Final answer:
To determine the time it takes for 1.00 g of palladium-103 to decay to 0.125 g with a 17.0-day half-life, we found that it takes 3 half-lives, which is equivalent to 51.0 days.
Step-by-step explanation:
To calculate how long it takes for 1.00 g of palladium-103 to decay to 0.125 g, given its half-life is 17.0 days, we can use the concept of half-lives. The mass of radioactive material remaining after a certain number of half-lives can be found by the formula:
Mass remaining = Initial mass / (2number of half-lives)
In this case, we want to find the number of half-lives it takes for the mass to go from 1.00 g to 0.125 g.
To find this, we set up the equation:
0.125 g = 1.00 g / (2n)
Solving for n, we find that n = 3, because 1.00 / (23) = 0.125.
This means it takes three half-lives for the mass of palladium-103 to decay to 0.125 g from 1.00 g.
Since the half-life is 17.0 days, we multiply the number of half-lives by the half-life duration:
Time = Number of half-lives × Half-life
= 3 × 17.0 days
= 51.0 days
Therefore, it takes 51.0 days for 1.00 g of palladium-103 to decay to 0.125 g.