Introduction:
In this question, we are given that a radioactive substance has a half-life of 30 seconds and there are 10^8 nuclei of the substance initially. We need to determine the number of nuclei left after 15 seconds.

Understanding Radioactive Decay:
Radioactive decay is a spontaneous process in which an unstable atomic nucleus loses energy by emitting radiation. The rate at which the nuclei decay is measured by the half-life, which is the time taken for half of the radioactive nuclei to decay.

Calculating the Number of Nuclei Left:
To calculate the number of nuclei left after 15 seconds, we can use the concept of exponential decay.

Step 1: Calculate the number of half-lives that have elapsed.
The number of half-lives can be determined by dividing the elapsed time (15 seconds) by the half-life (30 seconds).
Number of half-lives = 15 seconds / 30 seconds = 0.5 half-lives

Step 2: Calculate the remaining fraction of nuclei.
Since there are 0.5 half-lives, the remaining fraction of nuclei can be calculated using the formula:
Remaining fraction = (1/2)^(number of half-lives)

Step 3: Calculate the number of nuclei left.
The number of nuclei left can be obtained by multiplying the remaining fraction by the initial number of nuclei.
Number of nuclei left = Remaining fraction * Initial number of nuclei

Final Calculation:
Number of nuclei left = (1/2)^(0.5) * 10^8

Result:
After calculating the above expression, we find that the number of nuclei left after 15 seconds is approximately 7.0711 x 10^7.

7×10^7