Orbitals and the periodic table

Question 1

Give the n, l and ml numbers for the following atomic orbitals.

Answer 1

Next card.

Question 2

1s

Answer 2

n = 1
l = 0
ml = 0

Question 3

2s

Answer 3

n = 2
l = 0
ml = 0

Question 4

3s

Answer 4

n = 3
l = 0
ml = 0

Question 5

2pz

Answer 5

n = 2
l = 1
ml = 0

Question 6

2py

Answer 6

n = 2
l = 1
ml = -1

Question 7

2px

Answer 7

n = 2
l = 1
ml = +1

Question 8

3pz

Answer 8

n = 3
l = 1
ml = 0

Question 9

3px

Answer 9

n = 3
l = 1
ml = +1

Question 10

3py

Answer 10

n = 3
l = 1
ml = -1

Question 11

List the five 3d atomic orbitals and give their n, l and ml numbers on the next flashcards.

Answer 11

3dxy, 3dyz, 3dxz, 3dx^2-y^2, 3dz^2

Question 12

3dxy

Answer 12

n = 3
l = 2
ml = -2

Question 12

3dxz

Answer 12

n = 3
l = 2
ml = +1

Question 13

3dx^2-y^2

Answer 13

n = 3
l = 2
ml = +2

Question 13

3dyz

Answer 13

n = 3
l = 2
ml = -1

Question 13

3dz^2

Answer 13

n = 3
l = 2
ml = 0

Question 13

Does it matter which 2p, 3p or 3d orbital has which ml number?

Answer 13

For subshells like 2𝑝 3𝑝, or 3𝑑, it doesn’t matter which orbital is assigned to which 𝑚𝑙
value. The assignments are interchangeable and chosen based on convention, without affecting the physical or chemical properties of the atom.

Question 14

Images of orbitals are on the summary sheet.

What do the red and blue mean?

Answer 14

Alternating wave phases.

Question 15

What does wave phase refer to?

Answer 15

Oscillating sign (+ve or -ve) of a wavefunction (𝚿).

Question 16

When 𝚿>0, what is the phase?

(refer to summary sheet for a full diagram of a wave and +ve/-ve half cycles)

Answer 16

Positive.

Question 17

What is a wavefunction?

Answer 17

Describes the probability distribution of electrons around an atom.

Question 18

When 𝚿<0, what is the phase?

Answer 18

Negative

Question 19

n, l, ml and ms are the allowed eigenvalues for atomic orbital wavefunction.

What is n?
Give the range of numbers it can be.

Answer 19

Principle quantum number.

Can take any positive integer.

Question 20

What is l?
Give the range of numbers it can be.

Answer 20

Secondary/angular/azimuthal/orbital quantum number.

0 to (n-1).

Question 20

What is ms?
Give the range of numbers it can be.

Answer 20

Spin quantum number.

-1/2 or +1/2
(for spin down or spin up)

Question 21

What is the Aufbau principle?

Answer 21

Electrons fill subshells of the lowest available energy in the ground state of an atom/ion.

Question 21

What is ml?
Give the range of numbers it can be.

Answer 21

Magnetic quantum number.

-l to +l

Question 22

What is Hund’s rule of maximum multiplicity?

Answer 22

In the lowest energy electron configuration, electrons fill orbitals singly before pairing (they have parallel spins).

Question 23

What is the Pauli exclusion principle?

Answer 23

No two electrons can have exactly the same set of four quantum numbers: n, l, ml, ms.

Question 24

Give some examples of hydrogen (one electron) bodies.

Answer 24

H, He+, Li2+

Question 25

Give 3D Cartesian co-ordinates.

Answer 25

x, y, z

Question 26

Give 3D polar co-ordinates.

Answer 26

θ, ϕ, r
(angle, elevation, distance)

Question 27

Write 3 sets of co-ordinates to illustrate how electrons are represented as a wave function.

Answer 27

𝚿(x, y, z)
𝚿(θ, ϕ, r)
𝚿(n, l, ml)

Question 28

Write the wavefunction broken into two smaller functions.
Explain what they are.

Answer 28

R(n) = radial wave function
- describes how the probability density of
an electron varies with distance from the
nucleus in an atom.

Y(ml, l) = angular wave function
- describes the orientation and shape of the
electron’s probability distribution

Question 29

What is effective nuclear charge?

Answer 29

The effective nuclear charge (𝑍eff) is the net positive charge experienced by an electron in a multi-electron atom. It represents the actual attractive force that a specific electron “feels” from the nucleus, after accounting for the shielding effects of other electrons.

The effective nuclear charge experienced by an electron is typically calculated as:
𝑍eff=𝑍−𝑆
where 𝑍 is the atomic number (total positive charge from the protons), and 𝑆 is the shielding constant, which represents the average repulsion effect from other electrons.

Slater’s rules = method to estimate shielding constant.

Question 30

When the radial distribution function (4πr^2R(r)^2) is plotted against R(r)^2, what does this show?

Why are there no negative values?

(refer to small diagram in summary sheet and full diagram in course manual)

Answer 30

The probability of finding an electron at distance r from the nucleus.

R(r)^2

Question 31

There is a peak in the 1s curve. What does this tell us?

Answer 31

The most probable distance from the nucleus for 1s electrons.

This is equivalent to the Bohr radius in the Bohr model.

Question 32

What is a radial node?

Answer 32

The probability of finding an electron at a particular distance from the nucleus is 0 because the electron density drops to 0.

Question 33

Why is the 1s peak shifted closer to the y axis than the 2s peak?

Answer 33

The majority of electron density of 1s is closer to the nucleus than 2s (there is an overlap).

Question 34

How do you work out how many radial nodes an s orbital peak has?

Answer 34

n - 1

Question 35

How do you work out how many radial nodes a p orbital has for r>0?

Answer 35

n - 2

Question 36

How do you work out how many radial nodes a d orbital has for r>0?

Answer 36

n - 3

Question 37

How do you work out how many radial nodes an f orbital have for r>0

Answer 37

n - 4

Question 38

Generally, for r>0, the first time an orbital occurs it has no…

Answer 38

radial node (1s, 2p, 3d, 4f orbitals).

Question 39

As n increases, the peaks of a radial wave functions become…

Answer 39

broad and shallow.

Question 40

Why is this?

Answer 40

Due to the increase in the size and spread of orbitals, formation of additional radial nodes and decreased electron density near the nucleus.

Question 41

Describe and explain the periodic trend in atomic radii (pm).

(see the course manual for all these periodic trend graphs)

Graph = atomic radii as a function of atomic number.

Answer 41

Generally atomic radii decrease across a period due to increasing nuclear charge so electrons are pulled closer to the nucleus.

Generally atomic radii increase down a group due to more electron-electron repulsion between valence and core electrons and increasing quantum number (so constant effective nuclear charge).

Question 42

What are the exceptions to atomic radii trends?

Answer 42

Exceptions in K-Br and Rb-I on graphs are due to electrons moving into orbitals for electron-electron pairing.

Exceptions from Cs-P due to d-orbitals experiencing lots of penetration. D

Question 43

Define metallic/covalent radius.

Answer 43

1/2 the distance between nuclei of adjacent atoms.

Question 44

What kind of atomic radius do group 18 elements have? Why?

Answer 44

Van der Waals - they are monatomic.

Question 45

What is a Van der Waals radius?

Answer 45

1/2 distance between nuclei of two identical non-bonded atoms.

Question 46

Give the periodic trends in ionisation energy (kJ/mol).

Graph = first ionisation energy as a function of atomic number.

Answer 46

Across period first ionisation energy increases due to increasing nuclear charge, similar shielding and decreasing atomic radius.

Down group first ionisation energy decreases due to increasing atomic radius and shielding which decreases effective nuclear charge.

Question 47

Give exceptions to the periodic trends in ionisation energy.

Answer 47

Very high first ionisation energies for group 18 due to stable electron configuration (full valence shells).

Exceptions due to outermost electron being in higher energy orbitals so easier to remove and electrons being paired so easier to remove because of repulsion.

Question 48

Give the periodic trends of first electron affinity (kJ/mol).

Graph = electron affinity as a function of atomic number.

Answer 48

Across period first electron affinity becomes more negative due to increasing nuclear charge (more favourable to accept electrons), decreasing atomic radius (so greater effective nuclear charge) and elements closer to filling p orbitals want to gain electrons.

Down group, becomes less negative due to increasing atomic radius and more shielding.

Question 49

What are the exceptions to the first electron affinity trends?

Answer 49

Group 2 - less negative than expected due to full s subshell.

Group 15 - less negative than expected due to electron-electron repulsion caused by adding electrons (e.g. N = 2p3).

Noble gases - positive values as they don’t readily gain electrons.

F slightly less negative than Cl due to small atom causing electron-electron repulsion.