Final answer:
To find out how long it takes for 1.00 g of palladium-103 to decay to 0.125 g, we can use the concept of half-life. The half-life of palladium-103 is 17.0 days, and it will take 3 half-lives for the mass to decrease to 0.125 g. Therefore, it will take a total of 51.0 days.
Step-by-step explanation:
To find out how long it takes for 1.00 g of palladium-103 to decay to 0.125 g, we can use the concept of half-life. The half-life is the time it takes for half of a sample to decay. In this case, the half-life of palladium-103 is given as 17.0 days.
Since we know the half-life, we can calculate the number of half-lives it would take for the mass to decrease to 0.125 g. Each half-life reduces the mass by half, so we can set up the following equation:
Initial Mass × (1/2)number of half-lives = Final Mass
1.00 g × (1/2)number of half-lives = 0.125 g
Now, we can solve for the number of half-lives:
(1/2)number of half-lives = 0.125/1.00
(1/2)number of half-lives = 0.125
Using logarithms, we can solve for the number of half-lives:
number of half-lives = log1/2(0.125)
number of half-lives = 3
Therefore, it will take 3 half-lives for 1.00 g of palladium-103 to decay to 0.125 g. The total time that elapses will be 3 half-lives multiplied by the half-life of 17.0 days:
Total Time = 3 × 17.0 days
Total Time = 51.0 days