Knowledge of mathematics basic to radioactivity measurement is an important and required element of radiation worker training. This edition of NUtrino presents the basics of calculating radioactive decay and converting counts to activity. Radiation Safety Handbook sections 9 and 10 present a more complete discussion. [note: For simplicity these examples are written in "old" units instead of SI units.]

Radioactive decay is a random process. We can describe the decay of any particular atom only as a probability that it will occur within a specified interval. This probability is described by the radionuclide's unique decay constant, lambda (l). Lambda is equal to the natural logarithm of 2 divided by the half-life ( t_1/2):l = .693/ t_1/2.

The decay equation is N = N_oe^-lt where N = activity or number of atoms after elapsed time t, N_o = activity or number of atoms we start with, and e = base of natural logarithms. When you perform this calculation, make sure to use the same units for elapsed time and half-life (e.g., days or years).

Example 1: Suppose you received a 250 uCi shipment of P-32-labeled dATP on February 18 and today is February 27. How much activity is left?

Example 2: You received 2 mCi of H-3 on June 18, 1996. How much activity is left on February 18, 1998?

Need to convert count rate to activity (e.g., to calculate activity of liquid scintillation vials for a waste card)? First, use a standard of known activity and similar quench to calculate the counter's efficiency. If the standard's activity is expressed in units of uCi, convert that to disintegrations per minute (dpm). The simplest way is to multiply the activity in uCi by the conversion factor 2.22 x 10⁶ dpm/uCi. Count the standard and divide the count rate in counts per minute (cpm) by the standard's dpm. The result is your counter's efficiency (eff) for that radionuclide. Next, count your samples and convert the sample count rate in cpm to dpm: cpm/eff = dpm. Finally, convert the sample dpm to activity: dpm/2.22 x 10⁶ dpm/uCi = uCi.