Question
An isotope has a 6 hour half life. What % of the parent nuclei will be left. after 24 hours? Time elapsed & 0 hours & 6 hours & 12 hours & 18 hours * of Half lives & 0 & 1 & 2 & 3 & 4 % of Parent & 100 % & & & & 10 % 25 % 50 % 6.25 %
Answer
4.3
(329 Votes)
Harriet
Elite · Tutor for 8 years
Answer
6.25%
Explanation
1. This question involves the calculation of the remaining amount of a radioactive isotope after a certain period based on its half-life, which is a concept in physics, particularly in nuclear physics.2. The half-life of a substance is the time it takes for half of the substance to undergo radioactive decay.3. Every half-life period, the remaining amount of the substance halves.4. We are given a half-life of 6 hours for the isotope.5. We need to determine how much of the parent nuclei will be left after 24 hours.6. To calculate the amount remaining after 24 hours, we can use the formula N = (1/2)^(t/T) × N0, where N0 is the initial quantity (in this case, 100%), t is the elapsed time (24 hours), and T is the half-life period (6 hours).7. Since there are 4 half-lives in 24 hours (24 hours divided by the 6-hour half-life), we will apply the halving principle 4 times.8. After one half-life, the remaining amount is 50% of the initial. After two half-lives, it's 25% of the initial. After three half-lives, it's 12.5% of the initial. And after four half-lives, it's 6.25% of the initial.9. This can be also verified by (1/2)^4 = 1/16, and multiplying 100% (initial quantity) by 1/16 gives 6.25%.