Question

There are 6.50 g of ²⁴Na after 60 hours. How many grams were in the original sample if its half-life is 15 hours? Your answer must include the math used to arrive at the answer.

Answer 1

The original mass of the sample is approximately 52 g.

Step-by-step explanation:

The question asks for the original mass of the sample, given the remaining mass after a certain amount of time and the half-life of the substance.

We can use the formula for exponential decay to solve this problem. The formula is given by:

Amount remaining = Initial amount × (1/2)^(t/half-life)

In this case, the initial amount is unknown, the remaining mass is 6.50 g, the time is 60 hours, and the half-life is 15 hours. Substituting these values into the formula:

6.50 g = Initial amount × (1/2)^(60/15)

Now, we can solve for the initial amount:

Initial amount = 6.50 g / (1/2)^(60/15)

Initial amount ≈ 52 g