6. Model radioactive decay using the notation t = time (independent variable), r(t) = amount of particular radioactive isotope present at time t (dependent variable), -λ = decay rate (parameter). Note that the minus sign is used so that > > 0. (a) Using this notation, write a model for the decay of a particular radioactive iso- tope. (b) If the amount of the isotope present at t = 0 is ro, state the corresponding initial-value problem for the model in part (a).

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Chapter30: Nuclear Physics
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6. Model radioactive decay using the notation
t = time (independent variable),
r(t) = amount of particular radioactive isotope
present at time t (dependent variable),
-λ = decay rate (parameter).
Note that the minus sign is used so that λ > 0.
(a) Using this notation, write a model for the decay of a particular radioactive iso-
tope.
(b) If the amount of the isotope present at t = 0 is ro, state the corresponding
initial-value problem for the model in part (a).
7. The half-life of a radioactive isotope is the amount of time it takes for a quantity of
radioactive 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 pa-
rameter for C-14.
(b) The half-life of Iodine 131 (I-131) is 8 days. Determine the decay-rate param-
eter for I-131.
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Transcribed Image Text:6. Model radioactive decay using the notation t = time (independent variable), r(t) = amount of particular radioactive isotope present at time t (dependent variable), -λ = decay rate (parameter). Note that the minus sign is used so that λ > 0. (a) Using this notation, write a model for the decay of a particular radioactive iso- tope. (b) If the amount of the isotope present at t = 0 is ro, state the corresponding initial-value problem for the model in part (a). 7. The half-life of a radioactive isotope is the amount of time it takes for a quantity of radioactive 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 pa- rameter for C-14. (b) The half-life of Iodine 131 (I-131) is 8 days. Determine the decay-rate param- eter for I-131. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
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