Is radioactive decay spontaneous or random? When it comes to radioactive decay, what is the difference between random and spontaneous?
For example, when the count rate of a radioactive isotope is measured, the readings fluctuate. Is this a demonstration of the randomness of the process, or of its spontaneous nature?
 A: I believe spontaneous means it happens on its own. You don't need any outside influence to get the isotope to decay. This term is sometimes used in contrast to stimulated.
Random means one cannot know precisely when the next decay will happen, though one can predict the probability of such events occurring in some time interval.
A decay process can be both spontaneous and random, but only one of these two options touches on the statistical nature of decay.
There's a small bit in the introductory paragraph of the Wikipedia page on radioactive decay.
A: The best way to differentiate is to look at the count-rate vs time graph. Random nature of radioactivity is indicated by the fluctuation of the count-rate.
Whereas, spontaneous means that the process of radioactivity is not dependent upon any external environmental conditions like temperature, pressure, magnetic/electric field. For example: Plot a count rate graph at 100 degrees and then at 200 degrees. Graph of the shape will be the same and also half life in both the cases will be same indicating the spontaneous nature of the process of radioactivity. 
A: Spontaneous means unpredictable process which is governed from within rather than by external conditions like temperature and pressure.
Random implies any time, it may happen without any pattern.
A: Spontaneous means to me as anything that takes place on its own without any inflience of any external factor e.g 
Temperature
Pressure
Magnetic field
Electric field.etc ...........
Radioactivity or radioactive decay is a spontaneous process. It is because the radioactive elements continuously emit radiation from them  as a result of reactions taking place within them. It can be understood easily by the following experiment.
Once henry bacquerel(a physicist) accidently observed that the uranium salt crystal emitted some radiations that turned the photographic plate black. It was seen that he did nothing during this observation but still these radiations were emitted. This shows that radioactivite ie. The emission of radiations by particles is a spontaneous process.
