Question

Uranium-238 disintegrates and transforms to stable lead-206. The half-life of this reaction is 7.6 billion years. Estimate the geologic age of a rock that contains 0.05 and .0005 wt% U-238 and Pb-206, respectively. List the assumptions implied in the estimate.

Answer 1

• Uranium 238 Lead 206 that the number is the mass number (the total number of protons plus neutrons).
• Note that the mass number may vary for an element, because of a differing number of neutrons.
• Elements with various numbers of neutrons are called isotopes of that element.
• Each radioactive isotope has its own unique half-life.
• A half-life is the time it takes for half of the parent radioactive element to decay to a daughter product.
• Uranium 238 Lead 206 the half life of reaction is 7.6 billion years
• Radioactive decay occurs at a constant exponential or geometric rate.
• The rate of decay is proportional to the number of parent atoms present.
• The proportion of parent to daughter tells us the number of half-lives, which we can use to find the age in years.
• For example, if there are equal amounts of parent and daughter, then one half-life has passed. If there is three times as much daughter as parent, then two half-lives have passed.
• Radioactive decay occurs by releasing particles and energy.
• Uranium decays producing subatomic particles, energy, and lead. As uranium-238 decays to lead, there are 13 intermediate radioactive daughter products formed (including radon, polonium, and other isotopes of uranium), and 8 alpha particles and 6 beta particles released.
• There are three types of subatomic particles involved: 1.Alpha particles large, easily stopped by paper charge = +2 mass = 4 2.Beta particles penetrate hundreds of times farther than alpha particles, but easily stopped compared with neutrons and gamma rays.
• Charge = -1 mass = negligible 3.neutrons highly penetrating no charge mass = 1 Gamma rays (high energy X-rays) are also produced.
• Of these, U-238 is by far the most abundant (99.2739%). Radioactive elements tend to become concentrated in the residual melt that forms during the crystallization of igneous rocks.