Relationship between radioactive isotope and radioactive dating

The abundance of carbon-14 in atmospheric carbon and in living matter is 1.2 part in a trillion (1.2 x 10). Solution How many atoms decay each second in a 1.000 gram sample of natural uranium?

Solution The Earth's crust is about 2.1% potassium by weight. All natural potassium is 0.012% potassium-40, a radioactive isotope with a half-life of 1.2 billion years; the rest consists of stable isotopes of potassium.

It is equal to the inverse of the mean lifetime: For example, radium-226 has a half-life of 1,602 years, an mean lifetime of (1,602)/ln2 = 2,311 years, and a decay rate of 1/(2,311) = 0.000433 per year.To better understand the sources of the Earth's heat, scientists studied antineutrinos, elementary particles that, like their neutrino counterparts, only rarely interact with normal matter.Using the Kamioka Liquid-scintillator Antineutrino Detector (Kam LAND) located under a mountain in Japan, they analyzed geoneutrinos — ones emitted by decaying radioactive materials within the Earth — over the course of more than seven years.The researchers found the decay of radioactive isotopes uranium-238 and thorium-232 together contributed 20 trillion watts to the amount of heat Earth radiates into space, about six times as much power as the United States consumes. As huge as this value is, it only represents about half of the total heat leaving the planet.The researchers suggest the remainder of the heat comes from the cooling of the Earth since its birth.

The lifetime units are time units such as seconds or years.