Final answer:
The equation for radioactive decay provides that the number of nuclei decreases to exactly half after one half-life. For whole multiples of half-lives, simple division by 2 suffices, but for other times, exponential calculations are required.
Step-by-step explanation:
Understanding Radioactive Decay
The equation N = Noe-λt, where N represents the number of radioactive nuclei at time t, No is the initial number of radioactive nuclei, e is the base of the natural logarithm, and λ is the decay constant, describes the exponential decay of radioactive substances.
In the context of half-life, which is denoted as t1/2, the number of radioactive nuclei decreases to exactly half its original value after one half-life has elapsed. By substituting t = t1/2 into the equation, we find N = Noe-0.693 = 0.500No, illustrating that exactly half of the original quantity remains.
If we consider integral multiples of half-lives, we can sidestep the exponential equation by consecutively dividing the initial quantity by 2 for each half-life passed. For example, after ten half-lives, N would be reduced to N/1024. However, for times not corresponding to whole half-lives, it is necessary to utilize the exponential relationship to accurately determine the remaining quantity.