It can be shown that a 1.0-mg sample of 232 Th decays at the rate of 4.1 a emissions per second. Set up a mathematical equation for the rate of AN =-kN, where N is the number of nuclei in the 1.0-mg sample and - is 4.1 dps. Solve this equation for the rate constant for At AN decay, At this process. k= Then calculate its half-life.

Different radioisotopes (Links to an external site.) have different half-lives (Links to an external site.).  For example, the half-life of carbon-14 (Links to an external site.) is 5,700 years, the half-life of uranium-235 (Links to an external site.) is 704 million years, the half-life of potassium-40 (Links to an external site.) is 1.3 billion years, and the half-life of rubidium-87 (Links to an external site.) is 49 billion years. Explain why you would not use an isotope with a half-life similar to that of carbon-14 to determine the age of the Solar System. The age of the universe is estimated to be approximately 14 billion years. Does that mean that no rubidium-87 has decayed? Explain.

Archeologists continue to debate the arrival of the first humans in the Western Hemisphere. Radiocarbon dating of charcoal from a cave in Chile was used to establish the earliest date of human habitation in South America as 8700 years ago. This procedure involves comparing the 14C present in a sample of charcoal to the 14C present in a living tree of the same age. What fraction of the 14C initially present remained in the charcoal after 8700 years? The half-life of 14C is 5730 years. (Write the answer as a number with a decimal.)

The half-life of 14C is 5730 years, and the current decay rate in living organisms is 14.3 disintegrations per minute per gram of carbon (d.p.m./g C). What is the age (in years BP) of an artifact found to have a decay rate of 4.75 d.p.m/g C in 2013? IMPORTANT: When entering your answer: • Enter the number only (no units) • Do not leave any spaces • Report your number to the tens column (regardless of the significant figures) Correctly round your answer to the tens column (margin of allowed error is only ± 10, so always use un-rounded numbers in your calculations) Examples: 12340 or 5670 (include the zero in the units column, Canvas will add a comma for you)

The half-life of bromine-74 is 25 minutes.  How much of a 40 cpm sample is still active after 75 minutes?

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125I is an isotope used in nuclear medicine and commonly produced in a radioactive concentration of 931. mCi/mL (Ci, or Curie is a unit of measure of radioactivity). If the half life of 125I is 59.5 days, after production and delivery, requiring 28. days, what would be the concentration, in mCi/mL of the product? Answer to the nearest whole number.

If 1/8 of a radioactive element remains after 600 years, what is the element half life? Please explain steps?