Bananas are somewhat radioactive due to the presence of substantial amounts of potassium. Potassium-40 decays by two different paths: 40 K Ca+B (89.3%) 19 20 40 , K2 40 KA+B* (10.7%) 19 18 The half-life for potassium decay is 1.3x10° years. Calculate the overall and the rate constants for the individual branch reactions.
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- Potassium-argon dating is used to measure the age of rocks formed from cooled lava by determining the fraction of the original 40K remaining in a sample from the ratio of 40K:40Ar. Unusually, potassium-40 decays into both 40Ca (89.1% of the time) and 40Ar (10.9% of the time) with a half-life of 1:248 x 10^9 years. 1. Write out balanced nuclear equations for these two decay processes. 2. Calculate the specific activity of 40K.At t = 0 s, you have a pure sample of an unknown substance. At t = 948 s, 36.8% of the substance remains. Determine the decay constant and what t will be when 12% of the substance remains. λ = s1 t=Radioactive potassium-40 has a half-life of 4.2 x 1016 s. a) Calculate the decay constant of potassium-40. b) A sample of potassium-40 has an initial mass of 1.0 g. Calculate the number of parent nuclei present in the sample, as well as the initial activity of the source. (One mole of potassium-40 has a mass of 40 g and NA = 6.0 x 1023 mol-1) c) Calculate the number of parent nuclei present in the sample after 9.2 x 1016 s.
- Once again, the final products have less mass than the 2 nuclei that fuse together; find the missing mass that converts to energy in the last reaction. Using the numbers in the Atomic Mass column, calculate 3He + 3He H-H- 4He. Type the entire calculator answer carefully. [it should be positive, similar in style to 0.012179] (1) Atomic (2) Element (3) Symbol (4) Mass (5) % Abundance (or Radioactive Decay Mode) (7) Half-life (if radioactive) Atomic Number Number, Mass 0. (Neutron) 1.008665 10.4 min Hydrogen Deuterium Tritium H. 99.985% 0.015% 1.007825 2.014102 T. 1 3 3.016049 12.33 yr Helium Не 0.000137% 99.999863% 3 3.016029 4. 4.002602 3. Lithium Li 6.015121 7.016003 7.5% 92.5% 4 Beryllium EC, 7 100% Be 7.016928 53.29 days 9.012182 67 9Question 2. A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 1.00 kg sample of carbon from the wood has an activity equal to 5.00 x 10* decays per minute. Find the age of the charcoal. Hint: Living material has an activity equal to 15.0 decays/min per gram of carbon present.Archeologist extracted 179 gm of carbon from an animal bone from an archeological site. The carbon shows an activity of 15 decays/s. (Half-life of 146C = 5730 years, 1 year = 3.156 x 107 seconds, Avogadro's number = 6.02 x 1023 atoms/mol) (A) Total number of atoms in this carbon sample = . (B) Decay constant of 146C, λ = . (C) Number of 146C atoms in this sample = . (D) Activity of 146C at time (t = 0) = . (E) Age of the animal =
- Time 0 t₁2 20₁2 3₁/12 Number of nuclides, N x 10³ 1000 750 500 90/2 10/₁2 250 125 0 12 212 312 412 512 612 7h2 8h2 9h12 10/2 Time in multiples of t₁/2 The figure shows a typical radioactive decay (amount of undecayed nucleus (N) vs. time (t)) from a heavy nucleus. Such a decay may be best expressed by an equation like : ON = N₂ (xt) ON=N₂/λt -λt ON = N₂e N = N₂ e-1/At N 1,000,000 500,000 250,000 125,000 62,500 31,250 15,625 7,813 3,906 1,953 977 412 5/₁/2 61₁2 7h2 81/2A radioactive nucleus has half-life T1/2. A sample containing these nuclei has initial activity R0. Calculate the number of nuclei that decay during the interval between the times t1 and t2.