Question

in 1959 the Santa Susana Field Laboratory had the first and worst) nuclear meltdown in the US history. In this accident, radioactive isotopes 1-131 and Cs-137 were released into the surroundings. Given that the half-life of l-131 is 8.02 days, what percentage of the initial l-131 has decayed up to year 2021? 0 100 % O 0% O 50% 0 95% O 70%

Answer 1

To calculate the percentage of l-131 that has decayed up to the year 2021, we need to determine how many half-lives have passed from 1959 to 2021 and then calculate the remaining percentage.

The half-life of l-131 is 8.02 days.

First, calculate the number of half-lives that have passed from 1959 to 2021:

Number of years = 2021 - 1959 = 62 years

Since each year has approximately 365 days:

Number of days = 62 years * 365 days/year = 22,630 days

Now, calculate the number of half-lives:

Number of half-lives = Number of days / Half-life = 22,630 days / 8.02 days/half-life ≈ 2822 half-lives

Now, we know that each half-life reduces the remaining amount to half. So, to calculate the percentage remaining after 2822 half-lives:

Percentage remaining = (1/2)^2822 * 100 ≈ 0%

So, approximately 0% of the initial l-131 has decayed up to the year 2021.