A radioactive element has two isotopes, "G" and "H", with half lives of 5 min and 15 min respectively. An experiment starts with 4 times as many atoms of "G" as of "H". Radioactive decay is a first order reaction. how long will it be before the number of atoms of "G" left equal the number of atoms of "H" left?

Explanation

Option C is correct.To determine how long it will be before the number of atoms of isotope "G" equals the number of atoms of isotope "H," we need to consider their respective half-lives and the initial ratio of atoms. Let's start by looking at the decay of isotope "G" and isotope "H" individually:1. Isotope "G" has a half-life of 5 minutes. This means that after 5 minutes, half of the initial number of atoms of "G" will remain.2. Isotope "H" has a half-life of 15 minutes. Therefore, after 15 minutes, half of the initial number of atoms of "H" will remain.Given that the experiment starts with 4 times as many atoms of "G" as of "H," the initial ratio of "G" to "H" is 4:1.Now, let's consider the time required for the number of "G" atoms to equal the number of "H" atoms:After 5 minutes, "G" will have undergone one half-life, resulting in half the initial number of atoms.After 15 minutes, "H" will have undergone one half-life, resulting in half the initial number of atoms.Since the initial ratio is 4:1, when "G" has undergone one half-life (5 minutes) and "H" has undergone three half-lives (15 minutes), the number of atoms of "G" left will equal the number of atoms of "H" left.Therefore, the correct answer is: C. 15 minutes To determine how long it will be before the number of atoms of isotope "G" equals the number of atoms of isotope "H," we need to consider their respective half-lives and the initial ratio of atoms. Let's start by looking at the decay of isotope "G" and isotope "H" individually:1. Isotope "G" has a half-life of 5 minutes. This means that after 5 minutes, half of the initial number of atoms of "G" will remain.2. Isotope "H" has a half-life of 15 minutes. Therefore, after 15 minutes, half of the initial number of atoms of "H" will remain.Given that the experiment starts with 4 times as many atoms of "G" as of "H," the initial ratio of "G" to "H" is 4:1.Now, let's consider the time required for the number of "G" atoms to equal the number of "H" atoms:After 5 minutes, "G" will have undergone one half-life, resulting in half the initial number of atoms.After 15 minutes, "H" will have undergone one half-life, resulting in half the initial number of atoms.Since the initial ratio is 4:1, when "G" has undergone one half-life (5 minutes) and "H" has undergone three half-lives (15 minutes), the number of atoms of "G" left will equal the number of atoms of "H" left.Therefore, the correct answer is: C. 15 minutes