Atomic Structure and Periodic Trends

Question 1

What is the classical energy of a hydrogen electron and how has it been calculated?

Answer 1

E total= (1/2 mv²) - (e²/4πεr)

where m is the mass of an electron, e the fundamental charge, v the speed of the electron, and epsillon a constant, and r the distance between a proton and electron

This comes from the kinetic energy + potential energy of an electron

Question 1

What are the implications of a classical perspective on the energy of hydrogen?

Answer 1

V and R can have an infinite number of values, meaning the energy can take any value
The energy is continuous
Transitions should be possible for the entire spectrum

Question 2

How has a hydrogen emission spectrum been produced?

Answer 2

An electrical current is passed through hydrogen gas, resulting in EM radiation being released
This is passed through a prism in which the wavelengths are separated, producing a line spectrum

Question 3

What does the hydrogen emission spectrum show and how?

Answer 3

Energy is quantized
As the electron is absorbing energy, it will excite to a higher energy level, sometimes several
As the electron returns to its original energy level, EM radiation is emitted, corresponding to a wavelength seen

Question 4

What is the Rydberg equation?

Answer 4

v= -cRy(1/(n1²) - 1/(n2)²)

where v= frequency, c=speed of light, n=quantum number, Ry=Rydberg constant

Question 5

What are the series within the hydrogen spectra and how can they be used?

Answer 5

Using different starting values for the electron, i.e N1= 1 or 2 or 3… , we can calculate different frequencies for the different transitions
These are visible in the hydrogen spectra

For n=1, Lyman series UV
For n=2, Balman series, Visible light
For n=3, Paschen series, IR

The distance between two lines on the spectrum can be used to calculate the energy difference between quantum levels

Question 6

What is the formula for the energy of an orbital in hydrogen?

Answer 6

E= -Ryhc/n²

Question 7

What was Bohr’s theory and why did it fail?

Answer 7

Bohr proposed the observed frequencies could be explained by limiting the electron orbits to be circular and the equation
However, this provides no explanation for quantisation and just fits the observations
Additionally, the calculations do not fit other atoms, just hydrogen

Question 8

How can electrons be described? How did the Davisson Germer experiment help with this?

Answer 8

As particles, characterised by mass, momentum, position…
And as waves, characterised by wavelength, frequency, amplitude…, and can show properties such as interference and diffraction

The experiment showed diffracted electrons varied in intensity suggesting constructive and destructive interference

Question 9

What is the De Broglie equation?

Answer 9

p=h/w
momentum= Planks constant/wavelength

Question 10

What is a wavefunction?

Answer 10

A mathematical function taking into account the wave-particle duality of an electron, containing all information there is to know about particle, including position with respect to time

Question 11

What is the Schrodinger equation?

Answer 11

(-ℏ²/2me)∇ψ(x) +V(x)ψ(x)=Eψ(x)

Kinetic energy contribution + Potential energy = total energy

A differential equation, where psi is the wavefunction

Question 12

What are the solutions of the Schrodinger equation called?

Answer 12

Atomic orbitals, which are a specific type of wave function

Question 13

How can a wave function be split? What do these lead to?

Answer 13

Into the radial part R(r), and the angular part Y(angle1, angle2)

These leads to 3 quantum numbers
Radial gives the principal quantum number n
Angular gives the angular momentum quantum
number l
and magnetic quantum number ml

Question 14

What can the values of each of the quantum numbers be?

Answer 14

n= 1,2,3,4…
l=0,1,2,3… (n-1 numbers)
ml= -l…0…l

Question 15

How do the values of l relate to orbitals and ml?

Answer 15

L relates to the type of orbital
0=s 1=p 2=d …
ml refers to the orientation of the orbital
e.g for l=1, could be -1,0,1 representing the direction of the p orbital

Question 16

What do the radial/wave function graphs look like for the s orbitals and why?

Answer 16

Start from infinity and asymptote with the x axis
For 1s, does not go below the axis
For each successive s, adds a node so goes through axis and a turning point

For the s orbitals, there is no quadratic term with radius in the wave function, leaving only the negative exponential, so they do not start at 0

Question 17

What do the p/d radial/wavefunction graphs look like?

Answer 17

Start from 0 for all
Up and then fall, eventually asymptote with x axis
Nodes for each orbital apart from first appearance, where it passes through 0
D peak of same energy level at a higher radius than p or s

Question 18

What is the born intepretation?

Answer 18

The square of a wavefunction is proportional to the probability of finding the particle at that point

Question 19

What do the s orbital radial/wavefunction squared look like? What is important about this?

Answer 19

Start from infinity, and still asymptote with x axis
Reflected at nodes
Successive turning points lower in amplitude

There is a probability that the electron will be found at the nucleus

Question 20

What do the p/d orbital radial/wavefunction squared look like?

Answer 20

As before but reflected at the nodes
The d turning point peaks are always higher than s/p at the same energy level, but shifted to the right

Question 21

What is the radial distribution function and how is it calculated?

Answer 21

P(r)= 4πr²ψ(x)²

P(r) is the probability of finding the electron in a shell of radius r, and thickness dr
By taking infinitesimal changes in cartesian coordinates and integrating the surface area with dr

Question 22

What does the radial distribution/radius graph look like for the s orbitals?

Answer 22

Now start from 0 as multiplying by the radius
1s- peak and approach x axis
2s- 2 peaks, second one larger and one node
3s- repeats with each successive peak larger and further away

Question 23

What does the radial distribution/radius graph look like for the p/d orbitals?

Answer 23

Similar to s, start from 0, peak, approach
Each higher quantum number increases the number of nodes and peaks but higher radi

Question 24

What are the spherical harmonics? What is special about the s orbital for this?

Answer 24

A set of functions which form the angular solutions of the Schrodinger equation, normally imaginary S orbital solution a constant, no angular dependence

Question 25

How are orbitals represented?

Answer 25

As boundary surfaces which contain 90% of the electron density

Question 26

Describe the 3s orbital?

Answer 26

Spherically shaped With 2 nodes at a specified distance from the nucleus, cannot rly see the section without electron density But after each node, the wave function changes sign often denoted by a colour change

Question 27

What do the p orbitals look like?

Answer 27

Dumb-bell shaped , with planar nodes depicting a change in sign Along the X,Y, and Z axis

Question 28

Look at the D orbitals please but try to describe them

Answer 28

4 of them are contain 4 lobes but orientated at different positions Each with 2 nodal planes. The name represents the plane not a nodal plane dxz, dxy, dyz, dx2y2 And then dumb bell shaped with a circular shape

Question 29

How are the energy levels in hydrogen organised?

Answer 29

Orbitals within the same shell are the same energy leve, degenerate All the energies are negative as an electron is bound n=infinity has an energy of 0

Question 30

What is the general formula for ionisation energy and specifically for hydrogen? Define ionisation energy?

Answer 30

IE= -Ryhc(1/infinity) - 1/n) For H= RyHc The energy corresponding to the total removal of an electron, to n=infinity

Question 31

What is the equation for the orbitals for species isoelectronic to hydrogen? How do orbitals change with these species? How does the spacing in these species change?

Answer 31

E= -(Z²RyhC)/n² where z is the nuclear charge and n the quantum number As Z increases, orbitals contracts, as in the radial distribution function its e^-p/2, where p= 2zr/nao So the decay is quicker resulting in contracted orbitals The spacing can be compared relative to hydrogen. e.g He+ is 4 x further apart, Be3+ 16x, but this is only an approximation as their is a small mass dependence for the Rydberg constant

Question 32

How are multi-electron atoms modelled, and why?

Answer 32

Using orbital approximation as the Schrodinger equation cannot be solved exactly Each electron now experiences repulsion from neighbouring electrons But instead, we model each electron as being on its own, look like a one electron atom Each electron experiences a modified effective nuclear charge, which takes into account electron repulsion, Zeff The orbitals take the form of those in hydrogen but with modified energies and sizes using Zeff This works as we are distributing the negative charge of the electrons, which is equivalent to a point at the centre of the distribution which experiences the charge, which is the nucleus

Question 33

How was spin calculated? What values can spin take?

Answer 33

Extension of wave mechanics to include special relativity and time as a coordinate Solution of this Dirac equations gives a new intrinsic angular momentum, spin S=1/2, spin up S=-1/2, spin down

Question 34

What is the Pauli Exclusion principle?

Answer 34

No two electrons can have the same 4 quantum numbers, n, l, ml, and ms Therefore, no more than 2 electrons can occupy an individual orbital And electrons occupying the same orbital but be paired, one spin up and one spin down

Question 35

What is electron shielding?

Answer 35

Core electrons will prevent outer electrons from experiencing the full nuclear charge, shielding them from it This is reflected in Zeff with more electrons reducing the nuclear charge experienced on average, but this is specifically for the electrons outside the core

Question 36

What is electron penetration?

Answer 36

Penetration is the ability for an outer electron to penetrate the core region In doing so, the electron can experience a larger nuclear attraction and so have a lower energy This is dependent on the the type of orbital occupied

Question 37

How do the 3s and 3p orbitals differ in electron penetration?

Answer 37

Although the 3p on average is closer to the nucleus, there is a small peak for the 3s within the core region This enables the 3s orbital to be better at penetrating the core region, with the 3s electron spending more time closer to the nucleus and so at a lower energy

Question 38

What are the ramifications of orbital penetration?

Answer 38

The energy of the orbitals of the same shell are now no longer completely dependent on n, and instead rely on l, meaning they are no longer degenerate

Question 39

How is shielding and penetration taken into account to the calculation of orbital energies?

Answer 39

Replace Z² with (Z-sigma)², which is Zeff sigma= shielding parameter Zeff is now a function of both n and l

Question 40

How does Zeff vary with periods and groups?

Answer 40

Overall, Zeff increases across a period and down a group as we are increasing the amount of protons, and the decrease by shielding is smaller in comparison Z eff increases more steeply across a period as electrons are added to the same shell, meaning the increase in shielding is smaller relative to adding a new shell such as down a group Notable exception across a period, when switching from s to p, as their is a considerable increase in the shielding constant

Question 41

Why does the 4s fill before the 3d?

Answer 41

The 4s orbital is highly penetrating, more so than the 3d Although on average the 3d is closer to the nucleus, the penetrating effect of the 4s means its electron spends more time closer to the nucleus within the core region, experiencing a greater nuclear attraction and so lower energy This means the 4s is at a lower energy than the 3d, so is filled first

Question 42

What is the Aufbau principle?

Answer 42

The building up principle When establishing the ground state configuration of an atom, electrons must be filled from the lowest energy orbital, working their way up in order of energy

Question 43

What is Hund's rule?

Answer 43

When electrons occupy orbitals of the same energy, the lowest energy state corresponds to the configuration with the greatest number of unpaired electrons

Question 44

What is exchange energy? How does it relate to electron configuration?

Answer 44

Extra stability with greater parallel spin configurations as the electrons are indistinguishable and interchangeable, based on the wavefunction having to be antiparallel with respect to the exchange of electrons So if Explains why Chromium/Copper half fill s subshell, as greater parallel spins

Question 45

What is the order of subshells filling?

Answer 45

Follow the blocks of the periodic table 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²4f¹⁴5d¹⁰6p⁶7s²5f¹⁴6d¹⁰7p⁶

Question 46

When does the 3d orbital fall below 4s in energy? Why?

Answer 46

From Sc onward, the 3d singly occupied subshell is actually lower in energy than 4s Additional protons in the nucleus in Zeff pulling all shells closer to the nucleus. As the 3d on average is closer than the 4s, it is more greatly stabilised by increasing zeff The 3d electrons as less effective at shielding than the 4s Therefore overall the 3d falls in energy below the 4s with a high enough nuclear charge

Question 47

Why do the energy of the orbitals decrease down a group even though z effective increases?

Answer 47

e= constant x ( z squared / n squared) The increase in n is greater than the increase in zeff meaning overall energy decreases

Question 48

What is the lanthanide contractions and why does it occur? How is this similar to the transition metal contractions?

Answer 48

The atomic radi of the 3rd row d block are very similar to the 2nd row Would have expected the 3rd row to be larger due to higher quantum numbers However, the 3rd row are preceded by the lanthanides, with the f subshell having very poor shielding qualities This results in the increase of zeff down the group to be greater than expected, resulting in greater nuclear attraction so smaller atomic radii in spite of the additional electrons For the d block contraction, along the tms, the atomic radius does not decrease much as the 3d subshell is poor at shielding, meaning addition of electrons does not vary radius much

Question 49

What is the general trend of ionisation energies across a period and why?

Answer 49

Recall E= -(Z²RyhC)/n² for energy of an orbital and Koopman- IE= -orbital energy So across a period, n stays the same, but Zeff is increasing resulting in the orbital being at a higher energy Therefore more energy is required the electron so a higher ionisation energy

Question 50

What is ionisation energy and how is it determined?

Answer 50

The energy that corresponds to removing an electron from the neutral gas phase atom in one mole Either by electron impact, where an electron is accelerated through a potential difference Or photon electron spectroscopy, where an electron is removed if the energy of the light is high enough, the ionisation energy is the kinetic energy of this liberated electron - energy of the light

Question 51

Why does the ionisation energy drop between Be and B?

Answer 51

Lost in a higher energy p orbital for B instead of s for Be P is less penetrating than S so higher in energy

Question 52

How does exchange energy relate to the trends in ionisation energies?

Answer 52

When removing an electron, if you are removing an unpaired electron, this will require overcoming exchange energy, and lowers stabilisation But e.g for O, removing a paired up electron forms one more unpaired electron so instead helps stabilise the ion and so explains a drop in ionisation energy as exchange energy need not be overcome Additionally paired up electrons have greater repulsion so easier to remove an electron

Question 53

Why do the ionisation energies become similar between Al/Ga/In/Tl, down g3?

Answer 53

G3 after addition of d subshell, f subshell Al/Ga addition of 3d, not very good at shielding so noticeable increase in z eff Similarly, Ga/In, addition of 4d In/Tl addition of 5d and 4f As a result, the zeff for all down the group is higher than expected due to the poor shielding properties of the d and f subshell, meaning the increase in nuclear charge makes it harder to lose an electron And so the decrease in ionisation energies is less pronounced

Question 54

Why is there a large decrease in ionisation energies down G7 but not G3?

Answer 54

G3 has the addition of the d and f subshell immediately before it, meaning the zeff is much larger than expected, whilst the p subshell contains only one electron By G7, the p subshell is nearly full, meaning shielding effects reduce zeff more, resulting in greater differences in ionisation energy down the group

Question 55

Why is there such a significant increase in ionisation energy between Cs and Au?

Answer 55

IN between Cs and Au is addition of the 4f and 5d shells This means there is a substantial increase in nuclear charge with limited additional shielding due to the weak screening properties of the f and d orbitals Therefore there is a significant increase in the Zeff, resulting in greater nuclear attraction upon the valence electrons and so larger first ionisation energy for Au

Question 56

What do the second ionisation energies look like as a trend?

Answer 56

The trend across a period shifted one to the left and much higher i.e the dip from nitrogen to oxygen will now be seen between carbon and nitrogen

Question 57

How do successive ionisation energies vary for an element?

Answer 57

Increase with each ionisation as Zeff will increase Large increases when removing electrons from a lower energy shell, reflected in the Koopman equation

Question 58

What are the general trends for atomic radii and why?

Answer 58

Increase down a group as electrons are being added to higher energy shells further away from the nucleus, and the increase in Zeff is not as dominant as the higher energy orbital Decrease across a period as Zeff increasing whilst n stays the same, so orbital contraction

Question 59

What are the general trends for electronegativity and why?

Answer 59

Increase across a period, greater Zeff Decrease down a group, as increase in Zeff not as dominant as the increase in quantum number so larger atomic radii and so lesser nuclear attraction upon the outer shell, lower electronegativity

Question 60

Why does electron affinity decrease down a group and why?

Answer 60

Lower Zeff down the group, greater electron shielding, larger atomic radius

Question 61

What is the probability function and radial distribution function of an electron?

Answer 61

Probability function: psi mod (x,y,z)^2 whilst the radial distribution function p(r)= πr² psi mod (x,y,z)^2 so probability at a radius of r, of shell thickness dr

Question 62

What are the 3 types of wave function graphs?

Answer 62

radial wave function against r probability density (radial wave function squared) against r radial distribution function against r