The constant is called the decay constant, and it has different values for different
nuclides. A large value of corresponds to rapid decay; a small value corresponds
to slower decay. Solving Eq. (43.16) for shows us that is the ratio of the number
of decays per time to the number of remaining radioactive nuclei; can then be
interpreted as the probability per unit time that any individual nucleus will decay.
The situation is reminiscent of a discharging capacitor, which we studied in
Section 26.4. Equation (43.16) has the same form as the negative of Eq. (26.15),
with q and replaced by and Then we can make the same substitutions in Eq. (26.16), with the initial number of nuclei to find the