Question

The half-life of chromium-52 is 27 days. If the sample contained 610 grams, how much Cr-52 would remain after 54 days?

a) 2 half-lives, 152.5 grams remaining
b) 1 half-life, 305 grams remaining
c) 3 half-lives, 76.25 grams remaining
d) 4 half-lives, 19.06 grams remaining

Answer 1

After 54 days, there would be approximately 152.5 grams of Cr-52 remaining.

Step-by-step explanation:

The half-life of a radioactive isotope is the time it takes for half of the sample to decay. In this case, the half-life of chromium-52 is 27 days. To determine how much Cr-52 would remain after 54 days, we need to determine the number of half-lives that have passed. Since each half-life is 27 days, dividing 54 by 27 gives us 2 half-lives.

We can apply the formula for radioactive decay to calculate the remaining amount. The formula is given by:

Amount remaining = Original amount × (1/2)^(number of half-lives)

So, if the original amount of Cr-52 is 610 grams, after 2 half-lives, the amount remaining would be:

Amount remaining = 610 × (1/2)^2 = 610 × 1/4 = 152.5 grams

Therefore, after 54 days, there would be approximately 152.5 grams of Cr-52 remaining.