Making a precise prediction of when an individual nucleus will decay is not possible; however, radioactive decay is governed by statistics, so it is very easy to predict the decay pattern of a large number of radioactive nuclei. The rate at which nuclei decay is proportional to N, the number of nuclei there are:
R = -ΔN/Δt = λN
Whenever the rate at which something occurs is proportional to the number of objects, the number of objects will follow an exponential decay:
N = No e-λt
The decay constant is closely related to the half-life, which is the time it takes for half of the material to decay. Using the radioactive decay equation, it's easy to show that the half-life and the decay constant are related by:
T1/2 = ln2/λ = 0.693/λ
The activity of a sample of radioactive material (i.e., a bunch of unstable nuclei) is measured in disintegrations per second, the SI unit for this being the becquerel (Bq). A more common unit is the curie (Ci):
1 Ci = 3.7 x 1010 decays/s = 3.7 x 1010 Bq
A typical sample of radioactive material has an activity in the mCi or µCi range.
The black curve above represents the activity of a radioactive sample over time. Which curve represents the activity vs. time of a second sample with a larger decay constant?
Larger decay constants means the decay happens more quickly. The red curve represents a larger decay constant, and a shorter half-life.