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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- The isotope 238 U decays to 206Pb with a half-life of 4.47 x 10° y. (Although the decay occurs in many individual steps, the first step has by far the longest half-life, so the decay can be considered to go straight to lead.) A rock recovered far underground is found to contain 0.76 mg of 238U, 0.17 mg of 206pb, and 1.4 mg of 40 Ar. Assume that 40K decays to only 40 Ar with a half-life of 1.25 x 10 y. How much 40K will it likely contain? mgPotassium-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 =A 25g piece of charcoal is discovered in a prehistoric cave. Carbon 14 of the sample shows a radioactive activity of 250 disintegrations / minute. If we estimate that originally the decay was 376 decays / minute, for how long is the tree from which the carbon sample was taken dead? The half-life of carbon-14 is 5730 years.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 81/2
- Which of the following formula is used to calculate the decay constant λ which is related to the half-life (T)?A radioactive element 235U is present in a Zircon sample with 3500 atoms. It is known that 235U has a half-life of 700 million years. How long would it take to decay to 115 atoms? A 3200.12 million years В 3449.35 million years 3825.00 million years 3500.45 million yearsA 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.