Question

Ryan has 2,000 grams of Flerovium-289, which has a half life of 30 seconds. Use

the formula y = ab* to figure out how much Flerovium-289 you will have after
5 minutes. (Hint: x is the the total number of half lives in 5 minutes)
(.5)_
a.) 62.5 grams
b.) 1.95 grams
c.) 353.55 grams
d.) 1,000 grams
y =____

Answer 1

The given radioactive decay formula is:

y = ab^x

where,
y = final amount
a = initial amount
b = decay factor
x = number of half-lives elapsed

Here, the initial amount (a) is given as 2,000 grams of Flerovium-289, and the half-life (t1/2) is 30 seconds.

To find the decay factor (b), we can use the formula:

b = 1/2^(t/t1/2)

where, t is the time elapsed. Here, t = 5 minutes = 300 seconds.

b = 1/2^(300/30) = 1/2^10 = 1/1024

Now, we can find the final amount (y) after 5 minutes by using the formula:

y = ab^x

where, x is the number of half-lives elapsed in 5 minutes.

x = t/t1/2 = 300/30 = 10

y = 2,000 * (1/1024)^10

y ≈ 1.95 grams (approx)

Therefore, the answer is option (b) 1.95 grams.