Can a nucleus be decayed to only half of it? I was wondering while studying radioactivity that can a nucleus out of millions of nuclei decay to only half of it. For example, say at any time t = 60 sec, the decay rate is 2.5 nuclei/second. it means that 2 nuclei and "0.5" nucleus decayed! what about other 0.5? Any help would be appreciated.
 A: Decay is inherently probabalistic. That means after X time, a nucleus has Y% chance of decaying (through some mechanism) into other particles. This translates into what is called an expectation value for the number of nuclei left in a sample after some time. This is a function of time. Differentiating this function with respect to time (i.e. finding the rate of change at that instant), we get 2.5 nuclei/second.
This doesn't mean we lose half a nucleus, because that's simply not how decay in this context works. (Nuclear fission is a thing, but it's not relevant to this discussion.) It means we expect to lose 2.5 nuclei, because there is some chance that over a second, we lose 1 nucleus, there is some more chance we lose 2 nuclei, there is a chance we lose 3 nuclei, there is even a really, really, really (and I mean astronomically) low chance that we lose ALL the nuclei (this is possible but we will never see it happen). 
All these chances mathematically average out to 2.5 nuclei/second, even there is zero chance that we will lose 2.5 nuclei in one second (simply because losing 0.5 nuclei to decay doesn't really make sense in this scenario).
This is a very common thing in probability, because working with expectation values (even if they don't precisely make physical sense, like "the average person has 2.75 children) makes it very easy to estimate things for large data sets. For example if we have 300,000,000 families, and we know that the average family has 2.75 children, then our estimate of how many children there are (300,000,000*2.75 = 825,000,000) will be pretty close to the actual number of children—even though 0.75 children doesn't make sense.
Hope this clears things up for you!
