The ratio is 2. To determine the ratio of the number of nuclei decaying during the first half of the half-life to the number of nuclei decaying during the second half of the half-life, we need to understand the concept of half-life.
The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei in a sample to decay. Let's say the half-life of the radioactive substance in question is represented by "t".
During the first half-life (t/2), half of the nuclei in the sample will decay. So, if we start with "N" nuclei, after the first half-life, we will have "N/2" nuclei remaining.
During the second half-life (t/2), another half of the remaining nuclei will decay. So, starting with "N/2" nuclei, after the second half-life, we will have "N/2" divided by 2, which is "N/4" nuclei remaining.
Therefore, the ratio of the number of nuclei decaying during the first half of the half-life to the number of nuclei decaying during the second half of the half-life is:
(N/2) / (N/4)
Simplifying this expression, we get:
(N/2) * (4/N)
This simplifies to:
2
So, the ratio is 2.
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