Radioactive Decay and Dating Methods - lect 6

Used for dating minerals, fossils, and meteors.
Unlike carbon-14 dating, the initial amount of the isotope in the sample is generally unknown.
Ratios of isotopes are used for dating.

Uranium-238:- The most common form of naturally occurring uranium (99%).
- Undergoes a complex decay series to lead (stable).
- Half-lives vary within the decay series, ranging from fractions of seconds to billions of years.
Uranium-235:- About 1% of naturally occurring uranium.
- Decays to lead-207.
Mass spectrometers are used to measure the amounts of uranium and lead isotopes.
Assumption:- The sample initially contained only uranium.
By measuring the ratio of uranium to its decay products (lead isotopes) and knowing the half-lives, the age of the sample can be determined.

Importance: Determining the rate and extent of sedimentation is crucial.
Uranium's Role:- Uranium is soluble and abundant in water (rivers, seas).
- It does not react with water but decomposes into other products, including thorium.
Thorium:- Thorium (specifically thorium-230) is reactive.
- It reacts with oxides or hydroxides, causing it to precipitate and settle into sediment.
Methodology:- Measure the radioactivity of thorium-230 at different sediment depths.
- Thorium at greater depths is older and has lower activity.
Sedimentation Rate Example:- If sedimentation rate = 2 cm per 1000 years, a plot of thorium activity vs. depth can be created.
- Samples are taken at different depths (e.g., every 1.5 cm down to 7.5 cm).
- Thorium activity decreases with depth.
Calculating Sedimentation Rate:- Plot the natural log of thorium-230 activity against depth.
- The plot should form a straight line.
- The gradient of this line is used to calculate the sedimentation rate.
- Sedimentation = {ln2 \over slope}

Measurements from a deep-sea bed:- Depths: 1 cm, 11 cm, 22 cm, 31 cm, 41 cm, 51 cm, 61 cm.
- Thorium-230 activity measured at these depths (high radioactivity allows for accurate measurements).
- The half-life of thorium-230 is 75,000 years (7.5 \times 10^4).
Process:- Take the natural log of the thorium-230 activity values.
- Plot these values against the depth.
- A straight line is expected, with a gradient of -0.0535 in this case.
Sedimentation Calculation:- Slope = 0.0535 (ignoring the minus sign).
- Sedimentation = {ln2 \over slope} = {0.693 \over 0.0535} = 13 cm per half-life.
Convert to cm per thousand years:- {13 \over 75} = 0.17 cm per thousand years.

Used extensively for dating volcanic rock.
Involves potassium-40, which has a long half-life (1.1 \times 10^9 years).
Decay Process:- Potassium-40 decays to argon-40 (a gas).
- Unlike carbon dating (where nitrogen is lost to the atmosphere) or uranium dating (where lead remains), argon-40 is trapped within the volcanic rock's crystal lattice.
Advantages:- Potassium is abundant in many minerals and volcanic rocks.
- Argon, being a gas, is not present when the volcano erupts and lava solidifies, providing a clear starting point.
- Argon can be easily extracted by crushing the rock and collecting the gas.
Complication:- Potassium-40 can decay into two different elements:- 11% decays to argon-40.
- The rest decays to calcium-40.
- While the calculation is more complex due to the two decay pathways, the dating method is still effective.

A useful analytical technique for stable materials (non-radioactive).
Process:- Samples are bombarded with neutrons in a nuclear reactor, making them radioactive.
- The isotopes in the sample become excited and enter a high-energy state.
- As the isotopes return to their ground state, they emit gamma radiation.
- The energy of the emitted gamma radiation is specific to each element, allowing for the identification and quantification of the elements present in the sample.
Application:- Analysis of arsenic in human hair to detect arsenic poisoning.
Advantages:- Non-destructive technique (samples become radioactive for only a short period).
Complementary Method: Prompt Gamma Ray Activation Analysis (PGA)

Neutron capture: Neutrons fired at the sample interact with the nucleus. After receiving the neutrons, goes into an excited state that decays very quickly and emits prompt gamma radiation.- The nucleus can be a stable nucleus again, or it can be a radioactive one.
NAA works with radioactive nuclei- The radioactive nucleus decay through the beta- decay. That means a beta- is emitted, and a cascade of gamma rays are afterwards also emitted.
- NAA works with this delayed gamma radiation
Information gained from this gamma radiation:- The energy of the gamma rays that are characteristic for each element.
- The intensity of these, gamma rays are also proportional to the amount of the elements inside a sample.
Typical elements that are determined with PGA are low set elements like, for example, hydrogen, nitrogen, and boron.
Practical application of this method:- Forensic science.
- Archaeology.

A question with a randomly generated ratio is presented to the students. Most students got the answer wrong.