The half live of Iodine-131 is 8 days. if you started out with 40 mg sample of iodine-131, then what would be the mass of the sample after 32 days? please show your work
32 days is 4 half-lives. So, the mass is reduced to 1/2^4 = 1/16 of 40mg, or 2.5mg
Just to be picky I think this problem is not stated correctly (although who am I to know what the author was thinking when this problem was written?). However, I think the spirit of the question expects an answer that Steve gave. Let me point out though that the question asks for the mass of the SAMPLE and that is the mass of I-131(2.5 mg) + the mass of the decay products whatever they may be.
To determine the mass of the sample after 32 days, we need to calculate the number of half-lives that passed during that time period.
Given that the half-life of Iodine-131 is 8 days, we can find the number of half-lives by dividing the total time (32 days) by the length of one half-life (8 days):
Number of half-lives = 32 days / 8 days = 4 half-lives
Each time one half-life passes, the mass of the sample is halved. Therefore, after each half-life, the remaining mass is reduced by half.
Starting with a 40 mg sample of Iodine-131, let's track the mass after each half-life:
- After the 1st half-life: 40 mg / 2 = 20 mg
- After the 2nd half-life: 20 mg / 2 = 10 mg
- After the 3rd half-life: 10 mg / 2 = 5 mg
- After the 4th half-life: 5 mg / 2 = 2.5 mg
So, after 32 days, the mass of the Iodine-131 sample would be 2.5 mg.