Question

Curium-243 has a half-life of 28.5 days. In a sample of 5.6 grams of curium-243, how many grams will remain after 12 days?

A) 1.08 grams
B) 2.8 grams
C) 4.18 grams
D) 2.09 grams
E) 5.6 grams

Answer 1

To determine the amount of curium-243 left after 12 days, we apply the half-life formula to the initial 5.6 grams, using 28.5 days as the half-life. After the calculations, we find that approximately 4.18 grams of curium-243 will remain, which corresponds to answer option C.

Step-by-step explanation:

To calculate the amount of curium-243 remaining after 12 days from an initial 5.6 grams, we need to use the concept of half-lives. The formula to calculate the remaining amount of a substance after a certain time is:

Remaining amount = Initial amount ×
`\rm (1/2)^{(time \ elapsed / half-life)`

For a half-life of 28.5 days, and time elapsed of 12 days:

Remaining amount = 5.6 grams ×
`(1/2)^{(12 / 28.5)`

First, we calculate the fraction of a half-life that 12 days represents: 12 / 28.5 ≈ 0.4211. Next, we use this fraction to determine the remaining amount of curium-243:

Remaining amount = 5.6 grams ×
`(1/2)^{0.4211`

After the calculations, we find that the remaining amount is approximately 4.18 grams

Therefore, the correct answer is C) 4.18 grams.

Answer 2

After 12 days, approximately 4.2 grams of curium-243 will remain in a sample of 5.6 grams.

Step-by-step explanation:

To calculate the remaining grams of curium-243 after 12 days, we can use the half-life and exponential decay formula. The formula is:

R = R0 * (1/2)^(t/T)

where R is the remaining amount, R0 is the initial amount, t is the time, and T is the half-life. Plugging in the values, we have:

R = 5.6 grams * (1/2)^(12 days / 28.5 days)

R = 5.6 grams * (1/2)^(4/9)

R = 5.6 grams * 0.750

R = 4.2 grams