In a sample of radioactive material, what fraction of the material will decay after half of its half-life?

Explanation

The half-life of a radioactive material is the time it takes for half of the radioactive atoms in a sample to decay. So, after half of the half-life, half of the radioactive atoms in the sample will have decayed. The fraction of the material that will decay after half of its half-life is given by the following formula: f = 1 - (1/√2)^2 where f is the fraction of the material that will decay and (1/√2)^2 is the probability that a single atom will decay in half of its half-life. The value of (1/√2)^2 is approximately equal to 0.25, so the fraction of the material that will decay after half of its half-life is approximately equal to 1 - 0.25 = 0.75, or √2 - 1.