Instantaneous Decay rate per unit Volume

[Polarbear]

'A radioactive element has a 0.5 probability of decaying to a more stable element after a particular time-span T.

What is the instantaneous decay rate per unit volume? In other words determine a general expression for the number of decay events occurring per unit volume between t=t1 and t=t2 as the difference between these two times t2-t1 approaches zero.'

This is the last part of a group presentation we have to prepare and has us all stumped. Any thoughts?

 

[quantumdude]

'A radioactive element has a 0.5 probability of decaying to a more stable element after a particular time-span T.

You can interpret that statistically. If each nucleus has a 0.5 probability of decaying within time T, then you would expect half of a sample to have decayed by time T.

In other words, T is the half-life of the sample.

What is the instantaneous decay rate per unit volume? In other words determine a general expression for the number of decay events occurring per unit volume between t=t1 and t=t2 as the difference between these two times t2-t1 approaches zero.'

Use the standard model for exponential decay. Since they want the number of events per unit volume, I would divide both sides by the volume.