Cracking the SAT Physics Subject Test

A = A 0 e−λt

where A 0 is the activity at time t = 0 and λ is the decay constant (not to be

confused with wavelength).

Activity is expressed in disintegrations per second: 1 disintegration per second is
one becquerel (Bq). The greater the value of λ, the faster the sample decays. This
equation also describes the number (N) of radioactive nuclei in a given sample, N =

N 0 e−λt, or the mass (m) of the sample, m = m 0 e−λt.

The most common way to indicate the rapidity with which radioactive samples
decay is to give their half-life. Just as the name suggests, the half-life is the time
required for half of a given sample to decay.

Half-life, T1/2, is inversely proportional to the decay constant, λ, and in

terms of the half-life, the exponential decay of a sample’s mass (or

activity) can be written as

A sample’s activity or mass can be graphed as a function of time; the result is the
exponential decay curve, which you should study carefully.