17. Radiometric dating and applications to sediment transport

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1 OCEAN/ESS Radiometric dating and applications to sediment transport William Wilcock

2 Lecture/Lab Learning Goals Understand the basic equations of radioactive decay Understand how Potassium-Argon dating is used to estimate the age of lavas Understand how lead-210 dating of sediments works Concept of supported and unsupported lead-210 in sediments Concept of activity Steps to estimate sedimentation rates from a vertical profile of lead-210 activity Application of lead-210 dating to determining sediment accumulation rates on the continental shelf and the interpretation of these rates - LAB

3 Radioactive decay - Basic equation The number or atoms of an unstable isotope elements decreases with time dn dt dn dt N T N = λn dn = N N 0 N 0 N - Number 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 ) dn = λ dt N N T T 0

4 Radioactive decay - Basic equation N T dn = N N 0 N 0 dn = λ dt N N T T 0 ln N N 0 = ln N 0 N T N T = λt T = λt 0 Setting N T = ½N 0, the time for half the radioactive atoms to decay is give by T 12 = ln2 λ T 1/2 - half life is the time for half the atoms to decay

5 Potassium-Argon (K-Ar) Dating The isotope 40 K is one of 3 isotopes of Potassium ( 39 K, 40 K and 41 K) and is about 0.01% of the natural potassium found in rocks 40 K is radioactively unstable and decays with a half life T ½ = 1.25 x 10 9 years (λ = 1.76 x s -1 ) to a mixture of 40-Calcium (89.1%) and 40-Argon (10.9%). Because Argon is a gas it escapes from molten lavas. Minerals containing potassium that solidify from the lava will initially contain no argon. Radioactive decay of 40K within creates 40Ar which is trapped in the mineral grains. If the ratio of 40Ar/40K can be measured in a rock sample via mass spectrometry the age of lava can be calculated.

6 K-Ar Dating Formula ln N 0 N T = λt If K f is the amount of 40-Potassium left in the rock and Ar f the amount of 40-Ar created in the mineral then N T = K f N 0 = K f + Ar f / T = 1 K + Ar / λ ln f f K f Note that the factor 1 / accounts for the fact that only 10.9% of the 40 K that decays created 40 Ar (the rest creates 40 Ca)

7 K-Ar dating assumptions Ar concentrations are zero when the lava solidifies (in seafloor basalts which cool quickly Argon can be trapped in the glassy rinds of pillow basalts violating this assumption) No Ar is lost from the lava after formation (this assumption can be violated if the rock heats up during a complex geological history) The sample has not been contaminated by Argon from the atmosphere (samples must be handled carefully).

8 Lead-210 dating 210 Pb or Pb-210 is an isotope of lead that forms as part of a decay sequence of Uranium U è 234 U è 230 Th è 226 Ra Half Life 4.5 Byr Rocks Half life 1600 yrs, eroded to sediments è 222 Rn è 210 Pb è 206 Pb Gas, half life 3.8 days Half life, 22.3 years Stable

10 Pb-210 in sediments Supported 210 Pb Sediments contain a background level of 210 Pb that is supported by the decay of 226 Ra (radium is an alkali metal) which is eroded from rocks and incorporated into sediments. As fast as this background 210 Pb is lost by radioactive decay, new 210 Pb is created by the decay of 226 Ra. Excess or Unsupported 210 Pb Young sediments also include an excess of unsupported 210 Pb. Decaying 238 U in continental rocks generates 222 Rn (radon is a gas) some of which escapes into the atmosphere. This 222 Rn decays to 210 Pb which is efficiently washed out of the atmosphere and incorporated into new sediments. This unsupported 210 Pb is not replaced as it decays because the radon that produced it is in the atmosphere.

11 Activity - Definition In order understand how 210 Pb is used to determine sedimentation rates we need to the activity of a sediment A A = cλn Activity is the number of disintegrations in unit time per unit mass (units are decays per unit time per unit mass. For 210 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)

12 Activity - Equations We know previously defined the equation for the rate of radioactive decays as dn dt = λn Multiplying both sides by the constant cλ gives an equivalent equation in activity da dt = λ A

13 Pb-210 activity in sediments A B Pb-210 activity Surface mixed layer - bioturbation Measured Pb-210 activity Region of radioactive decay. Excess or unsupported Pb-210 activity (measured minus background) Depth, Z (or age) Background Pb-210 levels from decay of Radon in sediments ( supported Pb-210)

14 Excess Pb-210 concentrations A 2 A 1 Excess Pb-210 activity t 1 t 2 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 Age of sediments, t t = z S

15 Solving the equation - 1 da dt = λ A A 2 da = λ dt A A 1 t 2 t 1 The equation relating activity to the radioactive decay constant Integrating this with the limits of integration set by two points A ln A 2 A1 = λ t t 2 t1 ln A 2 + ln A 1 = ln A 1 ( ) A 2 = λ t 2 t 1 A relationship between age and activity

16 Solving the equation - 2 ( ( ) z = 2 z ) 1 t 2 t 1 ( ) ln A 1 A 2 = λ t 2 t 1 λ ( z S = 2 z ) 1 ln A 1 A 2 S ( ) ln A λ z 1 = 2 z 1 A S 2 Substitute in the relationship between age and depth An expression for the sedimentation rate

17 Pb-210 sedimentation rates Plot depth against natural logarithm of Pb-210 activity ln(a) Ignore data in mixed layer Depth, z Slope = S λ Ignore data with background levels

18 Summary - How to get a sedimentation rate 1. Identify the background ( supported ) activity A B - the value of A at larger depths where it is not changing with depth. 2. Subtract the background activity from the observed activities at shallower depths 3. Take the natural logarithm to get ln(a)=ln(a observed -A B ) 4. Plot depth z against ln(a). 5. Ignore in the points in the surface mixed region where ln(a) does not change with depth. 6. Ignore points in the background region at depth (A observed A 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.

19 Limitations Assumption of uniform sedimentation rates. Cannot use this technique where sedimentation rate varies with time (e.g., turbidites). Assumption of uniform initial and background Pb-210 concentrations (reasonable if composition is constant).

20 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-210 and you are going to interpret a data set of many such measurements obtained off the coast of Washington.

16. Radiometric dating and applications to sediment transport

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