Consider the radioisotope ²²⁶Ra (half life = 1.60 × 10³ years). What is the first order rate constant for ²²⁶Ra?

The half life for the radioactive decay of rubidium-87 to strontium-87 is 4.88 × 10¹⁰ years. Suppose nuclear chemical analysis shows that there is 0.423 mmol of strontium-87 for every 1.000 mmol of rubidium-87 in a certain sample of rock. Calculate the age of the rock. Round your answer to 2 significant digits. years x10

Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32, in milligrams, is left from an original sample of 175 mg of Na₃³²PO₄ after 41.5 days? Assume that the atomic mass of ³²P is 32.0

The half-life for P-32, a radionuclide used in DNA sequencing, is 14.28 days. Calculate the percentage of P-32 remaining after 94.2 days. Use 3 significant figures for the percentage.

The half life for the radioactive decay of carbon-14 to nitrogen-14 is 5.73 × 10³ Suppose nuclear chemical analysis shows that there is 0.790 mmol of nitrogen-14 for every 1.000 mmol of carbon-14 in a certain sample of rock. Calculate the age of the rock. Round your answer to 2 significant digits. years x10 years. X

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.)

A rock contains the radioactive isotope K − 40 that decays with a half-life of 1.3 billion years and the radioactive isotope Rb− 87 that decays with a half-life of 48.6 billion years. The rock is100 million years old. The rock currently has 1000 times as many Rb− 87 atoms as there are K − 40 atoms. (That is, N Rb= 1000 × N K) When the rock first formed it had M times as many Rb − 87 atoms as L − 40 atoms. (That is, N Rb, 0 = M × N K,0.) What is the value of M?

Three radioisotopes X, Y, and Z have half-lives of 1, 2 and 5 years respectively. Each of the three radioisotopes has the same activity now in July 2020. Which radioisotope will be hotter (meaning it will have more activity remaining) if you were to examine them at different times in the future, specifically in July 2023 for X, July 2024 for Y, and July 2040 for Z? Provide a full explanation of your reasoning. O Y because 2 half-lives will have passed by July 2024. OX because July 2023 is sooner than July 2024 or July 2040. OX because 3 half-lives will have passed by July 2023. O Z because July 2023 is sooner than July 2024 or July 2040. Z because July 2040 is later than July 2023 and July 2024. O Y because July 2023 is sooner than July 2024 or July 2040. O Z because 4 half-lives will have passed by July 2040.

Americium-241 is widely used in smoke detectors. Calculate the amount of americium-241 consumed in a smoke detector (initially containing 3.60 µg of Am), in micrograms, that has been used for one year if the half-life is 433 years.