16. Radiometric dating and applications to sediment transport

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1 16. Radiometric dating and applications to sediment transport William Wilcock OCE/ESS 410 Lecture/Lab Learning Goals Understand the basic equations of radioactive decay Understand how Potassium-rgon dating is used to estimate the age of lavas Understand how lead-10 dating of sediments works Concept of supported and unsupported lead-10 in sediments Concept of activity Steps to estimate sedimentation rates from a vertical profile of lead-10 activity pplication of lead-10 dating to determining sediment accumulation rates on the continental shelf and the interpretation of these rates - LB Radioactive decay - Basic equation he number or atoms of an unstable isotope elements decreases with time d d = λ d = - umber of atoms of an unstable isotope λ - radioactive decay constant is the fraction of the atoms that decay in unit time (e.g., yr -1 ) d = λ 0 Radioactive decay - Basic equation d = ln 1 = ln λ d = λ 0 = ln = λt 0 = λ Setting = ½, the time for half the radioactive atoms to decay is give by 1/ - half life is the time for half the atoms to decay 1

2 Potassium-rgon (K-r) Dating he isotope K is one of 3 isotopes of Potassium ( 39 K, K and 41 K) and is about 0.01% of the natural potassium found in rocks K is radioactively unstable and decays with a half life ½ = 1.5 x 10 9 years (λ = 1.76 x s -1 ) to a mixture of -Calcium (89.1%) and -rgon (10.9%). Because rgon is a gas it escapes from molten lavas. Minerals containing potassium that solidify from the lava will initially contain no argon. Radioactive decay of K within creates r which is trapped in the mineral grains. If the ratio of r/k can be measured in a rock sample via mass spectrometry the age of lava can be calculated. ln K-r Dating Formula = λ If K f is the amount of -Potassium left in the rock and r f the amount of -r created in the mineral then = K f = K f + r f / = 1 λ ln K + r f f / K f ote that the factor 1 / accounts for the fact that only 10.9% of the K that decays created r (the rest creates Ca) K-r dating assumptions r concentrations are zero when the lava solidifies (in seafloor basalts which cool quickly rgon can be trapped in the glassy rinds of pillow basalts violating this assumption) o r is lost from the lava after formation (this assumption can be violated if the rock heats up during a complex geological history) he sample has not been contaminated by rgon from the atmosphere (samples must be handled carefully). Lead-10 dating 10 Pb or Pb-10 is an isotope of lead that forms as part of a decay sequence of Uranium U è 34 U è 30 h è 6 Ra Half Life 4.5 Byr Rocks Half life 1600 yrs, eroded to sediments è Rn è 10 Pb è 06 Pb Gas, half life 3.8 days Half life,.3 years Stable

Pb-10 in sediments Supported 10 Pb Sediments contain a background level of 10 Pb that is supported by the decay of 6 Ra (radium is an alkali metal) which is eroded from rocks and incorporated into

3 Pb-10 in sediments Supported 10 Pb Sediments contain a background level of 10 Pb that is supported by the decay of 6 Ra (radium is an alkali metal) which is eroded from rocks and incorporated into sediments. s fast as this background 10 Pb is lost by radioactive decay, new 10 Pb is created by the decay of 6 Ra. Excess or Unsupported 10 Pb Young sediments also include an excess of unsupported 10 Pb. Decaying 38 U in continental rocks generates Rn (radon is a gas) some of which escapes into the atmosphere. his Rn decays to 10 Pb which is efficiently washed out of the atmosphere and incorporated into new sediments. his unsupported 10 Pb is not replaced as it decays because the radon that produced it is in the atmosphere. ctivity - Definition In order understand how 10 Pb is used to determine sedimentation rates we need to the activity of a sediment = cλ ctivity is the number of disintegrations in unit time per unit mass (units are decays per unit time per unit mass. For 10 Pb the usual units are dpm/g = decays per minute per gram ) C - detection coefficient, a value between 0 and 1 which reflects the fraction of the disintegrations are detected (electrically or photographically) ctivity - Equations We know previously defined the equation for the rate of radioactive decays as d = λ Multiplying both sides by the constant cλ gives an equivalent equation in activity d = λ 3

4 Pb-10 activity in sediments B Pb-10 activity Excess Pb-10 concentrations 1 Excess Pb-10 activity Surface mixed layer - bioturbation Region of radioactive decay. Measured Pb-10 activity Excess or unsupported Pb-10 activity (measured minus background) t 1 t Work with data in this region For a constant sedimentation rate, S (cm/yr), we can replace the depth axis with a time axis z = St Depth, Z (or age) Background Pb-10 levels from decay of Radon in sediments ( supported Pb-10) ge of sediments, t t = z S d = λ Solving the equation - 1 d = λ 1 t t 1 ln 1 = λ t t t1 he equation relating activity to the radioactive decay constant Integrating this with the limits of integration set by two points ln + = = λ( t t 1 ) relationship between age and activity Solving the equation - = λ t t 1 ( t t 1 ) = z z 1 S = λ z z 1 S S = λ z z 1 Substitute in the relationship between age and depth n expression for the sedimentation rate 4

5 Pb-10 sedimentation rates Plot depth against natural logarithm of Pb-10 activity ln() Depth, z Slope = S λ Ignore data with background levels Ignore data in mixed layer Summary - How to get a sedimentation rate 1. Identify the background ( supported ) activity B - the value of at larger depths where it is not changing with depth.. Subtract the background activity from the observed activities at shallower depths 3. ake the natural logarithm to get ln()=ln( observed - B ) 4. Plot depth z against ln(). 5. Ignore in the points in the surface mixed region where ln() does not change with depth. 6. Ignore points in the background region at depth ( observed B ). 7. Measure the slope in the middle region. It will be negative. 8. Multiply the minus the slope by the radioactive decay constant (λ = yr -1 ) to get the sedimentation rate. Limitations ssumption of uniform sedimentation rates. Cannot use this technique where sedimentation rate varies with time (e.g., turbidites). ssumption of uniform initial and background Pb-10 concentrations (reasonable if composition is constant). Upcoming lab In the lab following this lecture you are going to calculate a sedimentation rate for muds on the continental shelf using radioactive isotope Lead-10 and you are going to interpret a data set of many such measurements obtained off the coast of Washington. 5

17. Radiometric dating and applications to sediment transport

OCEAN/ESS 410 17. Radiometric dating and applications to sediment transport William Wilcock Lecture/Lab Learning Goals Understand the basic equations of radioactive decay Understand how Potassium-Argon