what are the selection rules of vibrational spectroscopy; gross and selection
gross rule- wether the molecule will interact with that electromagnetic radiation at all
specific- tell you which transitions between energy levels are allowed (same for rotational)
why can homonucleur molecules not have a vibrational spectra but heteronucleur can
homonucleaur- no dipole
heteronucleur - dipole and when the bond vibrates (stretches and compresses) the electron density is distorted therefore the dipole changes
why is a symmetric stretch not infrared (vibrational) active , so you wouldn’t see an IR peak from this stretching
[for polyatomics some stretches are IR active and some are not]
dipole doesn’t change
why do we only see one peak on a vibrational spectrum (IR) and not a series of lines
because all the energy gaps are the same so
why is there less spreading out of molecules In vibrational energy levels as oppose to rotational (more molecules will be in the lower vibration energy states, whereas rotational will be spread over loads of levels)
these are rotational spectra graphs for a low and high temperature. Why does the spreading out look like this
rotational energy levels are quite close together
at low temp- not many molecules are getting to high rotational levels small spread (maybe reaches J=8)
high temp- molecules can reach higher rotational energy levels so there is more spreading out
question- how much thermal energy needs to be added to the system to move 1% of molecules from V=0 to V=1 [in HCl for example]
Kb = 1.38 x 10-23
these are rotational spectra at low and high temperatures. vibrational levels are much further apart than rotational, so most molecules will be in V=0 for rotational levels and very few in V=1
number molecules in V=1/ number molecules in V=0 is **equal to 0.1 (for 10%)
-ΔE is energy gap between V=1 and V=0
-use natural logs to get rid of e (write this down somewhere)
h=6.62 x 10^-34
wavenumber is related to energy in the form
E= hcṽ
µ= m1 x m2 / m1 + m2
HF has a stronger force constant than HI. What does this tell you about the bond strength of HF and HI
(e.g how is force constant related to bond strength)
ṽ=stretching frequency
k= force constant
shorter bonds = higher force constants
stronger bonds = higher force constants
HF will have a stronger bond than HI
when µ gets smaller what happens to E
E gets bigger
lighter/heavier atoms will give you higher wavenumber vibrations
lighter atoms
If isotopes change (e.g H is swapped for D) what happens to µ and therefore E
µ increases, so E (wavenumber) decreases
two equations relating E to k and E to µ
why does C≡C vibrate at a higher wavenumber than C-C and C=C
the stronger the bond, the faster the bond will vibrate
why does C-H vibrate at a higher wavenumber than C-D
where does the finger print region of the molecule come from (vibrational modes)
it is the number of vibrational modes molecule has (eg. aspirin has 21 atoms so 3N= 63 DoF, and 3N-6 leaving 57 vibrational modes)
This diagram of aspirin has 57 vibrational peaks in the fingerprint region
when does this assumption not hold [not simple harmonic motion]
x axis- how far the bond stretches
y=energy level
bond breaks when curve goes flat (dissociation limit)
at large extension and at large compression potential energy is not symmetric
-short distances atoms overlap and E will spike dramatically
-large distances bond will break and potential energy will disappear
how does this equation change for anharmonic
gaps get smaller and smaller in anharmonic/ dont stay the same size like in harmonic
v= energy level (e.g 1, 2, 3)
A= constant
v= frequency
what happens to the selection rules in a more realistic situation (anharmonic)
-will see smaller peaks at double [V=0–>V=2] or triple [V=0–>V=3] the wavenumber called overtones
for this slide the main peak is at 2143 which is V=0 to V=1, but 4260 is V=0 to V=2
which peak is the overtone peak
the smaller one (will be jumping two energy levels not just one like the big peak)
what needs to happen for a peak in V-R spectra (jumping from both rotational and vibrational levels)
needs to obey rules for energy level jumping in rotational and vibrational spec
Rules are can only go up one level in both (e.g V=0 –> V=1 and J=1 –>J=2
This is a vibrational-rotational spectra.
How does the image on the left explain the shape of the diagram on the right
left diagram= Vibrational levels in green V=0 and V=1
and rotational levels in red J
The arrows are allowed transitions
-the blue line will not show up on the spectra because there is a change in V but no change in J
low population at tails of graph due to low population of high rotational states
-grey lines are less energy than blue line
-red lines are more energy than blue lines
what is the ramen effect
photons are shined onto a molecule where it doesn’t meet the energy gap to absorb. most photons go straight through and are scattered but a very small amount of photons go in with an energy and then come out with less or more of that energy.
why would a photon emerge with more energy or less energy
how are these 2 diagrams related
how are diatomic molecules ramen active but not IR active
not IR active as they dont have a dipole
-when the molecule vibrates the electron cloud changes shape
Deduce wether these stretches would be seen on Raman spectroscopy or IR
1- the polorizability has changed because the electron clouds are different shapes/ dipole isn’t changed by stretching bonds at same time
2- even though the electron cloud has changed shape, the two end ones are mirror images so the polorizability hasn’t changed
what makes one peak higher than the other
this is UV- visible light absorption spectra
bigger peak= bigger number of photons absorbed
what is the method to obtain a UV- visible light absorption spectra
cuvette containing solution into a machine
this is a cuvette containing solution for a UV- visible light absorption spectra. What is the equation for absorbance
what is the beer-lambert law
what does a weak/strong absorbance coefficient mean in terms of colour
strong coefficient- strongly coloured
weak- weakly coloured
what do we plot to get a linear graph
beer-lambert law is only applied on the linear section
what are the units for molar absorption co-efficinet (ϵ)
-A doesn’t have units
ϵ has to cancel out c and l as A doesn’t have units
So ϵ will be whatever c and l are
(e.g. mol-1 dm-3 cm-1)
the beer-lambert law is A=ϵcl
To get an absorbance of 0.01 A, what is the smallest amount of concentration of solution that can be used to get this
ϵ for this material is large = 250 m2 mol-1
4 x 10-6
For example, Iron has a very weak absorbance, so you would either need a very high concentration of it in the cuvette or have a long curve (increase l)
-what can we add to low absorbers to reduce their limits of absorption
complexing agent to make it a ligand
what does the angular momentum quantum number (L) tell you
what type of orbital the electron is in
L=0 is s orbital
L=1 is p orbital
L=2 d orbital
L=3 f orbital
what is the magnetic quantum number
tells us which way the orbital is facing
(e.g a p orbital can have directions of ml= -1, 0 or +1
what is a spin quantum number
tells you wether the electrons spin up or down
describe the two rules for promotion in transition metal compounds
spin rule- if the electron has an upwards spin, it must stay in that spin in the next level up
orbital rule- for symmetrical molecules you cant go from p orbital to p orbital, or s to s
-only can move up and down s to p to d
most transition metal complexes are symmetrical, and so cannot meet the selection rules, so electrons cant move between energy levels, and therefore most would be colourless- however this is not the case
-what is one way of a ligand complex overcoming the symmetrical selection rule
equatorial ligands can vibrate up and down, which breaks the symmetry
what is the way of breaking the orbital rule for transition metal complexes
the orbitals hybridise (mixing d orbitals with the ligands)- so when electrons jump its not technically from a d orbital to another d orbital, it Is from one hybridised orbital to another
OR
you can have electrons moving from ligands into empty orbitals on the metal (e.g. lone pair on oxygen move from p orbital to empty d orbital is metal)
explain why the top compound would be almost colourless but the bottom one would have some colour
-both have limited colour because moving from d orbital to d orbital which isn’t allowed (unless hybridisation)
-Mn has to change the spin of the moving electron swell as go from d–>d. Both are not allowed so very low probably of this promotion happening
-wheras Ti doesn’t have to change the spin of the excited electron/ can keep spin rule
-but d-d moving still isn’t allowed
why is permanganate so strongly coloured
rules- spin cant change
orbital- must travel between different orbitals
-electrons from Oxygens go into the Mn orbitals, which fits both of these rules so it has a high molar coefficient (ϵ)
-direct p orbital promotion to do orbital
why is the orbital rule partially obeyed, aswell as the spin rule for this compound
partial mixing of p and d orbitals mean electrons are jumping between hybridised orbitals which is partially allowed
-mixed pd orbital to another mixed pd orbital
what is L and ml in cm/m
what is the particle in a box method for calculating the energy of an electron in this box
kinetic E- energy to delocalise it up and down the chain
potential E- is keeping the electron inside the box (outside box, pe goes to infinity)
1. we assume electron has no potential e because the electron always stays in the box.
-Therefore electron energy only related to KE and we know this equation
- electron can only have certain wavelengths while its in the box
n is quantum number (e.g. 1,2,3)
this equation can show the energy of any molecule. What do each of the letters mean
m and h are constants
n= quantum number (1,2,3)
h= planks constant
l= length of molecule
m= mass of electron
energy for different quantum numbers
What is the energy of the photon between n=2 and n=3 (energy gap between 2 and 3)
the chain has 4 electrons and we want to promote one of the n=2 ones to n=3 (in green)
could also use the equation E= (2n+1) x h2/8ml2
where n = bottom energy level
m and h are always constant
this is the equation for the energy of any quantum level (e.g. n=1,2,3) in a molecule. What is the equation for finding the difference in energy between two quantum levels
m and h are always constant
longer conjugated molecules absorb lower/higher energy photons
longer = lower energy photons
also longer= absorb longer wavelengths so the energy gets lower
why does promoting an electron in a molecule from a bonding orbital (2e) to an anti bonding orbital (no e), create vibrations
-this is a UV-vis spectra but it is lots of small lines instead of a smooth curve
force constant K is related to electron density between 2 atoms. When you remove one electron from a bond and promote it, you are left with a bond with only one electron between the two atoms. This changes K the force constant
therefore moving electrons in a molecule also causes vibrations
what is the frank-condon principle,
this graph shows the ground and excited state of an electron and the x axis shows the distance between the 2 nucleus that the 2 electrons are between (this is a bond)
-the arrows on the graph show the movement of an electron
-why do we take the black arrow route and not the orange
orange route from most stable ground state to most stable excited state would mean instantaneous movement of nuclei (x axis value changes)
-the nuclei mass is so big compared to the electrons that they cannot move instantaneously
-takes black path instead where it jumps up with no x axis change, then the vibrations relax towards the area on the graph where it is the more stable excited state
-basically on the black arrow path, the nuclei have more time to move and do not have to move instantaneously
How does the frank-condon explanation link to the diagram on the right
the electron will not move from green level to green level (most stable ground state to most stable excited state)
-it will move from ground state green to a red line in the excited state and take some vibrational energy with it
