Iodine-131 has a half-life of 8 days. How many grams of a 12 g sample will remain at the end of 40 days?
how do i solve this? i thought it was
12^40=1.5 but that's wrong...
Two ways to do it but both actually are the same.
k=0.693/t1/2
Substitute k into the equation below.
ln(12/N) = kt
Solve for N. I get 0.375 g.
Second way:
1/(2n)* 12
[1/2(40/8)]*12 = ??
Again, 0.375g.
To solve this question, we need to understand the concept of half-life and use the formula to calculate the remaining amount of a sample after a given time.
Half-life is the amount of time it takes for half of a radioactive substance to decay. In this case, the half-life of iodine-131 is 8 days.
To calculate the remaining amount of iodine-131 after a specific time, we can use the formula:
Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)
Let's calculate the remaining amount of iodine-131 in 40 days:
Amount remaining = 12 g * (1/2)^(40 / 8)
1/2^(40/8) simplifies to 1/2^5 = 1/32 = 0.03125
Amount remaining = 12 g * 0.03125 = 0.375 g
Therefore, at the end of 40 days, approximately 0.375 grams of a 12 g sample of iodine-131 will remain.
Your previous attempt of using 12^40 is incorrect because this calculation does not take into account the decay over time according to the half-life.