[Chris250]

How would I define the decay constant in an exam? I was always told it was a probability thing, but would I be right in saying that the decay constant is how many decays take place per second?

[Stonebridge]

It's defined in the equation

where A is the activity and N the number of nuclei.
This is also written as


It's the constant of proportionality in the equation relating the activity of a sample to the number of active nuclei present in it.

The physical significance of the constant is one of probability.
It signifies the probability of an active nucleus decaying in a interval of one second.
Or, the fraction of nuclei that decay in a sample in unit time.

[Hazza616]

The probability of an individual nucleus decaying per second, and it's the constant of proportionality. According to past papers you only get the mark for saying both.