= dating based on the steady decay of unstable isotopes
Atoms = nucleus of protons & neutrons orbited by electrons
Isotopes = different forms of element w/ different numbers of neutrons
unstable (Mother or Parent) isotopes
stable (Daughter) isotopes
decay
4.
Radiometric Dating Half-life = time required for ½ of the unstable isotopes in a sample to decay into stable isotopes Decay is a perfectly random process; every atom has a 50/50 chance of decaying in a given time period (i.e., the half-life)
5.
time (My) Proportion of unstable isotopes 1.0 Half-life = 1 My Radiometric Dating 1 2 3 4 0 0 5 0.5 0.25 0.125 0.0625
6.
Radiometric Dating P = P 0 e - kt P = # unstable isotopes (parent) at time t P 0 = # unstable isotopes (parent) at time 0 (the initial # of isotopes) e = 2.718… k = decay constant = 0.693/H (to be precise, -k = ln(½)/H = -0.693/H) H = half-life t = time
7.
Radiometric Dating P = P 0 e - kt To find the age of a rock, solve this eq. for t: But we don’t know how many parent isotopes we started with!! ln ∙ t = 1 k P 0 P
8.
Radiometric Dating P = P 0 e - kt To find the age of a rock, solve this eq. for t: ln ∙ t = 1 k P 0 P P 0 - P = # stable (daughter) isotopes at time t! Let’s call this D. + 1 ln ∙ t = 1 k P 0 - P P ln ∙ t = 1 k P 0 - P + P P
9.
Radiometric Dating P = P 0 e - kt To find the age of a rock, solve this eq. for t: This is the equations we’ll use. ln ∙ t = 1 k P 0 P + 1 ln ∙ t = 1 k D P
where t = age D = amount of daughter (stable) isotope P = amount of mother (unstable) isotope k = 0.693/H H = half-life + 1 ln ∙ t = 1 k D P
12.
How old are the oldest rocks on Earth? t = 6.45 Ga · ln(1.85) t = 6.45 Ga · 0.615 + 1 ln ∙ t = 1 k D P + 1 ln ∙ t = H 0.693 D P 0.85 + 1 ln ∙ t = 4.47 Ga 0.693 G = giga = billion a = annum = years
13.
t = 3.96 Ga + 1 ln ∙ t = 1 k D P How old are the oldest rocks on Earth?
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