The half-life of cesium-137 is 30 years. How many percent of the atoms of this isotope decay in 240 years?

To solve this problem, we need to understand the concept of half-life. Half-life is the time required for half of the atoms in a sample to decay.

Step 1: Determine the number of half-lives First, we need to determine how many half-lives have passed in 240 years. Since the half-life of cesium-137 is 30 years, we divide 240 by 30 to get 8. So, 8 half-lives have passed.

Step 2: Calculate the remaining percentage Next, we need to calculate how much of the original sample remains after 8 half-lives. We start with 100% of the sample, and each half-life reduces this by half. So, after one half-life, we have 50% of the sample left. After two half-lives, we have 25% left, and so on.

To calculate this, we can use the formula:

Remaining percentage = initial percentage * (1/2)^(number of half-lives)

Substituting the given values into the formula, we get:

Remaining percentage = 100% * (1/2)^8 = 0.39%

Step 3: Calculate the decayed percentage Finally, to find out how much of the sample has decayed, we subtract the remaining percentage from the initial percentage.

Decayed percentage = initial percentage - remaining percentage = 100% - 0.39% = 99.61%

So, approximately 99.61% of the atoms of cesium-137 decay in 240 years.