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help 數學 expontial decay 20分
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1.Strontium has a half-life of 25 a. How many years does it take for 20mg smaple to decay to a massof 2mg ? Answer is 83.02.Radium-221 has a half-life of 30 s . How long will it take for 95% of it to decompose? Answer 129.63. If 25 mg of a radioactive element decays to 20mg in 48 h, find the half-life of... 顯示更多 1.Strontium has a half-life of 25 a. How many years does it take for 20mg smaple to decay to a massof 2mg ? Answer is 83.0 2.Radium-221 has a half-life of 30 s . How long will it take for 95% of it to decompose? Answer 129.6 3. If 25 mg of a radioactive element decays to 20mg in 48 h, find the half-life of the element? Answer 149.1 help , 老師給了我answers,但是我不能計出來
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(1) Suppose that no. of half life = x, then: 20(1/2)x = 2 (1/2)x = 0.1 x log (1/2) = log (0.1) x = 3.32 Hence time required = 3.32 x 25 = 83.0 s (2) Suppose that no. of half life = x, then: (1/2)x = 0.05 (since 5% remains when 95% decomposed) x log (1/2) = log (0.05) x = 4.32 Hence time required = 4.32 x 30 = 129.6 s (3) Suppose that no. of half life = x, then: 25(1/2)x = 20 (1/2)x = 0.8 x log (1/2) = log (0.8) x = 0.32 Hence half-life = 48/0.32 = 149.1 hrs
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