The half-life of N is 6.5 s. A sample of this nuclide of hydrogen is observed for 32.5 s. The fraction of the original radioactive isotope remaining after this time is:

Explanation

The explanation is given below: To find the fraction of the original radioactive isotope of nitrogen (N) remaining after 32.5 seconds, we can use the concept of radioactive decay and the half-life of the isotope. The half-life of N is 6.5 seconds, which means that in 6.5 seconds, half of the original sample will decay, and the other half will remain. For each successive half-life period, half of the remaining sample will decay, and the other half will persist. To calculate the fraction remaining after 32.5 seconds, we need to determine how many half-life periods have elapsed during this time. 32.5 seconds ÷ 6.5 seconds per half-life = 5 half-life periods. For each half-life period, the fraction remaining is halved, so after 5 half-life periods, the fraction remaining is (1/2)^5, which is equal to 1/32. So, after 32.5 seconds, 1/32 of the original radioactive isotope of nitrogen remains.