Answer:
The half-life of a radioactive substance is the time it takes for half of the original sample to decay. We can use the information given to calculate the half-life of nitrogen-16 as follows:
Let t1/2 be the half-life of nitrogen-16.
At t=0 (initial time), the sample has a mass of 100.0 g.
After one half-life (t=t1/2), the sample will have decayed to 50.0 g.
After two half-lives (t=2t1/2), the sample will have decayed to 25.0 g.
After three half-lives (t=3t1/2), the sample will have decayed to 12.5 g.
We know that the sample decays from 100.0 g to 12.5 g in 21.6 seconds, which is equivalent to 3 half-lives (t=3t1/2). Therefore, we can write the following equation:
12.5 g = 100.0 g * (1/2)^(3)
Simplifying, we get:
(1/2)^3 = 12.5 g / 100.0 g
(1/2)^3 = 0.125
Taking the logarithm of both sides (to base 2, since we are dealing with half-lives), we get:
log2(1/2)^3 = log2(0.125)
-3*log2(1/2) = -3
3 = 3*t1/2/21.6
Simplifying, we get:
t1/2 = (3 * 21.6) / 3 = 21.6 seconds
Therefore, the half-life of nitrogen-16 is 21.6 seconds.
Step-by-step explanation: