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Lecture_40 - PHYS 342 Fall 2011 Lecture 40: Radioactive...

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PHYS 342 Fall 2011 Lecture 40: Radioactive Dating, Fission, and Fusion Ron Reifenberger irck Nanotechnology Center Birck Nanotechnology Center Purdue University Lecture 40 1
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The activity (R) of a source can also be defined: 2 1 / 1 () t o Nt N   Number of radioactive atoms remaining after a time t 1 12 2 0.693 0.693 / / 0.693 2 0.5 (just another way to write 1/2) ) t t e t N e Ne   decay constant; units [1/s]; robability that any one nucleus 0.693 oo  py y will decay in one second t o   o tt o Rt e e t NR   Decays/second after a time t Note that λ N o =R o is the activity (decay rate) when t=0 2
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Example: A radioactive source with a half-life of 30 mins. is measured to have a decay rate of 80,000 s -1 . How many radioactive nuclei are present? 0.693 eca constant; nits [1/s]   12 decay constant; units [1/s] () t Nt Ne () ( ) o tt o o R R N e e t    0.693 where oo o RN N 1 60 s 30 min 80,000 s min o R   8 0.693 0.693 2.08 10 o N  3
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Suppose you have a sample of 4.75×10 7 atoms of Radon? Radon has a half-life of 3.82 days. What is the activity of this sample? R(t)= e t o R 7 1/2 4.75 10 3.82 days o N  61 0.693 1day 1hr 1min 3.82days 24hr 60min 60s 1 10  7 2. 11 0 (2.1 10 )(4.75 10 ) 99.7 / Ci oo s RN s s   9 10 1Ci 99.7 Bq 2.7 10 Ci 0.0027 μ Ci 3.7 10 decays/s 1 (2.110 ) R(t)=[99.7 Bq] e st 4
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Radioactive Dating (Rutherford 1905) Assume the ratio of normal carbon (carbon-12) to carbon-14 in air (and in all living things) has remained nearly onstant over time constant over time. Calibration: today, 1 carbon-14 atom in about 7.4x10 11 carbon-12 atoms. Assume that at any time, all living organisms have approximately the same tio of carbon- to carbon- in their ratio of carbon 12 to carbon 14 in their tissues. When an organism dies, it no longer replenishes carbon and the decay of carbon-14 to carbon-12 changes the carbon-12 to carbon-14 ratio.
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Lecture_40 - PHYS 342 Fall 2011 Lecture 40: Radioactive...

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