17. Radiometric dating and applications to sediment

transport

William Wilcock

OCEAN/ESS 410

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

Radioactive decay - Basic equation

λ- radioactive decay constant is the fraction of the atoms that decay in unit time (e.g., yr-1)

N - Number of atoms of an unstable isotope

The number or atoms of an unstable isotope elements decreases with time

Radioactive decay - Basic equation

T1/2 - half life is the time for half the atoms to decay

Setting NT = ½N0, the time for half the radioactive atoms to decay is give by

Potassium-Argon (K-Ar) Dating• The isotope 40K is one of 3 isotopes of Potassium (39K,

40K and 41K) and is about 0.01% of the natural potassium found in rocks

• 40K is radioactively unstable and decays with a half life T½ = 1.25 x 109 years (λ = 1.76 x 10-17 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.

K-Ar Dating Formula

If Kf is the amount of 40-Potassium left in the rock and Arf the amount of 40-Ar created in the mineral then

Note that the factor 1 / 0.109 accounts for the fact that only 10.9% of the 40K that decays created 40Ar (the rest creates 40Ca)

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).

Lead-210 dating

238U 234U …230Th 226Ra

222Rn…210Pb…206Pb

Half Life 4.5 Byr Rocks

Half life 1600 yrs, eroded to sediments

Gas, half life 3.8 days

Half life, 22.3 years

Stable

210Pb or Pb-210 is an isotope of lead that forms as part of a decay sequence of Uranium-238

Pb-210 in sediments

Excess or Unsupported 210Pb

Young sediments also include an excess of “unsupported” 210Pb. Decaying 238U in continental rocks generates 222Rn (radon is a gas) some of which escapes into the atmosphere. This 222Rn decays to 210Pb which is efficiently washed out of the atmosphere and incorporated into new sediments. This unsupported 210Pb is not replaced as it decays because the radon that produced it is in the atmosphere.

Supported 210Pb

Sediments contain a background level of 210Pb that is “supported” by the decay of 226Ra (radium is an alkali metal) which is eroded from rocks and incorporated into sediments. As fast as this background 210Pb is lost by radioactive decay, new 210Pb is created by the decay of 226Ra.

Activity - Definition

In order understand how 210Pb is used to determine sedimentation rates we need to the activity of a sediment

Activity is the number of disintegrations in unit time per unit mass (units are decays per unit time per unit mass. For 210Pb 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)

Activity - Equations

We know previously defined the equation for the rate of radioactive decays as

Multiplying both sides by the constant cλ gives an equivalent equation in activity

Pb-210 activity in sedimentsPb-210 activity

Depth, Z (or age)

AB

Background Pb-210 levels from decay of Radon in sediments (“supported” Pb-210)

Surface mixed layer - bioturbation

Region of radioactive decay.

Measured Pb-210 activity

Excess or unsupported Pb-210 activity (measured minus background)

Excess Pb-210 concentrations

Excess Pb-210 activity

Age of sediments, t

For a constant sedimentation rate, S (cm/yr), we can replace the depth axis with a time axis

Wor

k w

ith d

ata

in th

is r

egio

n

t2

t1

A2 A1

Solving the equation - 1The equation relating activity to the radioactive decay constant

Integrating this with the limits of integration set by two points

A relationship between age and activity

Solving the equation - 2

Substitute in the relationship between age and depth

An expression for the sedimentation rate

Pb-210 sedimentation rates

ln(A)

Depth, z

Plot depth against natural logarithm of Pb-210 activity

Ignore data in mixed layer

Ignore data with background levels

Summary - How to get a sedimentation rate1. Identify the background (“supported”) activity AB - 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(Aobserved-AB)

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 (Aobserved ≈ AB).

7. Measure the slope in the middle region. It will be negative.

8. Multiply the minus the slope by the radioactive decay constant (λ= 0.0311 yr-1) to get the sedimentation rate.

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).

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.