Question

The radioactive isotope 239 Pu has a half-life of approximately 24100 years. After 1800 years, there are 3g of 239 Pu. (1) What was the initial quantity? (Round your answer to three decimal places.)

Answer 1

To calculate the initial quantity of a radioactive isotope with known half-life and remaining quantity after certain years, use the half-life decay formula. After plugging the values for 239 Pu and performing the calculations, we find that the initial quantity was approximately 3.161g.

Step-by-step explanation:

The radioactive isotope 239 Pu is known for its long half-life, which can pose a challenge in terms of radioactive waste management. To find the initial quantity of 239 Pu, we can use the half-life formula:

N_t = N_0 (1/2)^(t/T)

Where:

• N_t is the remaining quantity after time t (3g in this case)
• N_0 is the initial quantity (what we want to find)
• t is the time that has passed (1800 years)
• T is the half-life period (24100 years)

Using this formula:

N_0 = N_t / (1/2)^(t/T)

Substituting the given values:

N_0 = 3g / (1/2)^(1800/24100)

Now, we calculate the exponent first: 1800/24100 = 0.074689

Then raise (1/2) to this exponent:

(1/2)^0.074689 ≈ 0.9489

So:

N_0 = 3g / 0.9489 ≈ 3.161g

Therefore, the initial quantity of 239 Pu was approximately 3.161g.