An isotope has a half-life of 97 years. how much of a 19-gram sample is left after 150 years?
To determine how much of a sample is left after a given time, we need to use the concept of half-life. The half-life is the time it takes for half of the radioactive sample to decay.
In this case, the isotope has a half-life of 97 years, which means that after 97 years, half of the sample will have decayed. After another 97 years (194 years in total), half of the remaining sample will decay, leaving only one-fourth of the original sample. This process continues for every additional half-life.
To find out how much of the 19-gram sample is left after 150 years, we need to calculate the number of half-lives that have occurred within that time period.
Number of half-lives = (time elapsed)/(half-life)
Number of half-lives = 150 years / 97 years ≈ 1.546
Since we cannot have a fraction of a half-life, we can round down to 1. Therefore, one half-life has occurred within 150 years.
Now, we need to calculate the remaining sample after one half-life.
Remaining sample = original sample * (1/2)
Remaining sample = 19 grams * (1/2) = 9.5 grams
After 150 years, approximately 9.5 grams of the 19-gram sample would be left.
amount = 19 (1/2)^(150/97)
= appr 6.5 g