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The radioactivity of a substance is measured by how many decays per
unit time occur. Two popular units of the activity
are used: the curie (Ci),
defined as

1 Ci = 3.7 x 10^{10} decays/s
 (8)

and the becquerel (Bq), defined as
Note that, by themselves, these units do not measure accurately
how dangerous a given amount of
radiation might be for humans  for medical purposes
other units of radioactivity reflecting this aspect are more appropriate.
It is found that, if a given radioactive substance at a certain time
contains N nuclei, then at a short time t later a certain
number N have decayed which is given by
where is called the decay constant. Note that
has units of inverse time, or s ^{ 1}.
The decay rate,
R , is defined as the number of decays per unit time:

R = = N.
 (11)

For finite times it is found that the number of nuclei present after
a time t is given by
where N_{0} is the number of nuclei present at t = 0 and
e = 2.71828...
is the base of the ``natural'' logarithms (compared to the base 10 of the
``common'' logarithms). Thus, from Eq. (29.12),
in a time t = a fraction
e^{  1} = 0.36787944... of a substance remains.
It is sometimes convenient to introduce the halflife, T_{1/2} , of a
substance, defined as the time over which exactly one half of a substance
remains. From Eq. (29.12) one finds

e^{  T1/2} = T_{1/2} =
 (13)

where
ln 2 = 0.693... is the natural logarithm of 2 (note
ln e = 1 , which is analogous to log 10 = 1 for the common
logarithm). In terms of
the halflife Eq. (29.12) can be written as

= ^{t/T1/2}.
 (14)

Thus, after a period of one halflife of a substance remains,
after another half life
x =
of a substance remains, and so on. Halflives of
substances range from tiny fractions of a second to millions of years.
Next: Nuclear Reactions
Up: Nuclear Physics
Previous: Radioactivity
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10/9/1997