Questions: A radioisotope has a half-life of 7.5 hours. How many half lives have occured after 67.5 hours? a 7 half-lives b 8 half-lives c 9 half-lives d 10 half-lives

Solution Steps

We need to determine how many half-lives have occurred after 67.5 hours, given that the half-life of the radioisotope is 7.5 hours.

To find the number of half-lives, we divide the total time elapsed by the duration of one half-life. The formula is:

\[ \text{Number of half-lives} = \frac{\text{Total time elapsed}}{\text{Half-life duration}} \]

Substituting the given values:

\[ \text{Number of half-lives} = \frac{67.5 \text{ hours}}{7.5 \text{ hours}} \]

Calculate the division:

\[ \text{Number of half-lives} = \frac{67.5}{7.5} = 9 \]

Final Answer