ENVSC202-25A Environmental Chemistry and Geochemistry Notes

The Origin of the Elements

• Nucleosynthesis
• Formation of the planets and distribution of the elements in the Solar System

Learning Objectives - Nucleosynthesis

• Explain the general trends in abundances of elements and how they are distributed through the solar system
• Understand how elements are formed by different processes:
  • first & second generation stars
  • S and R processes
• Explain the formation and differences between the inner and outer planets and why these differences have arisen.
• Explain why knowing the density of planets is useful

Representing Elements

• $Cl$: Example of element representation.
  • Atomic number (Z) = number of protons in the nucleus. Defines the element (e.g., Cl always has 17 protons).
  • Mass number = sum of neutrons + protons.
  • Number of neutrons = Mass number – Atomic number.
  • Example: $^{35}Cl$ has 17 protons and 18 neutrons (35-17 = 18).
  • Isotopes: Atoms with the same number of protons but different numbers of neutrons (e.g., $^{16}O$, $^{18}O$).
  • Example: $^{37}Cl$ also exists with 17 protons and 20 neutrons (37-17 = 20); $^{35}Cl$ and $^{37}Cl$ are isotopes.
  • Isotones: Elements with the same number of neutrons but different numbers of protons (e.g., $^{37}Cl$, $^{39}K$).
  • Isobars: Different elements with the same mass number (e.g., $^{40}Ar$, $^{40}K$, $^{40}Ca$).

Stable Nuclei and Radioactive Decay

• Stable nuclei range from $^1H$ to $^{209}Bi$.
• Light nuclei have a proton:neutron ratio close to 1 (1:1).
• Heavy nuclei have a proton:neutron ratio < 1 (approximately 1.518:1).
• Unstable nuclei undergo spontaneous radioactive decay.

Spontaneous Radioactive Decay Processes

• Three main processes interconvert elements:
  • Beta (β) decay
  • Beta (β) capture
  • Alpha (α) decay
• β particle: An electron (-ve).
• α particle: Consists of 2 protons & 2 neutrons (+ve).
• Decaying element: Parent nuclide.
• Resulting element: Daughter nuclide.

1. Beta Decay (β- = electron emission)

• Isobaric process.
• Example: $^{14}C !\rightarrow ^{14}N + e^-$
  • A neutron transforms into a proton plus an electron.
  • Atomic number (z) increases by 1, forming a new element.
• Applications: Radiocarbon dating, radiotherapy.
• Other examples: $^{32}P \rightarrow ^{32}S$, $^{99}Tc \rightarrow ^{99}Ru$, $^{90}Sr \rightarrow ^{90}Y$

2. Beta Capture (β+ = electron capture)

• Example: $^{40}K + e^- \rightarrow ^{40}Ar$
  • A proton plus an electron transforms into a neutron.
  • Atomic number (z) decreases by 1, forming a new element.
• Electron capture: Proton-rich nucleus absorbs an electron, converting a proton into a neutron.
• Applications: K-Ar dating of minerals.
• Other examples: $^{22}Na \rightarrow ^{22}Ne$, $^{26}Al \rightarrow ^{26}Mg$, $^{59}Co \rightarrow ^{59}Fe$

3. Alpha Decay

• Loss of a $^4He$ nucleus (alpha particle +ve).
• Example: $^{238}U \rightarrow ^{234}Th + ^4He$
  • Atomic number (z) decreases by 2; neutrons decrease by 2.
• Application: U-Th dating of minerals, bones, teeth, calcium carbonates.
• Other examples: $^{234}Ra \rightarrow ^{230}Rn$, $^{230}Rn \rightarrow ^{210}Po$, $^{210}Po \rightarrow ^{206}Pb$

Origin of the Universe

• Big Bang: Approximately 13.8 - 15 billion years ago.
• The universe is expanding; distant stars recede faster than nearby ones.
• Evidence for expansion: Redshift in the spectra of light from distant galaxies.
  • Light is part of the electromagnetic spectrum and consists of waves.
  • Blue light has a short wavelength; red light has a long wavelength.
  • As a light source moves away, the wavelength is stretched (redshift).
• Atomic emission and absorption lines occur at known wavelengths. Shifts in these lines indicate redshift.
• Hubble’s Law: The speed of recession of a galaxy (v) is proportional to its distance (d).
  • Equation: $v = H<em>0d$, where $H</em>0$ = Hubble’s Constant, $v$ = velocity, $d$ = distance.

Composition of the Universe

• The present universe differs significantly from its state 13.7 billion years ago, with stars, planets, and interstellar regions having distinct compositions and chemistry.
• Hydrogen (H) and Helium (He) constitute approximately 99% of all matter in the universe.
• Matter constitutes a relatively low abundance in the Universe (5%).
• Dark Matter: Its exact nature remains uncertain.
• Dark Energy: Its existence is known through its effect on the universe’s expansion, but its nature is largely unknown.

Formation of Solar Systems

• A multi-step process:
  1. Contraction: A cloud of interstellar gas and dust collapses under its own gravity, heats up, and compresses in the center.
  2. Accretion disk: Matter around the center spins up and flattens into a disk; heat vaporizes the dust.
  3. Protostar: Forms in the center when the core becomes opaque; eventually becomes the Sun.
  4. Condensation: The disk radiates away its energy and cools off. Some gas condenses into tiny dust grains made of metal, rock, and ice (far enough out).
  5. Planetesimals: Dust grains stick to each other (ice helps) and sweep their paths, forming larger particles. Accretion continues until objects are large enough to attract matter with their gravity.

The Sun and the Hertzsprung-Russell Diagram

• The solar system's mass is dominated by the sun, a fairly typical star.
• Hertzsprung-Russell (H-R) diagram plots relative luminosity (to our sun) against surface temperature.
• Luminosity is proportional to the surface area of a star.
  • Surface area of a sphere = $4πr^2$, so a larger radius (r) results in a much bigger surface area.
• The color of a star is related to its temperature.
• Most stars lie on the main sequence, including our sun.
• Exceptions:
  • White dwarfs: Very small (small radius ⇒ low luminosity), hot remnants of stars.
  • Red giants and super giants: Extremely large (high luminosity), but lower temperature stars.

Cosmic Abundance of Elements

• Derived from spectroscopic studies of the sun and chemical analyses of chondritic meteorites.
• Key points:
  1. Dominance of H and He.
  2. Li, Be, and B have much lower abundances than expected.
  3. Relatively high abundance of Fe.
  4. General decline in abundance with increasing atomic number (Z).
  5. Sawtooth appearance: Elements with even numbers of protons are more abundant than elements with odd numbers.

Element Production during the Big Bang

• Matter was originally present as neutrons.
  • Neutrons are not stable alone ⇒ underwent spontaneous radioactive decay (half-life = 10.3 minutes) to form protons & electrons.
  • $^1<em>0n \rightarrow ^1</em>1H + ^0_{-1}e + \nu^*$
• Big Bang Nucleosynthesis (lasted ~17 minutes) ⇒ Rapid expansion & cooling.
• Collisions between protons and neutrons formed Deuterium (D) = $^2H$.
• Other collisions lead to formation of other light elements: $^3He$, $^4He$, $^6Li$, $^7Li$ as well as radioactive or reactive light nuclei ($^3H$, $^7Be$, $^8Be$) which decayed or were captured by other nuclei.
• No stable nucleides with a mass of 5 or 8.
• Three particles needed to collide to form Li, Be and B (e.g. Two $^1H$ with $^4He$ to form $^6Li$). Requires all three particles to be in the same place at the same time in the correct orientation.

Element Production in Stars – Stellar Nucleosynthesis

• The H and He (+ traces of slightly heavier nuclei) then condensed into stars, in which other elements are synthesized.
• In the cores of stars nuclear fusion occurs due to: very high temperatures & pressures.
• Atoms must move fast enough to collide: The hotter an atom, the faster it moves.
• High velocities overcome electrostatic repulsion force (Coulomb barrier).
• For two protons to collide the temperature needs to be: ~ 50 million °C.
• Einstein realized that for a nuclear reaction to lead to the release of heat, there must be a reduction in the mass of constituent atoms.
• Energy and mass are interconvertible: $E = mc^2$.
  • $m$ is rest mass.
  • $c$ is the speed of light (ca. $3 \times 10^8 m s^{-1}$).
• A small amount of mass can be converted (through fusion) to produce a large amount of energy.
• The escaping heat creates pressure and stops the star collapsing.
• 4 $H$ are required to form 1 $He$, therefore:
  • 4 $H$ = $6.696 \times 10^{-24} g$
  • 1 $He$ = $6.648 \times 10^{-24} g$
  • Mass loss = $0.048 \times 10^{-24} g$
• Converting 1g $H$ -> $He$ produces $1.5 \times 10^{11}$ calories ⇒ enough energy to heat 2 million L of water from room temp to boiling point.

First Generation Stars

• Overall process:
  • $4 ^1<em>1H \rightarrow ^4</em>2He + 2 ^0_1e + 2 \nu + energy$
  • positron = A positively charged electron. A particle of antimatter.
  • Neutrino = Similar to an electron but has no electrical charge.
• Formation of helium: When the central temperature of a star reaches about $10^7 K$, protons in the H/He mixture are in sufficiently rapid motion for fusion to occur.
• H atoms collide and form He.
• Collapse of the star is stopped by: Internal pressure created by escaping heat (energy) produced by H->He.
• In the core of the star, He atoms do not interact with each other (it is not hot enough or dense enough). The star is building up a source of He.
• Large stars will exhaust their H fuel supply faster than smaller stars.

He Fusion – the α process

• As H is consumed, the star loses the ability to hold gravity back and starts to contract. It becomes smaller and denser. This collapse causes the temperature of the core rises to $10^8 K$.
• He fusion can then begin (He nuclei have 2 protons hence a 2+ charge, so are harder to fuse compared to H nuclei with 1+ charge).
• Rapid capture of $^8Be$.
• Overall: $3 ^4He \rightarrow ^{12}C + energy$
  • The mass of C is less than 3 x He ⇒ energy appears as heat.
• This reaction can then be followed by successive α-particle fusion processes, with further core contractions and temperature increases

Cycle of a Star

• Stepwise build-up of elements where atoms formed have concentric shells of progressively hotter and denser matter, forming heavier nuclei.
  • No neutrons are produced in these processes.
  • Unable to create isotopes or odd mass elements.
  • There is a stepwise build-up of even-mass elements.
• $^{12}C \rightarrow ^{16}O + energy$
• $^{16}O \rightarrow ^{20}Ne + energy$
• $^{20}Ne \rightarrow ^{24}Mg + energy$
• $^{24}Mg \rightarrow ^{28}Si + energy \rightarrow ^{32}S, ^{36}Ar, ^{40}Ca \rightarrow ^{56}Fe$
• A 25 solar mass star: Atomic # increasing in multiples of 2, Mass # increasing in multiples of 4.
• Fuel depletion -> Renewed collapse -> Rise in core temperature -> Ignite the next fuel.

Fusion Stages

• Very large stars are very hot and luminous but use their hydrogen up very quickly, so have short lifespans.
• In contrast, red dwarfs use their fuel slowly and have extremely long lifespans.
• Nuclear fusion stops at Iron ($^{56}Fe$).
  • Merge of nuclei does not lead to mass loss and heat must be added ⇒ a different process is used to form these elements.
• Iron is an extremely stable element as it has the highest nuclear binding energy. Accounts for Fe having 1000x expected abundance.
• Stars are unable to trigger Fe fusion ⇒ they can no longer prevent gravitational collapse.

The Fate of a Star

Small Stars

• These stars gradually expand, cool, and become dimmer (“slow demise”).
• Not the answer to redistribution of elements or creating heavier elements.

Large Stars

• Once all nuclear fuel is consumed, there is nothing to hold back gravity, and the star begins to collapse ⇒ Fe atoms get very close together.
• Triggering a supernova followed by formation of either a neutron star or a black hole.
• Supernovae disperse synthesized elements throughout space.
• Subsequent stars begin their lives containing small amounts of the heavier elements (N, C, up to Fe).

Second (and subsequent) Generation Stars

• Same as the 1st generation star but a different pathway.
• $^{12}C$ is a catalyst.
• Alternative H fusion route (C-N-O cycle) (stellar core T > $14 \times 10^6 K$).
  $^{12}C \space + \space ^1H \rightarrow ^{13}N + \gamma$
  $^{13}N \rightarrow ^{13}C + e^+ + \nu$
  $^{13}C \space + \space ^1H \rightarrow ^{14}N + \gamma$
  $^{14}N \space + \space ^1H \rightarrow ^{15}O + \gamma$
  $^{15}O \rightarrow ^{15}N + e^+ + \nu$
  $^{15}N \space + \space ^1H \rightarrow ^{12}C + ^4He$
• Overall: $4 ^1<em>1H \rightarrow ^4</em>2He + 2 ^0_1e + 2 \nu + energy$
• A 2nd or later generation star will have converted some $^{12}C$ into $^{13}C$ through the CNO cycle; some of the $^{13}C$ survives in a region dominated by $^4He$.
• When the star enters the Red Giant stage, the temperature increases, and the following reaction occurs: $^{13}C + ^4He \rightarrow ^{16}O + ^1n$ => This reaction occurs faster than $3 ^4He \rightarrow ^{12}C$ => one neutron is produced for each $^{13}C$.
• In a star, neutrons are in close-packed conditions. Neutrons will enter the nucleus of iron before they have a chance to decay, unlike neutron production during the Big Bang where they were unstable & quickly decayed.

Neutron Production in Nucleosynthesis Processes

• Now that neutrons are available, they are readily captured by other atoms (but not $^4He$) to produce:
  • Elements beyond Fe
  • Isotopes of elements whose masses are not multiples of 4
• The entry of a neutron into a nucleus:
  • Not repelled because they do not have a charge.
  • Can occur at low temperatures.
• Neutron addition occurs through two processes:
  • Slow (s) process
  • Rapid (r) process

Slow neutron capture process (s-process)

• Build-up of elements in a slow, controlled manner.
• Neutron hits are spaced out.
• Allows nuclides time to achieve stability through β-decay.
• Reaction chain terminates at a cycle involving Bi, Po, and Pb.

Rapid neutron process (r-process)

• In a supernova explosion, Fe is rapidly hit with neutrons.
• Excess neutrons decay to a proton + electron ⇒ change in element.
• Elements are unable to decay to a stable isotope during this time.

Shortly after the supernova explosion: R-process - Part 2

• Neutrons disappear, and the neutron-rich isotopes can undergo radioactive decay until the element reaches a stable neutron-to-proton ratio.
• For some elements, this decay is still occurring (e.g., U - long ½ life).
• Many neutrons are produced.
• Multiple neutron additions occur without the opportunity for complete decay.
• Nuclides are neutron-rich and thus displaced from the stability curve to the right-hand side.
• Neutron addition carries on past the heaviest ‘stable’ nucleus ($^{209}Bi$), creating radioactive nuclei.
• Heavy nuclei continue to form until incoming neutrons trigger fission.

Comparing the R and S processes

Evidence for Stellar Nucleosynthesis

1. Energy: Only nuclear fusion would provide sufficient energy to keep stars burning. Temperature and pressure are high enough to allow fusion of elements.
2. Direct observation:
   • Observe stars becoming supernovae.
   • Presence of technetium (Tc): All isotopes of Tc are radioactive ($T_{1/2} = 10^6$ years). All would have disappeared since the solar system formed ($10^9$ years).
   • Gamma rays emitted by $^{56}Co$ light up nebulas created by explosion. Brightness decays exponentially following ½ life of Co.
3. Relative abundances of the elements:
   • Dominance of H and He: produced during the Big Bang.
   • Li, Be & B trough: only produced in small quantities (3 particle collisions).
   • Fe peak: the end of nuclear fusion assembly line.
   • General decline in abundance with increasing atomic # (z): lighter elements are made in stars, heavier elements only during supernova.
   • Sawtooth appearance: Nuclides with even mass numbers strongly favored – more stable when grouped together into helium nuclei/ alpha particles: i.e 2 protons, 2 neutrons.

Evidence of planet formation from the sun

• $M = RV^2/G$
  • $M$ = mass of host planet
  • $R$ = distance of moon from planet
  • $V$ = velocity of moon orbiting planet
  • $G$ = universal gravitational constant, $6.67 \times 10^{-11} N m^2 kg^{-2}$
• Important features of planets in solar system:
  1. All planets are spinning in the same direction as the sun.
  2. The orbit of each planet around the sun is almost circular, and they all lie in nearly the same plane (corresponding to the sun’s equator).
  3. Roughly even spacing between planets (increase is ~1.7 x – Bode’s Law).
• Mass of planet: Determined from the gravitational influence it exerts on its moons, other planets, and space probes.

Planet Properties

General Trends

• Radius & Mass: Large range, no systematic trend
• Density: Provides strong clues on the chemical composition of each planet
• Clear distinction between terrestrial and giant planets.
  • Terrestrial planets: Relatively high densities ⇒ Metallic/solid core
  • Giant plants: Relatively low densities

Corrected Density

• Density of a planet WITHOUT the influence of gravity

• Needed because larger planets have larger gravitational pull
  Density = Mass/Volume $(\rho) = \frac{mass}{volume}$

• $V = \frac{4}{3} \pi r^3$

• $m = \frac{rv^2}{G}$

  Density provides strong clues on chemical composition, but there are a wide variety of combinations of elements. It is a rough approximation – the heavier an element the greater the density of the substances the element makes.

Distribution and abundance of elements in the solar system

• Depends on the volatility of the element
• Early in the formation of the solar system, ions produced by the Sun removed volatile elements from the inner solar system, leaving dust particles behind, enriched in the involatile elements, which subsequently condensed to form the terrestrial planets

Fate of Elements

1. Highly volatile elements:
   • Mainly lost as gases to the outer solar system.
2. Moderately volatile elements:
   • Partially captured
3. Very low volatility elements:
   • Mainly captured

Oxygen - Fate 2 (Moderately volatile)

• Attracted to H, but more strongly attracted to form bonds with metals (transition metals) to form highly involatile oxide materials.
• Out of the first 10 elements, O is the only element sufficiently abundant and prone to form the solid phase.
• 5x more oxygen atoms than metal atoms -> only 20% of O could form compounds with metals (effectively trapped).
• The remaining 80% joined with H and was lost