What is the decimal amount of K-40 that remains? Since, the sample is 3.8 parts by mass Ar and 1 part K, the orginal sample contained 4.8 parts K and zero parts Ar. Problem #33: What is the age of a rock in which the mass ratio of Ar-40 to K-40 is 3.8? K-40 decays to Ar-40 with a half-life of 1.27 x 10 9 yr.
We will use 0.22, the decimal percent of K-40 remaining: In the present day, the sample contains 78% Ar-40 and 22% K-40. What is the age of the rock?Īssume the sample was 100% K-40 at start. A sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms. Problem #32: The radioisotope potassium-40 decays to argon-40 by positron emission with a half life of 1.27 x 10 9 yr. Solution to b: 0.9079 is the decimal fraction of the substance remaining since 0.0921 has gone away (b) What is the half-life of the nuclide? (a) What percentage of the nuclide will have decayed after 159 days? Problem #31: A radioactive sample contains 3.25 x 10 18 atoms of a nuclide that decays at a rate of 3.4 x 10 13 disintegrations per 26 min. Start by ignoring a few chemical realities and assume all the Ra-226 ends up as lead.Ħ.80 g / 205.974465 g/mol = 0.033013801 mol of Pb-206 decayedī) Calculate grams of Ra-226 initially present: Chemical analysis of a certain chunk of concrete from an atomic-bombed city, preformed by an archaeologist in the year 6264 AD, indicated that it contained 2.50 g of Ra-226 and 6.80 g of Pb-206. Problem #30: The isotope Ra-226 decays to Pb-206 in a number of stages which have a combined half-life of 1640 years. If the half life of tritium is 12.25 years, calculate the actual number of tritium atoms remaining in 10.0 g water after a period of 49 years. Problem #29: The ratio of tritium, H-3, to hydrogen, H-1, in a sample of water was 1:1x10 19. Solution: A has a half-life of 3 hrs, so 18 hrs = 6 half-lives.ī has a half-life of 6 hrs, so 18 hrs = 3 half-lives.Īfter 6 half lives, the fraction of A left is 1/(2 6) = 1/64 What is the expected ratio A/B after 18 hours?
The half-life of A is 3 hours and, that of B, 6 hours. Initially, the sample composition is 1:1, i.e., the same number of nuclei A as nuclei B. Problem #28: A sample of radioactive isotopes contains two different nuclides, labeled A and B. In 24 hours, the sample goes from 100% to 95% How long will it take for half the original to decay? Problem #27: You have 20.0 grams of P-32 that decays 5% daily. Therefore the total amount of elapsed time for A was 2.Ĭ) Allow B to go through several half-lives such that the total amount of time = 2. Find f.ī) Let us set the length of one half-life of A equal to 1. In the same period the number of radio-active nuclei in sample B decreases to a fraction f of the number present initially. In a certain period the number of radio-active nuclei in sample A decreases to one-fourth the number present initially. Problem #26: The half life in two different samples, A and B, of radio-active nuclei are related according to T(1/2,B) = T(1/2,A)/2. ChemTeam: Half-Life Problems #26 - 40 Half-Life Problems #26 - 40 Ten Examples Problems involving carbon-14 Probs 1-10 Problems involving uranium-238 Probs 11-25 Examples and Problems only (no solutions) Return to Radioactivity menu