Question

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

a. 52 g
b. 104 g
c. 208 g
d. 416 g

Answer 1

To find the original sample mass of 24Na, double the remaining mass of 6.50g for the number of half-lives passed. Four half-lives have passed (60/15), resulting in an original mass of 104 grams.

Step-by-step explanation:

To calculate the original sample mass of the isotope 24Na, given its half-life and remaining mass after a certain time, you can use the formula for exponential decay. The half-life of 24Na is 15 hours and there is 6.50g remaining after 60 hours. Four half-lives have passed in 60 hours (60 / 15 = 4). According to the half-life formula, the mass of the substance decreases by half with each half-life. So, if we reverse this process, we double the mass with each half-life moving backward in time.

Starting with 6.50 g and doubling it four times gives:

1. First half-life (15 hours ago): 6.50 g × 2 = 13 g
2. Second half-life (30 hours ago): 13 g × 2 = 26 g
3. Third half-life (45 hours ago): 26 g × 2 = 52 g
4. Fourth half-life (60 hours ago): 52 g × 2 = 104 g

The original sample contained 104 grams of 24Na.