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The half-life of $131I$ is 8 days. Given a sample of $131I$ at time $t=0,$ we can assert that
(A) no nucleus will decay before $t=4$ days
(B) no nucleus will decay before $t=8$ days
(C) all nuclei will decay before $t=16$ days
(D) a given nucleus may decay at any time after $t=0$

Last updated date: 21st Apr 2024
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Hint: We can say that in general, there is an inverse relation between the half-life and the intensity of radioactivity of an isotope. Isotopes with a long half-life decay very slowly, and so produce fewer radioactive decays per second; their intensity is less. Isotopes with shorter half-lives are more intense. The last element in the periodic table that has a stable isotope is lead (Z = 82), with stability (i.e. half-lives of the longest-lived isotopes) generally decreasing in heavier elements.

Complete step by step answer
We can say that the definition of elimination half-life is the length of time required for the concentration of a particular substance (typically a drug) to decrease to half of its starting dose in the body. Knowing about half-lives is important because it enables you to determine when a sample of radioactive material is safe to handle. They need to be active long enough to treat the condition, but they should also have a short enough half-life so that they don't injure healthy cells and organs.
We can add that the rate at which a radioactive isotope decays is measured in half-life. The term half-life is defined as the time it takes for one-half of the atoms of a radioactive material to disintegrate. Half-lives for various radioisotopes can range from a few microseconds to billions of years.
At time $\mathrm{t}=0$, the nuclei start to decay and at any time after that some of the nuclei may have decayed. Up to time $\mathrm{t}=8$ days, about half the initial number of the nucleus have decayed and up to 16 days, only one-fourth of the initial number of the nucleus are left undecayed.

Hence the correct answer is option D.

Note: We can say that isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom. Isotopes are simply atoms with more neutrons; they were either formed that way, enriched with neutrons sometime during their life, or are originated from nuclear processes that alter atomic nuclei. So, they form like all other atoms. Isotopes of an element share the same number of protons but have different numbers of neutrons. Chemically, all three are indistinguishable, because the number of electrons in each of these three isotopes is the same. So different isotopes of the same element are identical, chemically speaking.