Answer:
22.06 Hours
Step-by-step explanation:
- Half life is the time it takes for a radioactive material or isotope to decay by half of its initial amount.
We are given;
Radioactive isotope Iodine-133
Initial counts per minute = 3150 counts
Counts after decay = 3055 per minute
Time taken = 1 hour
But, we know that to calculate the remaining amount of the radioactive isotope, then,
Remaining amount = Initial amount × 0.5^n , where n is the number of half-lives.
Therefore;
3055 counts = 3150 × 0.5^n
0.5^n = 0.9698
To get n
n = log 1 ÷ log 0.9698
= 0.044
But, n is given by dividing time and the number of half lifes
Therefore, half life = time ÷ Number of half lives
= 1 hour ÷ 0.044
= 22.60 hours
Therefore, the half life of iodine-133 is 22.60 hours