Chem Chapters 7-8

Number of orbitals within the s subshell

1

First ionization energy trend

1. As you go across a period from left to right first ionization energy increases This happens bc all electrons in a column are still in the same orbital (so no electrons being "shielded" from positive charge of nucleus by other electrons) but as you move along the column, each atom has more protons that pull those electrons in more 2. First ionization energy decreases as you go down a group because the electrons being removed are increasingly further from the nucleus

What are the four quantum numbers that describe electron orbitals and what do they mean

1. Principal quantum number, n Tells you about the size of an orbital (and the orbital that an electron is in also tells you about its energy; all electrons with the same n have the same energy, E) Is always an integer, never less than 1. This is the same n we used in the hydrogen equation, ∆E= -hcR(1/nf²- 1/ni²) 2. Angular momentum quantum number, l Related to shape of an orbital Covers every integer from 0 to (n-1) So if n=3, then l= 0, 1, 2 Known as the "subshells" 3. Magnetic quantum number, ml Goes from -l to l (so if l=1 because n=1, then ml= -1, 0, 1) Tells you about how orbital is oriented in space 4. Electron spin quantum number, ms Can be one of two things: 1/2 (up) or -1/2 (down) Pauli exclusion principle: in an atom no 2 electrons will have same set of 4 quantum numbers This is the reason that you can only have 2 electrons per orbital (they already will have the same n, l, and ml; they need a different ms and there's only 2 possibilities)

Principal quantum number

1. Principal quantum number, n Tells you about the size of an orbital (and the orbital that an electron is in also tells you about its energy; with hydrogen atom, all electrons with the same n have the same energy, E) Is always an integer, never less than 1. This is the same n we used in the hydrogen equation, ∆E= -hcR(1/nf²- 1/ni²)

What are the 4 rules of the photoelectric effect

1. When frequency of light varied, no electrons are emitted by a given metal below a specific threshold frequency, v₀ 2. For light with frequency lower than the threshold frequency (v<v₀), no electrons are emitted regardless of the intensity of the light 3. For light with frequency greater than the threshold frequency (v>v₀): a. the number of electrons emitted increases with the intensity of the light b. the kinetic energy of the emitted electrons increases linearly with the frequency of the light

KE electron equation (what are v and v₀)

1/2 mv² or hv-hv₀ where v is the energy of the incident photon and v₀ is the energy required to remove electrons from the metal's surface

Angular momentum quantum number

2. Angular momentum quantum number, l Related to shape of an orbital Covers every integer from 0 to (n-1) So if n=3, then l= 0, 1, 2 Known as the "subshells"

What is the speed of electromagnetic radiation

2.99*10⁸ m/s in a vacuum

What does each part of this mean: 2p(sub x)

2=n l= l value x= orientation in spave (along x axis, seek book page 271)

How many subshells are in the n = 3 shell?

3

Number of orbitals within the p subshell

3

Magnetic quantum number

3. Magnetic quantum number, ml Goes from -l to l (so if l=1 because n=1, then ml= -1, 0, 1) Tells you about how orbital is oriented in space

Difference between shells and subshells

4 is a shell, 4f is a subshell

Electron spin quantum number

4. Electron spin quantum number, ms Can be one of two things: 1/2 (up) or -1/2 (down) Pauli exclusion principle: in an atom no 2 electrons will have same set of 4 quantum numbers This is the reason that you can only have 2 electrons per orbital (they already will have the same n, l, and ml; they need a different ms and there's only 2 possibilities)

Which orbital will fill first: 4s or 3d?

4s!! The (n+1)s orbitals always fill before the nd orbitals

Number of orbitals within the d subshell

5

Number of orbitals within the f subshell

7

What is one way to describe an orbital

A specific wave function (see page 267- wave function is coordinates of electron position in 3d space) Orbital is space where there's 90% probability of finding electron According to book, best to picture it as "three dimensional electron density map"

Anything that is traveling at any speed and has mass will also have

A wavelength (just very very small for most things)

Anything with mass also has _________________-

A wavelength bc of be Broglie's equation, m= h/λc

All matter exhibits both _______ and _______ properties

All matter exhibits both particulate and wave properties

Difference between polyelectronic atoms and the hydrogen atom

All the orbitals in a hydrogen atom in a give principal quantum level (n) have the same energy; not the case for polyelectronic atoms (Es<Ep<En<Ef) Ie electrons prefer to be in the s level, then p, d, f Bc it's more probable that electron in s level is closer to the nucleus

Arfbau principle

As protons are added one by one to nucleus, creating range of different elements, electrons are also added into the atom orbitals

Atomic radius trends

Atomic radius decreases moving from left to right (bc same amount of orbitals in a row, but more protons in nucleus pulling in electrons as you move down the row), and increases as you move down a column (more orbitals) See page 290 in book for visual representation

Diffraction

Bending of waves around an obstacle or a gap in a wall thing (think of ocean waves and rock drawing) Place where waves interact can be constructive or destructive

DIfference between orbital and bohr orbit

Bohr orbits aren't actually how electrons move; says that electrons move in distinct orbits, which predicts hydrogen, but nothing else. Orbitals, in contrast, are based on uncertainty bc you never really know where the electron is Leads to the heisenberg uncertainty principle: ∆x*∆(mv)≥h/4π States that for a very small particle like an electron, don't know exact motion of electron

What is the maximum number of electrons in the n = 3 shell?

Can hold 2n² Draw the triangle thing. 1s, 2s, 2p, 3s, 3p, 3d s-orbitals can hold 2 electrons, p-orbitals can hold 6, and d-orbitals can hold 10 Total of 18 electrons

Constructive vs destructive interference

Constructive: 2 waves whose peaks and troughs are in sync lead to bigger waves, amplitude increase Destructive: 2 waves whose peaks and troughs are out of sync, resulting wave has lower amplitude (or if perfectly out of sync they completely cancel each other out)

Max planck (what did he discover)

Discovered that energy was quantized, meaning that energy was gained or lost in a whole number multiple (he called this multiple the planck constant)

How to draw an orbital diagram

Do the normal 1s2s2p thing but under the s subshell draw one box to represent one orbital, under the p subshlells draw 3 boxes to represent 3 orbitrals Then within those boxes add one up arrow (for up spin) and one down arrow (for down spin) if there's two electrons; if only one electron in that orbital, just draw an up arrow See page 278 REMEMBER; let's say you have 4 electrons that are going to fit into the 2p orbital. You will need one box with an up and a down arrow, and the other two boxes will have one up arrow each THIS IS BECAUSE ELECTRONS WITHIN AN ORBITAL DO NOT WANT TO BE PAIRED Think of this like the electrons want a "single"; they don't want to have a roommate, and will only have a roommate if no "singles" are open

What is unique about hydrogen gas through prism

Does not give a continuous spectrum; only a few discrete wavelengths. This is bc only certain energies move the electron up to an excited orbital (and therefore it releases a distinct amountof energy w a distinct wavelength when that electron drops back down to n=2 wavelength)

Equation for hydrogen atom orbitals/energy. Also equation for change in energy (what are Z and n?)

E=-hcR (z²/n²) h is the planck constant, c is the speed of light, R is the Rydburg constant which is 1.097*10⁷ 1/s (all will be given) When multiplied together the constants come out to 2.178*10⁻¹⁸ joules Z is the nuclear charge, so +1 for hydrogen n is the orbital that it's in Therefore ∆E= Ef= Ei So use the E=-hcR (z²/n²) equation for both Ei and Ef, and the only thing that will change is n, the orbital #

Theory of relativity equations

E=mc² Which can be combined w E₀= hc / λ to get m= h/λc

Dual nature of light

Electromagnetic radiation has characteristics of both wave and particle

What are valence electrons (ie what are the valence electrons in a sodium atom)

Electrons in the outermost principal quantum level of an atom Ie valence electrons of sodium are the 2s and 2p electrons

Electron affinity trend

Energy needed to add an electron More positive down the group, more negative across the period Lots of exceptions (but as you would expect, elements like O and Cl that become anions easily have higher electron affinities)

Equation for the energy of a photon

Ephoton=hv=(hc)/v

Equations for E₀

E₀= hc / λ Which comes from the equations c=λv and E₀= hv₀

Equation for the minimum energy needed to move an electron

E₀= hv₀ The threshold frequency represents the minimum energy needed to move the electron from the metal's surface.

Which would be greater: first ionization energy, or second ionization energy?

First ionization energy is the energy required to remove the highest-energy electron of an atom. Second ionization energy is the energy needed to remove the next-highest-energy electron. I2 is a lot higher pretty much all of the time. For example if you go from I to I+, all of the remaining electrons are more closely bound to the atom bc it now has a positive charge. Also, if one electron is for example removed from the p orbital, and then the next one comes from the s orbital, it's easier to remove the p orbital one bc that orbital is higher energy Will also take a lot of energy to remove "core" electrons (any electrons that are not valence electrons)

What is the variable for frequency, and what is the unit for frequency and what does it mean

Frequency, v, units are hertz which are seconds⁻¹

How many subshells are within each shell

In the first shell (n=1), we have: The 1s orbitals In the second shell (n=2), we have: The 2s orbitals The 2p orbitals In the third shell (n=3), we have: The 3s orbital The 3p orbitals The 3d orbitals In the fourth shell (n=4), we have: The 4s orbital The 4p orbitals The 4d orbitals The 4f orbitals

What are the units for the planck constant

J*s which are equivalent to kg*m²s because 1 joule= 1 kg*m²/s²

What is KEe and what are the equations

KEe is the kinetic energy of the electron that is liberated KEe = 1/2 (me)(v²) Where me is the mass of the electron omitted and v is the frequency in hertz (seconds⁻¹) and the equation for the work function: KEe= hv-hv₀ Where hv is the energy of the incident photon, v₀ is the necessary frequency necessary to liberate the electron

What is the equation of the work function

KEe= hv-hv₀

When using the m=h/(λv) what are the units for m

Kg

Light with a frequency less than the threshold frequency produces_______ electrons

Light with a frequency less than the threshold frequency produces no electrons bc a photon with energy < E₀ (v<v₀) cannot remove an electron

What is E₀

Minimum amount of energy needed to liberate at least one electron from metal This is the work function (may be given as amount of energy needed to remove one mole of electrons from one mole of atoms on the surface of a metal, so just use avogadro's number bc you know how many atoms or molecules are in a mole)

What is the key thing to remember about the orbitals described by schrodingers equation

None of the orbitals are circular- this is not the Bohr model of the atom that we've been using for hydrogen

Orbital shapes and energy of H

Ok all of this is only true for hydrogen but: Know that E= -hcR(z²/n²) And that n= the principal quantum number, which is always an integer Therefore energy only changes if n changes All electrons with the same n have the same energy, even if s and ml and ms are different

How do electrons move in the hydrogen atom (what does the orbit look like/how does it work)

Only certain circular orbits have a circumference into which a whole # of wavelengths of the standing electron wave will fit. Other (non-integer) orbitals produce destructive interference of the electron wave and are therefore not allowed See slide in 11/7 notes

Difference between shells, subshells and orbitals

Orbitals that have the same value of the principal quantum number n form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number l. Chemists describe the shell and subshell in which an orbital belongs with a two-character code such as 2p or 4f. The first character indicates the shell (n = 2 or n = 4). The second character identifies the subshell. By convention, the following lowercase letters are used to indicate different subshells. s: l = 0 p: l = 1 d: l = 2 f: l = 3

The photoelectric effect

Phenomenon in which electrons are emitted from the surface of a metal when light strikes it.

bohr model of the hydrogen atom

Quantum model, suggests that electron moves around hydrogen atom only in certain circular orbits. Gives you the E=-2.178*10⁻¹⁸ J(Z²/n²) Works really well, but only for hydrogen atom

Identify allowable combinations of quantum numbers for an electron. Select all that apply. a. n=2, l=1, ml=1, ms=-1 b. n=4, l=1, ml=2, ms=1/2 c. n=3, l=-2, ml=-2, ms=-1/2 d. n=2, l=2, ml=1, ms=1/2 e. n=5, l=1, mf=1, ms=1/2 f. n=3, l=2, mf=-2, ms=-1/2

Remember L goes from 0 to (n-1) ml goes from -L to L ms can be one of two things: 1/2 (up) or -1/2 (down); 2 electrons Possible: e, f

Which electron is more closely attracted to the nucleus: an electron in the 1s orbital or 3d?

SO both of the negatively charged electrons in the orbitals are attracted to the positive nucleus. However, the electron in the 1s orbital is right next to the nucleus; the one in the 3d orbital has negative electrons that it is repelled by in between itself and the nucleus

Consider a single photon with a wavelength of λ, a frequency of ν, and an energy of E. What is the wavelength, frequency, and energy of a pulse of light containing 100 of these photons?

Same λ, same v, different E

Draw out a diagram of which orbitals fill for various parts of the periodic table

See page 281 of book

How is the size of a particular electron orbital determined

Size of space where there's a 90% chance of finding the electron

Why does the KE of omitted electrons increase linearly

So first you need a certain amount of energy to release the electron, which is E₀ Then all of the other energy that you give the electron after that point will give it more kinetic energy, which is why the KE increases linearly

How many orbitals are in the n = 3 shell?

So in the third shell, you have : The 3s orbital (s-kind has only one orbital) The 3p orbitals (p-kind has three orbitals) The 3d orbitals (d-kind has five orbitals) 1+3+5=9

Electron moved from n=1 to n=2, how much energy and what wavelength (hydrogen atom)

So nf=2, ni=1 Use ∆E= -hCR(1/nf² - 1/ni²) hcR= 2.178*10¹⁸ J Get 1.634*10¹⁸ J of energy Use λ= hc / ∆E λ= ?

Electron diffraction

So the atoms in the molecule are the "obstacles" which electrons are diffracted off of when an electron beam is shot through a crystalline structure. Because the resulting electrons that are bent around the atoms might have constructive or destructive interference with one another, when you detect the electron patterns on the other side after they move through the molecule, you can reconstruct what the molecules looks like A bright spot is constructive interference, and a dark spot is destructive interference

Work fxn for lithium is 279.7 KJ/mol (takes that much energy to remove 1 mol of electrons from 1 mole of atoms on surface of metal) What is maximum λ (in amount of light that can remove 1 electron from one atom)

So the work function, E₀, was given in 1 mole electrons per one mole atom Also given in KJ Need to get it into joules per atom/electron 279.7 KJ/mol * (1 mol/ 6.022 *10²³ atoms)= 4.65 * 10⁻¹⁹ joules/electron Then use E₀= hc / λ Looking for λ 426 nm

What wave function corresponds to the lowest energy level for the hydrogen atom

The 1s orbital (remember- orbitals are specific wave functions; wave functions are coordinates of electron position in 3d space)

What are quantum

The discrete "energy packets" that energy is gained or lost in whole number multiples (quanta is plural)

Electron affinity

The energy change associated with the addition of an electron to a gaseous atom If the addition of en electron is exothermic then the sign of the electron affinity will be negative If the addition of the electron is endothermic then sign will be positive Units are KJ/mol

Ionization energy

The energy required to remove an electron from a gaseous atom or ion, where the atom or ion is assumed to be in its ground state

The filling of the actinides corresponds to the filling of the __________orbitals

The filling of the seven 5f orbitals

Photon

The particles that compose electromagnetic radiation

How many orbitals are within the s, p, d, and f subshells

The s-kind has only one orbital The p-kind has three orbitals The d-kind has five orbitals The f-kind has seven orbital

The filling of the lanthanides corresponds to ________

The seven 4f orbitals

Pauli exclusion principle

This is the reason that you can only have 2 electrons per orbital (they already will have the same n, l, and ml; they need a different ms and there's only 2 possibilities: 1/2 up or -1/2 down)

For all of the elements except transition metals the group labels indicate the _________of valence electrons for the atoms in those groups

Total number. See page 282

Schrodinger (talk about electron model he created)

Worked out model for hydrogen atom where electron orbited in "Standing wave" pattern He thought this might explain why different electron orbits are different distances from nucleus, and energy therefore emitted in certain specific "quantized" amounts, because only a certain circumference would allow for a standing wave; the wrong circumference would lead to destructive interference (see page 266 of book) This led to the equation Hv=Ev (the v symbol actually has a line through it, and is called the wave function- function of coordinates of electron position

Energy can travel through space as _______________________

electromagnetic radiation

What is a shell

electrons in different shells will have different values of principal quantum number n.

If a wave has a higher frequency it will have a ___________

higher energy

wavelength and frequency have a ______ relationship

inverse remember: c=λv, where λ is wavelength and v is frequency in seconds⁻¹/hertz

What information is needed to determine the general shape of an orbital?

l

What are l, sublevel designation, ml, and number of orbitals for n=2

l=0 (2s), ml=0, 1 orbital l=1 (2p), ml= -1, 0, 1; 3 orbitals

What are l, sublevel designation, ml, and number of orbitals for n=3

l=0, 3s, ml=0, 1 orbital l=1, 3p, ml= -1, 0, 1; 3 orbitals l=2, 3d, ml=-2, -1, 0, 1, 2; 5 orbitals

What are l, sublevel designation, ml, and number of orbitals for n=4

l=0, 4s, ml=0, 1 orbital l=1, 4p, ml= -1, 0, 1; 3 orbitals l=2, 4d, ml=-2, -1, 0, 1, 2; 5 orbitals l=3, 4f, ml= -3, -2, -1, 0, 1, 2, 3; 7 orbitals

What are l, sublevel designation, ml, and number of orbitals for n=1

l=0, there is the 1s orbital, ml=0, 1 orbital

If n=2 what are your other quantum numbers

l=n-1; therefore, l= numbers 0 through 1 Designation for l=0, n=2, is 2s When l=0, since ml goes from l to -l, ml=0 Has one orbital because there is only one possible ml There are two possiblities per orbital for ms (1/2 up or -1/2 down) so with one orbital, that's 2= ms Designation for l=1 n-2 is 2p When l=1, since ml goes from l to -l, ml= -1, 0, 1 Has three orbitals because there are three mls There are two possiblities per orbital for ms (1/2 up or -1/2 down) so with three orbitals, that's 2+2+2=ms

Equation for the mass of a photon

m = h/(λc)

What information is needed to determine the orientation of an orbital?

ml

What information is most important in determining the size of an orbital?

n

What information is needed to determine the energy of an electron in a many-electron atom?

n, l

How many electrons can each orbital hold

s-orbitals can hold 2 electrons, p-orbitals can hold 6, and d-orbitals can hold 10

Wavelength

the distance from the peak of one light or sound wave to the peak of the next. Electromagnetic wavelengths vary from the short blips of cosmic rays to the long pulses of radio transmission

Frequency

the number of complete wavelengths that pass a point in a given time, represented by wierd u/v thing (called "nu")

In the ∆x= h/ (4πm∆v) equation what are the variables

uncertainty of an object's position=Δx uncertainty in its velocity=Δv mass in kg=m

What is the variable for the wave function and what does the wave function tell you

γ (but with a line through the middle) Gives you probability of where to find an electron

Schrodingers equation: Hγ=Eγ What does each variable represent

γ is the wave function, which is a function of the coordinates of the electron position. Gives you a probability of where to find the electron H is the Hamiltonian operator E is the total energy of the system (same as the E we've already been working with)

Equation for wavelength of a particle (units for mass?)

λ = h/mv; mass in kg

Equation relating wavelength and frequency

λv=c Lamba is the wavelength in meters, v is the frequency in cycles per second, and c is the speed of light (3*10⁸ m/s)

Electron moved from n=6 orbital to n=1 orbital in hydrogen. How much energy was released and what wavelength of light is this energy

∆E= Ef= Ei E=-hcR (z²/n²) Ef is when n=1 Ei is when n=6 Z= 1 for both, bc that's the nuclear charge for hydrogen hcR= 2.178*10⁻¹⁸ So -2.178*10¹⁸(1²/1²) - [2.178*10¹⁸(1²/6²)]= -2.66 *10¹⁸ joules So thats how much was emitted Then rearrange E= hc/λ to find λ h=6.626*10⁻³⁴ Plug in a positive E because you need a positive λ (wavelength) Get 938 nm

Equation for the change in energy for a system, ∆E

∆E= nhv n is a integer, h is planck's constant (6.63x10⁻³⁴ J*s) and v is the frequency of the electromagnietic radiation absorbed or emitted

Heisenberg uncertainty principle: ∆x*∆(mv) ≥ h/4π What is each variable

∆x is uncertainty in particle position ∆mv is uncertainty in particle momentum h is planck's constant