Iodine-131, a beta emitter, has a half-life of 8 days.How many grams of a 10.0g sample of iodine-131 would remain after 56.0 days?
k = 0.693/t1/2
ln(No/N) = kt
No = 10.0g
N = unknown
k from above
t = 56
Another way to solve this:
10/2n
56 days is 7 half lives so
10/27 = ?
To find the amount of iodine-131 remaining after 56.0 days, we can use the formula for radioactive decay:
N = N₀ * (1/2)^(t/t₁/₂)
Where:
N = final amount of iodine-131 remaining
N₀ = initial amount of iodine-131
t = elapsed time (in this case, 56.0 days)
t₁/₂ = half-life of iodine-131 (in this case, 8 days)
Let's calculate the amount of iodine-131 remaining:
N = 10.0g * (1/2)^(56.0/8)
First, let's simplify the exponent:
N = 10.0g * (1/2)^7
Now, let's calculate the value of the exponent:
N = 10.0g * (1/128)
N = 0.078125g
Therefore, after 56.0 days, approximately 0.08 grams of the 10.0 gram sample of iodine-131 would remain.