Final answer:
It is incorrect to assume a radioactive sample with a decay constant of 0.05 s−1 will fully decay in 20 seconds because the decay constant only represents the fraction that decays per second and not the complete decay. Radioactive decay follows an exponential pattern and is based on the concept of half-life, which explains that only half the sample decays after each half-life period. Therefore, the correct option is d).
Step-by-step explanation:
The presumption that a sample of radioactive material with a decay constant of 0.05 s−1 will fully decay in 20 seconds is incorrect because radioactive decay follows an exponential decay model. The decay constant provided signifies only the fraction that decays every second, not the total decay of the substance. This is because radioactive decay is a statistical process based on probabilities, not certainties, where a specific number of atoms may decay but not necessarily all of them.
Radioactive decay is a first-order process where the decay constant highlights the proportion of nuclei decaying in a unit of time. The concept of half-life is more relevant to understanding the decay of radioactive materials, as it indicates the time required for half of the isotopes in a sample to decay. For example, if we consider a sample of carbon-11 with a half-life of 20.334 minutes, even after its half-life has passed, 50% of the material would still remain, not achieve complete decay.
As the decay process is random, it is incorrect to assume that all atoms will decay after a set period. Additionally, half-life values vary significantly among different isotopes, emphasizing the unpredictability of the exact moment each atom will decay. Therefore, the correct option is (d) The decay constant represents only the fraction of a sample that decays in a unit of time, not the decay of the entire sample.