Answer :
Half-life = 19.4 minutes
The half-life of carbon-10, which decays by positron emission, is determined by the time taken for the mass to reduce by half. After calculating that two half-lives take 38.8 minutes, the half-life is found to be 19.4 minutes.
The question asks for the half-life of the radioactive isotope carbon-10, which decays by positron emission. To find the half-life, we can use the concept that the amount of a radioactive substance decreases by half after each half-life period. In the given question, the mass of carbon-10 decays from 80.6 micrograms to 20.2 micrograms in 38.8 minutes, which is equivalent to two half-lives.
This can be understood by recognizing that 80.6 micrograms decays to 40.3 micrograms in one half-life, and then from 40.3 micrograms to 20.2 micrograms in the next half-life. Thus, if two half-lives take 38.8 minutes, then one half-life is simply 38.8 minutes divided by 2.
The calculation for half-life (t1/2) is as follows:
t1/2 = Total time / Number of half-lives
t1/2 = 38.8 minutes / 2
t1/2 = 19.4 minutes
Therefore, the half-life of carbon-10 is 19.4 minutes.
