The radioactive element has a half-life of about 28 years and sometimes contaminates the soil. After 47 years, what percentage of a sample of the elements remain?
fraction remain = (1/2)^n where n is the number of half life
half life = p/n where p is the period of decaying i.e. 47 years
so, first find n (number of half life using the half life equation and then find the fraction remain. convert this fraction to %
hope that helps
29%
To determine the percentage of a radioactive element that remains after a certain period of time, we can use the concept of half-life.
In this case, the half-life of the radioactive element is 28 years, which means that after every 28 years, the amount of the element decreases by half.
To calculate the percentage of the element remaining after 47 years, let's break it up into two half-life periods: the first 28 years and the remaining 19 years.
After the first 28 years, the element would have gone through one half-life and reduced to 50% of its original amount.
So, after 28 years, we have 50% of the element remaining.
Now, let's look at the remaining 19 years. This is less than a full half-life, so we have to calculate the fraction of the element remaining.
Since the half-life of the element is 28 years, we divide the remaining time (19 years) by the half-life:
19 years / 28 years = 0.6785 (rounded)
This means that after 19 years, approximately 67.85% of the remaining 50% would decay.
To calculate the percentage of the element remaining after 47 years, we multiply the percentage remaining after the first 28 years by the fraction remaining after the remaining 19 years:
50% * 67.85% = 33.925% (rounded)
So, after 47 years, approximately 33.925% of the original amount of the radioactive element would remain.