Answer :
Final answer:
It takes 68 days for 16 g of palladium-103 to decay to 1.0 g, using the half-life of 17 days and the formula for exponential decay.
Explanation:
To determine how many days it takes for 16 g of palladium-103 (Pd-103) to decay to 1.0 g, we need to apply the concept of half-life, which is the time required for half of a radioactive sample to decay. The half-life of Pd-103 is given as 17 days. To solve this problem, we use the formula for exponential decay:
N(t) = N_0(1/2)^(t/T)
where:
- N(t) is the remaining amount after time t
- N_0 is the initial amount
- T is the half-life
- t is the time passed in the same units as the half-life
In this case, N_0 = 16 g, N(t) = 1 g, and T = 17 days. We can rearrange the formula to solve for t:
t = T * (log(N(t)/N_0) / log(1/2))
Plugging in the numbers:
t = 17 days * (log(1/16) / log(1/2))
t = 17 days * (log(1) - log(16)) / (log(1) - log(2))
t = 17 days * (-4) / (-1)
t = 17 days * 4
t = 68 days
It would take 68 days for 16 g of Pd-103 to decay to 1.0 g.
