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The formula for the half-life can be expressed as
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- Radioactive substances follow a specific law of decay. Namely, if you have a sample of some radioactive isotope, the quantity left after a certain time, called the half-life and denoted T1/2, is one-half of what you had initially. If you wait a second half-life, then there will be half f what was left at the end of the first half-life. Since 1/2-1/2 = 1/4, you will have one-fourth of the original quantity left after two half-lives. You can continue with this procedure to find the fraction of the original sample that hasn't decayed after any number of half- lives. However, this would become quite cumbersome if you are interested in the quantity left after, say, 10 half-lives. In this case, the quantity you are looking for would be found by multiplying the original quantity by 10 factors or 1/2. To solve this problem, we use exponents. An exponent, a small number written above and to the right, tells you how many copies of a particular number are multiplied together. In our example,…arrow_forwardA sample contains 1,174 nuclei of a radioactive isotope of chromium. If the half-life is 33 days, how many of the radioactive nuclei were present one year earlier? (This year lasted 365 days.) Give your answer to 3 significant figures in scientific notation (e.g. 3.29E6)arrow_forwardAn unknown radioactive element decays into non-radioactive substances. In 360 days the radioactivity of a sample decreases by 34 percent. (a) Find the decay constant k. (Round your answer to 5 decimal places.) (b) What is the half-life of the element? (Round your answer to two decimal places) half-life: (days) (c) How long will it take for a sample of 100 mg to decay to 59 mg? (Round your answer to two decimal places) time needed: (days)arrow_forward
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- MI * 00 因 44 -0.00002866t where A(t) is the amount of the isotope at time t (in years) and A, is the original amount. if the original The decay of an isotope is given by A(t)= Ap e amount is 100 pounds, find the half-life of this isotope. The half-life of the isotope is about years. (Do not round until the final answer. Then round to the nearest whole number as needed.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer Copyright © 2021 Pearson Equcation INC. All rignts reserved. | Terms of use | PrIvacy PolicyT Permissions ContaCL US to search PriSc F7 F8 F11 F12 F5 +DD & %23 7. 8. 3. 5. K B. Altarrow_forwardA 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.arrow_forwardThe half-life of a radioactive isotope is the amount of time it takes for a quantity ofradioactive material to decay to one-half of its original amount. (a) The half-life of Carbon 14 (C-14) is 5230 years. Determine the decay-rate parameter λ for C-14.(b) The half-life of Iodine 131 (I-131) is 8 days. Determine the decay-rate parameter for I-131.arrow_forward
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