Answer :
The decay of radioactive isotopes of astatine-218 will take 28.1 seconds to decay from a mass of 56.2 micrograms to 28.1 micrograms.
The time it takes for the mass of a radioactive isotope to decay is determined by its half-life. In this case, the half-life of astatine-218 is 2.00 seconds. To find out how long it will take for the mass of a sample of astatine-218 to decay from 56.2 micrograms to 28.1 micrograms, we can use the concept of half-life.
First, we need to determine how many half-lives have passed. Since the mass has decayed to half of its original value, one half-life has occurred. Now, we can calculate the number of half-lives needed for the mass to decay from 56.2 micrograms to 28.1 micrograms.
Each half-life is 2.00 seconds, so if one half-life is 2.00 seconds, then x half-lives will be x * 2.00 seconds. Therefore, we can set up the equation: 2.00x = 56.2 - 28.1. Solving for x, we find that x = 14.05 half-lives. Multiplying this by 2.00 seconds, we get the total time as 28.1 seconds.
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