A radioactive source with a half-life of 1.5×109 years1.5 \times 10^9\text{ years}1.5×109 years is placed near a radiation detector. The number of counts detected in five consecutive 1.0 s intervals are recorded as:
523,481,539,495,512 523, \quad 481, \quad 539, \quad 495, \quad 512 523,481,539,495,512Which statement correctly explains these observations?
The fluctuations demonstrate the spontaneous nature of decay, which means the decay constant of the source varies in response to minor ambient temperature changes.
The variation in successive counts demonstrates the random nature of decay, where the decay of individual nuclei cannot be predicted, resulting in statistical fluctuations about a constant mean.
The sequence of counts shows that the decay is exponential, with the fluctuations caused by the decay constant changing after each individual emission.
The variations are due to the spontaneous nature of decay, which causes the half-life of the source to fluctuate significantly from second to second.
