According to the definition of half-life, half of the original amount of the radioac- tive element should remain after one half-life has passed. Use the equation pro- vided for N(t) and set the time passed equal to one half-life (t = h) to illustrate this relationship. Suppose you know what N, N. and the half-life h of an element is, but you would like to know the time that has passed since a specimen was alive. Describe a procedure to solve for t. Accompany your procedure with the algebraic manipu- lation of N(t) to isolate 1.
According to the definition of half-life, half of the original amount of the radioac- tive element should remain after one half-life has passed. Use the equation pro- vided for N(t) and set the time passed equal to one half-life (t = h) to illustrate this relationship. Suppose you know what N, N. and the half-life h of an element is, but you would like to know the time that has passed since a specimen was alive. Describe a procedure to solve for t. Accompany your procedure with the algebraic manipu- lation of N(t) to isolate 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:According to the definition of half-life, half of the original amount of the radioac-
tive element should remain after one half-life has passed. Use the equation pro-
vided for N(t) and set the time passed equal to one half-life (t = h) to illustrate
this relationship.
Suppose you know what N, N. and the half-life h of an element is, but you would
like to know the time that has passed since a specimen was alive. Describe a
procedure to solve for t. Accompany your procedure with the algebraic manipu-
lation of N(t) to isolate t.
Transcribed Image Text:Part B: Exploration
-
In 1949, Willard Libby and a team of scientists at the University of Chicago discov-
ered that the age of an organism could be found based on the amount of radioac-
tive carbon it contains a process known as carbon dating. Every object contains
two types of carbon; radioactive carbon, carbon-14, and non-radioactive carbon,
carbon-12. In living objects, the ratio of these two carbons is fixed, i.e., the amount
of each carbon in living things remains the same. When a living organism dies,
the carbon-14 is no longer replenished and starts to decay. The process of carbon
dating aids scientists in determining the amount of time that has passed since an
organism was alive. To calculate how long ago the carbon-14 stopped being replen-
ished, scientists use logarithms. Let's investigate how logarithms are used.
Radioactive elements, such as carbon-14, have a specific rate of decay. The amount
of time it takes for half of the radioactive component in the element to decay is
known as the element's half-life, h. If N(t) is the amount of radioactive material as a
function of time, t, and if N is the amount of radioactive material that was originally
in the sample, and t is the amount of time passed since death, then the amount of
radioactive material remaining in the sample after time, t, is represented by N(t),
where
In 2
N(t) = Noe h
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