EARTHSS 152 Study Guide - Midterm Guide: Radioactive Decay, Geochemistry, Electronvolt
1 May 2018
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ESS 152
Isotope Geochemistry – 2018 Midterm Review
Concepts to understand
● Chart of the Nuclides:
● z=# of protons
● n=# of neutrons
● A= n+ z (mass #)
○ radioactive vs stable isotopes
■ Stable isotopes are more towards the middle
■ Radioactive- towards the outside and top
● z>83, no stable nuclei
○ binding energy and nuclear stability
■ Higher Binding energy/nucleon=lower internal energy= more stable
■ Mass defect=calculated-actual mass
● The mass of an atom is always less than the sum of its parts
(protons, electrons, neutrons)
■ Binding energy=mc^2
● Convert mass (amu) to kg
● Convert joules to MeV
● Divide by the # of nucleons
■ Magic numbers
● All even #’s= most stable, high abundance
● Protons or neutron only even #=fairly abundant
● Odd # of protons and neutrons=not abundant
● Most abundant when… Z or N=2, 8, 20, 28 ,50, 82, 126
○ valley of stability
■ Z<20, most stable nuclei have 1:1 ratio of N/Z
■ @ higher masses Neutrons(N) become greater than Protons(Z)
● N/Z ratio ~ 1.5
■ Z>83 no stable nuclei
■ ** higher up the valley wall= shorter half-life
● Nuclei on vall walls are unstable and will decay towards the valley
floor
■ # of stable isotopes << # of radioactive ones
● nucleosynthesis – diff types
○ Element abundance as a result of…
■ Nuclear Stability
■ Nucleosynthesis
● 4 phases
○ 1. Cosmological (Big Bang)
○ 2. Stellar (Stars)
■ H burning
■ He burning
○ 3. Explosive (Supernova)
■ Fe is the most stable form of matter
■ No heat to balance gravity→ collapse= Supernova
○ 4. Galactic/Cosmogenic (Space)
■ stellar nucleosynthesis up to Mass 56
● Begins with H burning
○ Proton-proton chain
■ 99% of Sun’s energy
● then...helium/carbon burning
● a and e process
■ Synthesis of heavier elements by p, r, s processes
●Synthesizing elements with A>56
●S process: radioactive isotopes have time to decay before next
neutron capture
○ Follows s pathway
○ If B- is protected by an r only, it is an s-only process
isotope
○ All others on the path are s&r
●R-process: neutron capture outpaces decay
○ r-only , elements that follow B- but are not on the S path
●P-process: proton bombardment
○ Explains the existence of heavy nuclei on the proton rich
side of s-process pathway
○ Elements not on the s-path and protected from B-
■ relationship to isotope abundance
● Most stable= s pathway
○ Most abundant
● Larger atomic weight= less abundant
○ Abundance
■ Magic #’s are most abundant (Z or N= 2,8,20,28,50,82,126)
● Even is better than odd
● Radioactive decay (α, β-, β+) , half-lives, decay constants
○ Alpha decay: A - 4, Z - 2
■ Emission of 4He (alpha particle)
■ Daughter experiences recoil (alpha and daughter have equal and
opposite momentums)
○ Beta - : A - 0, Z + 1
■ Converts one neutron → proton + electron
■ Release of electron (Beta particle)
○ Beta + : A - 0, Z - 1
■ Converts one proton → neutron + electron
■ Release of positron (beta particle)
○ Electron capture: A - 0, Z - 1
■ Convert one proton→ neutron
○ Gamma decay- photon emission, no change in A or Z
○ Spontaneous Fission- Z=92 or above, generates two smaller nuclei
○ Half-Lives
■ The shorter the half life= more radioactive
■ Long half life= more stable
○ Abundance
■ Only stable nuclei
■ How abundant they are in nature
● Isochron method & Assumptions
○ Comparing ratio of parent (N) to daughter (D) yields the age of the sample
■ Known from half life
○ We must assume…
■ Half life is constant and correct
■ It is a closed system (no gain of D isotopes except through decay)
■ Initial D=0
● Rb-Sr dating methods
○ Different chemistry of Rb and Sr (incompatibility)
■ Rb prefers melt, is more incompatile than Sr
■ Parent is more incompatible
■ Incompatible: ions that do not fit into major rock forming minerals
● Usually large ions
■ Ions are sorted by size and charge during crystallization of a cooling
magma
■ High Rb/Sr= more 87Sr
■ Low Rb/Sr = less 87 Sr
○ why continental crust and oceanic crust differ
■ Continental = Granite
● (Rb and K)
● Higher Rb/Sr ratio
● Higher radiogenic (87Sr/86Sr) isotope ratio
■ Oceanic= basalt
● (Sr and Ca)
○ Why isochron approach is necessary
■ 87Sr/86Sr= (e^(λt) -1) (87Rb/86Sr) + 87Sr/86Sr(initial)
● y=mx+b
■ slope= (e^(λt) -1)
● Can be used to find t
■ y-intercept = 87Sr/86Sr(initial)
■ Assumptions..
Document Summary
Stable isotopes are more towards the middle. Higher binding energy/nucleon=lower internal energy= more stable. The mass of an atom is always less than the sum of its parts (protons, electrons, neutrons) All even #"s= most stable, high abundance. Odd # of protons and neutrons=not abundant. Z<20, most stable nuclei have 1:1 ratio of n/z. @ higher masses neutrons(n) become greater than protons(z) ** higher up the valley wall= shorter half-life. Nuclei on vall walls are unstable and will decay towards the valley floor. # of stable isotopes << # of radioactive ones. Fe is the most stable form of matter. No heat to balance gravity collapse= supernova. Synthesis of heavier elements by p, r, s processes. S process: radioactive isotopes have time to decay before next neutron capture. If b- is protected by an r only, it is an s-only process isotope. R-only , elements that follow b- but are not on the s path.
