carbon-14

Examples of carbon-14 in the following topics:

• Half-Life and Rate of Decay; Carbon-14 Dating

  • Carbon-14 dating is a radiometric dating method that uses the radioisotope carbon-14 (14C) to estimate the age of object.
  • There are also trace amounts of the unstable radioisotope carbon-14 (14C) on Earth.
  • Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.
  • Both processes of formation and decay of carbon-14 are shown in .
  • Diagram of the formation of carbon-14 (1), the decay of carbon-14 (2), and equations describing the carbon-12:carbon-14 ratio in living and dead organisms

• Paramagnetism and Diamagnetism

• Calculations Involving Half-Life and Decay-Rates

  • A sample of 14C, whose half-life is 5730 years, has a decay rate of 14 disintegrations per minute (dpm) per gram of natural carbon.
  • We have: $N = N_o e^{-t/\tau} \text{ where } N/N_o=4/14≈0.286 $, $\tau = t_{1/2}/ln2 \approx 8267 \text{ years, } t=−\tau lnN/N_o≈10360 \text{ years.}$

• Surface Tension and Capillary Action

  • The effect can be seen in the drawing-up of liquids between the hairs of a paint-brush, in a thin tube, in porous materials such as paper, in some non-porous materials such as liquified carbon fiber, and in a cell.

• Greenhouse Gases and Global Warming

  • If we approximate the Earth as a perfect absorber and emitter of the radiation received from the sun (called a blackbody), we would expect the Earth to be at an average temperature of 5°C, rather than the 14°C which we observe.
  • On the other hand, greenhouse gases such as carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) are characteristically strong absorbers of the energy radiated by the Earth's surface.

• Further Reading

  • To learn more about radiation from moving charges, consult Chapter 14 of

• Problems

  • Consider that the mass fraction of the different atoms are hydrogen (0.7), helium (0.27), carbon (0.008), oxygen (0.016) and iron (0.004).

• A few examples

  • 3.14 Give specific (nonzero) examples of 2 by 2 matrices satisfying the following properties:

• Mass Spectrometer

  • This one is for the measurement of carbon dioxide isotope ratios as in the carbon-13urea breath test.

• Complex numbers and constant coefficient differential equations

  • To see this, plug an exponential $e^{pt}$ into Equation 1.1.14.
  • The i-th derivative with respect to time is $p^i e^{pt}$, so Equation 1.1.14 becomes
  • (Figure 1.4. )