Answer:
To calculate the remaining grams of the isotope after 120 days, we need to determine the number of half-lives that have occurred within that time frame.
Given:
Half-life of the isotope = 70 days
Initial mass of the isotope = 600 grams
Time elapsed = 120 days
To find the number of half-lives, we divide the elapsed time by the half-life:
Number of half-lives = elapsed time / half-life
= 120 days / 70 days
≈ 1.714 (rounded to three decimal places)
Since we cannot have a fraction of a half-life, we consider the integer part, which is 1. This means that one full half-life has occurred within the 120-day period.
To calculate the remaining mass, we use the formula:
Remaining mass = Initial mass * (1/2)^(Number of half-lives)
Substituting the values:
Remaining mass = 600 grams * (1/2)^(1)
= 600 grams * 0.5
= 300 grams
Therefore, after 120 days, approximately 300 grams of the radioactive isotope remains.