3. A sample of a radioactive isotope is found to have an activity of 115.0 Bq immediately after it is pulled from the reactor that formed it. Its activity 2 h 15 min later is measured to be 85.2 Bq. (a) Calculate the decay constant 7 and the half-life t1/2 of the sample. (b) How many radioactive nuclei were there in the sample initially?
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- Question 1. Tritium has a half - life of 12.33 years. What fraction of the nuclei in a tritium sample will remain (a) after 5.00 yr? (b) after 10.0 yr? (с) after 123.3 yг?A certain isotope has a half-life of 5.9 h and an atomic mass of 95.98 u. What will the activity in Bq of a 1.36-g sample be after 19.8 h?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.
- Barium-133 is a radioactive element used in certain medical procedures. A sample of pure Barium133 has a mass of 18.000 grams. Determine the activity of the sample 47 years after it was created, in units of Curies.After 1.80 days, the activity of a sample of an unknown type radioactive material has decreased to 80.4% of the initial activity. What is the half-life of this material?Question 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.
- E c) For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No e¯‹, where A is the decay constant. i) Derive the relationship between the half-life t₁ and the time constant □ = = 1/λ. ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of one gram of radium in Becquerels. iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a daughter product present will vary with time, Na(t). Sketch two graphs, with appropri- ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0, for the two extreme cases where the daughter product is much more radioactive than the parent (\d >> \) and where the daughter product is much less radioactive than the parent (\a << λ). Given that the half-life of radon-226 is 3.8 days, indicate which graph is relevant and estimate the amount of radon in equilibrium with one mole of radium.Thorium 22890Th produces a daughter nucleus that is radioactive. The daughter, in turn, produces its own radioactive daughter, and so on. This process continues until bismuth 21883Bi is reached. What are (a) the total number Nα of α particles and (b) the total number Nβ of β- particles that are generated in this series of radioactive decays?Chromium's radioactive isotope 51Cr has a half-life of 27.7 days and is often used in nuclear medicine as a diagnostic tracer in blood studies. Suppose a 51Cr sample has an activity of 2.36 µCi when it is placed on a storage shelf. (a) How many 51Cr nuclei does the sample contain? Answer:__________ nuclei (b) Calculate the sample's activity in Bq when it is removed from storage one year later. Answer:____________Bq
- Both 1)Given a half-life of a radioactive source is 435 years. Calculate the time taken for its activity to reduce from 4.5 Ci to 0.14 Ci? 2) Equation shows nuclear reaction of gamma radiation which incident on an isotope helium. Calculate the energy of the gamma ray in MeV unit? (Given mass of Helium = 3.016029 u, mass of proton = 1.007276 u and mass of neutron = 1.008665 u) 23??+?→211?+01?There is more than one isotope of natural uranium. If a researcher isolates 0.7 mg of the relatively scarce 235U and finds this mass to have an activity of 78.0 Bq, what is its half-life in years? =___years11. Radium-226, 226Ra, undergoes an alpha decay. The current sample of Radium-226 has an initial activity of 5.50 × 101º Bq. (a) Identify the daughter nucleus by name, nucleon number, atomic number and neutron number. (b) What is the decay constant? (c) How many radioactive nuclei were initially present in the sample? (d) How long will it take the sample to reach an activity of 5.00 x 1010 Bq?