Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

100 CHAPTER 4
Figure 4-11. Generalized semilog
plot of the decrease in activity due to
radioactive transformation.
a straight line is obtained. If time is measured in units of half-lives, the straight line
shown in Figure 4-11 is obtained.
The illustrative example given above could have been solved graphically with the
aid of the curve in Figure 4-11. The ordinate at which the time in units of halflife,
0.189, intersects the curve shows that 87.7% of the original activity is left. The
correction factor, therefore, is the reciprocal of 0.877:
Correction factor =
1
= 1.14.
0.877
The fact that the graph of activity versus time, when drawn on semilog paper, is
a straight line tells us that the quantity of activity left after any time interval is given
by the following equation:
A = A0 e −λt , (4.18)
where A0 is the initial quantity of activity, A is the amount left after time t, λis the
transformation rate constant (also called the decay rate constant, or simply the decay
constant), and e is the base of the system of natural logarithms.
The transformation rate constant is the fractional decrease in activity per unit
time and is defined as
Limit
t→0
N/N
t
=−λ, (4.19)
where N is a number of radioactive atoms and N is the number of these atoms
that are transformed during a time interval t. The fraction N/N is the fractional
decrease in the number of radioactive atoms during the time interval t. A negative
sign is given to λ to indicate that the quantity N is decreasing. For a short-lived
radionuclide, λ may be determined from the slope of an experimentally determined
transformation curve. For long-lived isotopes, the transformation constant may be