Elements and Minerals

Question 1

What reactions are possible at 10¹-10³ K, 10⁷-10¹⁰ K and around 10¹² K and what forms of matter are stable at these temperatures?

Answer 1

10¹-10³ K - chemical reactions, molecules and solids 10⁷-10¹⁰ K - nuclear reactions, nuclei and electrons 10¹² K - elementary particle reactions, elementary particles

Question 2

What do chemical synthesis and nuclear synthesis reactions require?

Answer 2

Chemical Synthesis requires manipulation/changes in valence electrons Nuclear synthesis requires temperatures > 10²

Question 3

State Coulomb’s law of electrostatics and compare the size amnd potential energy of atoms and nuclei

Answer 3

Coulomb’s law:

V = q₁q₂/4πε₀r

V = potantial energy q = charge ε₀ = vacuum permitivity

r = distance

Atom: r = 200 pm = 2x10^-10 m

V = 1.2x10^-19 J (7eV) or 700 kJmol^-1

Nuclei: r = 10 fm = 10x10^-14 m

V = 1 MeV or 100 GJmol^-1

Question 4

Explain the differences between the strong interaction and electrostatic interaction

Answer 4

The string interaction operates equally between protons and neutrons

The strong interaction has very short range (2 fm or less)

Question 5

Which force dominates when particles are at different distances?

Answer 5

The stability of the nucleus is based on the balance between the strong interation *(between all nucleons) and the electrostatic interation between protons (replusive).

For a pair of nuclei, coulombioc interatiuons dominate.

Approaching a distance of 2 fm the strong interaction dominates

Question 6

WHat is binding energy and what is the most stable nucleus?

Answer 6

The energy required to break up the nucleus into constituent nucleons

⁵⁶Fe is the most stable nucleus

Question 7

How can the binding energy be calculated?

Answer 7

Using Einstein’s theory of relativity: E = mc²

m is calculated as the difference between the mass of an element b y definition (carbon 12 has a mass of 12) and the sum of all the protons, neutrons and electrons (¹²C = 12.09893876)

m = 0.09893976

c = 9x10¹⁶ Jkg^-1 = 931.5 MeV

E = 92.1 MeV

Question 8

What affects nucleus stability?

Answer 8

While electrons can be seen as quantised so can nucleons in the nucleus.

Nuclei with even number of protons and neutrons are more stable than odd numbers

Certain numbers are particularly stable: 2,8,20,28,50,82,126

Sometimes referred to as magic numbers similar to closed shell configurations of nobel gases: 2,8,18,32…

Question 9

What are radioactive elements?

Answer 9

PArticles that decay by a number of pathways with the release of energy (gamma) and particles

Question 10

Describe alpha radiation

Answer 10

The emission of an alpha partic;le (loss of He nucleus)

All nuclei with Z > 82 are alpha emitters

Occurrs via tunnelling through the string interation/coulombic barrier

e.g ²³⁸₉₂ U ——> ²³⁴₉₀Th + ⁴₂α(He)

Question 11

What are the three types of beta decay?

Answer 11

Beta (β^-) emission - loss of an electron

electron capture (EC) - gain of an electron

positron (β⁺) emission - loss of an anti-electron

Question 12

Describe beta (β^-) emission

Answer 12

e.g ¹³⁷₅₅Cs —–> ¹³⁷₅₆Ba + e^- + ~ve

~ve = an anti neutrino

This occurrs when a neutron —–> a proton and an electron

Question 13

Describe electron capture (EC)

Answer 13

e.g ²²₁₁Na —-> ²²₁₀Ne^- + v_e

This releases a neutrino

This occurrs when an electron and a proton combine to form a neutron

Question 14

Describe positron (β⁺) emission

Answer 14

e.g ²²₁₁Na —> ²²₁₀Ne^- + e⁺ + v_e

e⁺ is a positron

This occurrs when a proton breaks into a neutron and an electron

The different types opf decay can be competative with each other as a particular nucleus may decay by more than one method

Question 15

What does the line of stability show in terms of β decay

Answer 15

The line of stability shows neutron number vs atomic number

More neutrons are required at higher atomic number to reduce the coulombic repulsion between protons .

The binding energy per nucleon reduces leading to instability.

Above the line there are too few neutrons whereas under the loine there are too many neutrons.

Question 16

What are some important long lived radioactive nuclides

Answer 16

⁴⁰K, ⁸⁷Ru, ¹⁴⁷Sm, ¹⁸⁷Re, ²³²Th, ²³⁵U, ²³⁸U

All have significant earth abundances

Fuel geological processes (heat the mantle) and cause genetic mutations driving evolution

Question 17

Describe what happoened in the big bang timeline at t = 10^{-35 s}

Answer 17

The universe began 13.7 billion years ago

At this time it was a hit dense plasma

T = 10³² K

No matter - radiation, sea of photons and neutrinos

Radiation described as a black body (U_AVE = 2.7 KT)

Question 18

Describe what happened in the big bang theory time lone at

t = <0.5 s

Answer 18

T = 10³² K —> 10¹³

Photons materialise pairs of particles

2γ <—-> p⁺ + ~p^- (antiphoton)

2γ <—-> n + ~n

2γ <—–> e^- +~e^- Positron/antielectron

Photons must have enough energy to form matter particles

E = 2.7kT > 2mC²

Question 19

Describe what happened in the big bang theory time line at

t = >0.5-1 s

Answer 19

T = 10¹³ - 10⁹

Photons will lack the energy to form new protons below a threshold energy

2.7kT_p = 2mc² = 10¹³ K

No new proton-antiproton pairs materialise and protons and antiprotons then annihilate each other:

p⁺ + ~p^- —–> 2γ

However, a slight excess of matter over antimatter remains at equlibrium [p^~+]/[γ] 10^-9

Question 20

Describe what happened in the big bang theory timeline at

t = 1-100 s

Answer 20

Protons and electrons interact to form neutrons and neutrinos:

p⁺ + e^- —-> n + v_e

Half life deoends on temperature and density of the universe

t = 1s T = 10¹⁰ K

Therefore neutrons and other matter no longer materialise

[n]/[p] =~ 1/5

neutrons then decay - half life = 11 mins

As the temperature falls neutrons react faster with protons to form stable deuterium

n + p⁺ —–> ²H⁺ + γ

All neutrons end up as deuterium which is reactive

Question 21

Which reactions are involved in the cascade of reactions after protons and neutrons have reacted?

Answer 21

²H + ¹H —–> ³He + γ

²H + n —-> ³H + γ

²H + ²H —–> ⁴He + γ

³He + n —–> ⁴He + γ

³H + ¹H —–> ⁴He + γ

Net reaction: 2¹H (p⁺) + 2n —-> ⁴He + γ

⁴He + ³He —–> ⁷Be —-> ⁷Li + γ - minor reaction

Process blocked - no stable 5 or 8

²H is slow to be formed due to low binding energy

Question 22

What are the three pieces of evidence in support of the big bang theory?

Answer 22

The big bang theory correctly predicts the relative concentration of the lighter elements particularly the H:He ratio of 8:1

The big bang theory predicts that between 100s and 4x10⁵ years ago radiation and matter were at equilibrium and homogenously distributed (black body distribution) - Cosmic Background Radiation

The universe is expanding in accordance with Hubbles law:

v = Hod

v = velocity Ho = hubble’s constant d = distance

Question 23

Between 100s and 4x10⁵ years what happened with radiation and matter?

Answer 23

Radiation interacts with free electrons leading to an opaque universe. Radiation and matter in equilibrium and homogenously distributed. Wait 4x10⁵ years and the universe expands and cools to the point where radiation and matter are no longer equilibrated

At T<3000 all electrons are bound in atoms - these scatter radiation weakly. MAtter and radiation become decoupled (leads of CMS) and the universe is transport.

Question 24

At t>4x10⁵ what happens to matter and radiation?

Answer 24

H and He atoms spread evenly over universe - too colf for nuclear reactions - gravity begins to be felt- shapes the universe - releases energy

Space continues to expand - not uniformly

Matter (mainly H and He atoms) clump together underngravity to form galaxies and eventually stars

Question 25

What are stars?

Answer 25

Molecular clouds located in the spiral arm of a galaxy can collapse under gravity ti form protostars

Gravitational nergy converted to kinetic energy

Temp rises to T = 10⁷ K - nuclei begin to fuse to give heavier nuclei - stars begin t shine

Essentially stars are dense sphere of gas

Question 26

What are the characteristics of stars

Answer 26

Luminosity - product of the brightness x distance² x mass

Spectral type (colour) - gives surface temperature

Cool stars with high luminosity must be very large where as hot stars must be very small

Question 27

Where does a star spend ost of its lifetime and what does it depend on?

Answer 27

Many stars lie in the main sequence - majority of the active life

Lifetime depends on mass

The sun lifetim: 10¹⁰ γ, age = 4.5x10⁹ γ

Question 28

Can nucleosynthesis occur in stars?

Answer 28

Stars are hot enough for nucleosynthesis to begin again

During the big bang thee was only 3 minutes for reactions but in stars these conditions last for million of years - slower reactions are more important

T = 10⁷ but no neitrons

Question 29

What is the main sequance of H burning?

Answer 29

Question 30

What makes up the star in the main sequence?

Answer 30

Core of ⁴He²⁺ which forms. The energy generated is balanced by escaping radiation.

The star is supported against gravity by the thermal pressure generated by fusion.

Main sequence stars are not expanding or contracting much and are in hydrostatic balance. Rate of fuel burning (lifetime) depends on luminosity (L) and the mass

Question 31

How do stars evolve?

Answer 31

Low mass stars (<4 suns) evolve into red giants - sources of ¹²C + ¹⁶O. Corpse is usually a whte dwarf or if another star is close by in a so called binary system mass transfer can occur which can lead to a type 1 supernova.

High mass stars (> 4 suns) evolve into super red giants - sources of C, N, O, Si. - Burn to ⁵⁶Fe.

The corpse is usually a neutron star or a black hole via a type 2 supernova

Question 32

What happens in a red giant?

Answer 32

When ¹H becomes exhausted in the core the thermalmpressure cannot support the gravity core contacts raising T to 10⁸ K - helium starts to burn

Energy released blows out the envelope to form Red giant

After 10⁷ years He is exhausted and the star evolves into a white dwarf

Question 33

What happens in a super red giant?

Answer 33

Core of ¹²C and ¹⁶O contracts

Fusion of heavier nuclei makes envelope swell

Question 34

What is neutron capture?

Answer 34

Slow process that absorbs energy

Protons are introduced via beta decay after neutron absorption

Question 35

What is explosive nucleosynthesis?

Answer 35

Type 2 supernova = when the iron core develops all the fuel will become exhausted and the thermal energy from fusio will no longer be able to support the weight of the star This leads to a catastrophic gravitational collapse occuring in seconds

The core disintergrates: T = 10¹⁰

⁵⁶Fe => p + n - lots of neutrons

THe outer part of the core bounces of the hard central part and shock wave leads of explosion

Question 36

Does neutron capture occur in a neutron star?

Answer 36

Neutron capture occurs causing rapid necleosynthesis (r-process) forming all the heavier elements up to ²³²Th and ²³⁸U

The explosion causes matter to be spread out into space and the core is left as a black hole or neutron star

Question 37

What is the difference between old and young main sequence stars?

Answer 37

Old main sequance stars form from the debris of the big bang - contain mainly protons and helium

PPI cycle catalysed by ²H - 4¹H => ⁴He + 2e⁺ + 2v

Young main sequence starts form from the debris of a super nova and these are kmown as metal rich. The sun is a young star and these are important sources of isotopes like ¹³C, ¹⁴N, ¹⁵N, ¹⁷O

H burning is catalysed by ¹²C - CNO cycle

Question 38

Can nucleosynthesis occur in an insterstellar medium?

Answer 38

A few nucleons are not formed in stars (or the BIg Bang)

⁶Li, ⁹Be, ¹⁰B, ¹¹B are not formed by any of the process descirbed so far and are easily destroyed in stellar interiors

Formed as fragments by collisions (spallation) of very energetic galactic cosmic rays (including neutrinos, ¹H, ⁴He, ¹²C and ¹⁶O with interstellar gas

Cosmic rays are accelerated by shock waves driven by the rapidly moving ejecta of supernova - sort of naturally occurring fission

¹⁵N, ¹⁷O, ¹⁸O, ¹⁹F, ²¹N are spallation products

Question 39

What is the solar system like?

Answer 39

Isolated - distnace to nearest star is 5x10⁴ time the diameter of the sun

Formed 4.6 x 10⁹ years ago - it didn’t exist exist for most of the history of the universe

Now agreed that the sun and the planets have a common origin

Question 40

What is the nebular theory of the solar system origin?

Answer 40

Planets form concurrently or consecutively from the same nebular as the sun

Question 41

What is the cndensationtheory of the formation of the solar system?

Answer 41

4.6x10⁹ years ago a small fragment of a molecular cloud detached from the arm of the milky way probably triggered by a near by supernova.

The cloud condensed towards the centre under gravity and the dust settled into the plane of a rotating dish

The angular momentum ransferred towards.

Question 42

How did the planets form?

Answer 42

The centreof the nebula heated by gravitational contraction at 10⁷ K - nuclear reaction begin and surface temp rises to 4000 K

Turbulaent gas eddies caused by heating of the sun lead to aggregation of particles under gravity to give planetisimols (<1km).

Gases are not included in the planetisimols due to heating from the sun. The surviving planetisimols aggregate further into the four inner terrestrial planets

Question 43

Is the composition of the earth the same as the solar system?

Answer 43

Composition of earth is generally similar to the solar system but some are different -

oxygen, aluminium and silicon are very abundant

Question 44

What kinds of elements are found on earth?

Answer 44

Lithophiles: rock loving found predominantly as oxides in the crust - early condensers

Siderophiles: iron loving elements found predominantly as metals or alloys in the core - volatiles > 600 K

Atmophiles: volatiles found in the ocean or atmosphere - volatiles < 600 K and extreme volatiles

Question 45

Why is it thought the elements are found in the states they are found in?

Answer 45

Elements condensing at different temperatures due to their enthalpies of atomisation (for sidophiles) and oxide formation (for lithophiles).

There is a strong correlation between the form the leements are found in on earth and the rate at which they are predicted to condense.

Question 46

What happened in the early history of the earth?

Answer 46

Accretion - (coagulation of dust) 4.6x10⁹ years ago

Impacts and radioactivity of 238U lead to heating and some melting

Fe and Ni form core and a crust forms on an ocean of magma. Giant impact era ends 3.9x10⁹ years ago and a supercontinuent formed 2.7 x 10⁹ and plate techtonics become operational

Question 47

What is the composition of the layers of the earth?

Answer 47

Atmosphere - atmophiles

Ocean + crust - lithophiles

Mantle - Mg₂SiO₄ (s) - viscous melt

Outer core - sidophiles FeS (l)

Inner core - Fe, Ni - (s)

Question 48

Why do the crust and the mantle have different copositions?

Answer 48

The mantle partially melts to form magma due to radioactive heating - this rises and solidifies to form the crust

seen as cycles of of melting and recrystalisation to from essentially ionic mixture

This leads to mineral formaton and the concentration of elements in certain rocks - Since the earth’s formation the distribution of the elements has changed dramatically

Mg rich solids precipitate out (and fall) before the iron containing solids which leads to the crust being rich in Fe and the mantle rich in Mg

Question 49

Why was life not possible in the early years of Earth?

Answer 49

The temperature in the accretion period was too high for abundant C, N, H₂O to be bound. However, ice and C, and N compounds are rich in the asteroid belt. The formation of plamets like Jupiter scattered volatile rich planetisimals into the solar system

During the first 600x10⁶ years large impacts would have sterilised the earth with no life possible

After the possibility of life increases

Question 50

What is a mineral?

Answer 50

A solid compound found in nature with a cryystalline structure and unique chemical composition

e.g. halite = NaCl

Question 51

What is a rock?

Answer 51

A mixture of usually 3-4 mnerals with some glassy amorphous materials - no unique chemical composition

e.g. granite

Question 52

What is the study of minerals and rocks?

Answer 52

Mineralogy - study of minerals

Petrology - study of rocks

Question 53

How are rocks classified?

Answer 53

Igneous - solidified magma#

Metamorphic - rocks changed by high T and P

Sedimentary - rom action of air, water or biological process

Rocks may have been through more than ne process

Question 54

What are the major mineral classes?

Answer 54

Silicates: 70% of crust - greatest ,mass of minerals e.g. Mg₂SiO₄, Fe₂SiO₄

Oxides: include many important ores e.g. Fe₂O₃, Fe₃O₄, TiO₂

Sulfides: HgS, FeS (pyrite) MoS₂

Carbonates: e.g. CaCO₃

Sulfates: CaSO₄.2H₂O

Phosphates: Ca₅(PO₄)₃OH

Halides: NaCl, CaF₂

Elements: gold, silver, carbon (graphite / diamond)

Question 55

What are minerals classified by?

Answer 55

Crystal structure

density

colour

refractive index

cleavage

property - fluoroescence, magnetism, radioactivity

Question 56

What structures can minerals have?

Answer 56

Range from amorphous to crystalline

Quartz - crystalline

Glass - amorphous

Unique composition may have more than one crystal structure - These are called polymorphs

Only one polymorph will be thermodynamically stable at a particular temperature and pressure

Question 57

Can solid state compounds mix?

Answer 57

Some are miscible and can mix on the atomic scale usually due to similar radii of matal ions

The ratio of elements is non stochiometric

Question 58

What is important about the Si-O bond?

Answer 58

It is the strongest bond containing O and is used to polymerise a range of structures

Si-O skeleton is -vely charged so requires cations for charge and occupy spaces

Question 59

What are the factors determining site occupation?

Answer 59

Cation size (ionic radii) - major influence of crystal structure

A little bit of covalency which will be determined by the relative electronegativity and charge density

Question 60

How can SiO₄ tetrahedra link?

Answer 60

Share cornersvia bridging Os

Question 61

What are some examples of SiO₄ tetrahedra polymerisation?

Answer 61

Question 62

What is the structure of olivines?

Answer 62

Exhibit solid solution between two end members forserite (Mg₂SiO₄) and faylite (Fe₂SiO₄)

Solid solution is possible because of similar size of Mg²⁺ and Fe²⁺ ions that can replace each other without causing strain in the structure

From the phase diagram when a melt is cooled the crystalline solid will be rich in Mg and the liquid rich in Fe

Question 63

When is zoning often present?

Answer 63

common in minerals where solid solutions are present and depends on the rate of cooling

Very slow cooling gives large crystals of the end members.

Zoning and crystalline size give an indication of geological process conditions during crystalisation

Question 64

What are otho and clinopyroxenes?

Answer 64

Orthopyroxenes contain Mg²⁺ and Fe²⁺ which are a similar size leading to solid solution

Clinopyroxenes contain Ca²⁺ whihc is much larger

The structures of these two are different and often separate into different phases (both solids) called intergrowths

Question 65

What does the phase diagram of ortho/clinalpyroxene look like?

Answer 65

HAs an area of 2 phases in the solid phase area that is cslled the immiscibility dome.

Two phases are observed because at these temperatures a single silicate structure is not stable cotaining Ca²⁺ and Mg²⁺ ions.

Outside the dome a single solid solution is observed

The size of the ions is a function of T and P due to vibration - at higher T the ions vibrate more and are effectively bigger which can stabalise a structure

Question 66

Describe layered silicates

Answer 66

Formulas can be complex because lots of ions can fit between the layers and they contain variable water content

Structures can cintain single, double or mixtures of silicate sheets

Various metal ions can be accomidated between the silicate layers

Question 67

Describe Framework silicates

Answer 67

All the corners of the SiO₄ tetrahedra are shared e.g. SiO₂ which has many polymorphs

Incluydes Feldspars - used as abrasives and moonstone - constructed by substituting Al³⁺ into crystolographic sites pf SiO₄

When large pores are present which can accomidate other molecules These are referred to as zeolites which can be used as catalysts and in ion exchange processes

Question 68

What are extrinsic and intrinsic defects?

Answer 68

foreign atoms inetuded in the sturcture either by addition or by sustitution

Atoms are displaced from their crystolographic position or their missing from the structure (point defects)

Other defects arise from the relative dislacement of places of atoms (dislocations)

Question 69

What causes colour in diamond?

Answer 69

Caused by extrinsic and intrinsic defects

Extrinsic: carbon substituted by nitrogen (yellow), boron (blue)

Colour due to extra (N) or absence (B) of an electron

Intrinsic: Point defects and dislocation give colours like brown, opurple, green, pink

usually caused bybradiation or heat - heat can alter the structural defects and change the colour

Question 70

What are ruby and saffires made of?

Answer 70

Al₂O₃

Pure it looks hard and transparent

Has hexagonal close packed structure with 2/3 interstitial sites filled with aluminium atoms

Extrinsic defects are most important: substituion of Al for Cr gives red colour (ruby)

All other oclours are called saffire - Ti = blue, V = purple, Fe = yellow-green Different oxidation states give different colour

Question 71

What is the origin of colour?

Answer 71

All essentuially arise from the excitation of an electron

The original location and final destination is dependent on the atomic composition and structure

Question 72

How do extrinsic defects absorb light?

Answer 72

d-d transitions, metal - ligand transitions, logand to metal transitions

In crystals containing two metals of different oxidatuon states charge transfer also occurs

Question 73

How does excitation occur across a band gap?

Answer 73

In a crystal with billion of atoms molecular orbitals are shown as bands collectively

The band gap energy determines which freuencies are absorbed (colour)

In diamond energy required to excite across the band gap is outside the visible region - no colour

If there is no band gap all visible frequncies are absorbed and itappears black

Question 74

How do extrinsic impurities affect the band gap?

Answer 74

Can introduce and extra band

In diamond the N impurity contains an extra electron not used in bonding genrate a filled band between the filled and empty conduction bands

B impurity introduces an empty set of orbitals

Excitation across this gap is in the visible region leading to colour

Question 75

How do intrinsic defects affect colour?

Answer 75

Missing atoms or structural imperfections can lead to ‘trapped’ electrons that can be excited in the visible region

Usually coused by radiation or heat

NaCl irradiated with gamma rays is blue - CL₂ is illiminated leaving a solvated/trapped electron which is required for charge balance

Heat can change the structure and therefore the colour - heating blue NaCl will cause structural rearrangement and colour loss