Answer :
Final answer:
The half-life is the time it takes for half of a radioactive substance to decay. By using the formula N = log(initial_amount/final_amount) / log(2), it can be calculated that it would take approximately 68 days for 16g of palladium-103 to decay to 1g.
Explanation:
Palladium-103, like all radioactive substances, decays according to a concept known as half-life, which is the time it takes for half of a radioactive substance to decay. If the half-life of palladium-103 is 17 days, then after 17 days, half of the original quantity would remain.
To determine how many half-lives it takes for 16g to decay to 1g, you can use logarithms. The formula for calculating the number of half-lives is N = log(initial_amount/final_amount) / log(2). Inputting the values, N = log(16/1) / log(2) = 4 half-lives.
Since the half-life of palladium-103 is 17 days, we then multiply the half-life by the number of half-lives: 17 days/half-life x 4 half-lives = 68 days.
Therefore, it would take approximately 68 days for 16g of palladium-103 to decay to 1g.
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