Iodine-131 has a half life of eight days. What mass of iodine-131 would remain from a 20g sample after 32 days?
k = 0.693/t1/2
ln(No/N) = kt
No = 20g
N = solve for this
k from above.
t = 32 days.
To calculate the mass of iodine-131 remaining after 32 days, we first need to determine the number of half-lives that have passed.
Since each half-life is eight days, we can divide the total time (32 days) by the duration of a single half-life (8 days): 32 days / 8 days = 4 half-lives.
Each half-life reduces the mass of the sample by half. So, after one half-life, 50% of the sample remains. After two half-lives, 25% remains. After three half-lives, 12.5% remains, and after four half-lives, 6.25% remains.
To calculate the mass of iodine-131 remaining, we can multiply the initial mass (20g) by the fractional amount remaining after four half-lives (6.25% or 0.0625):
Mass remaining = Initial mass × Fraction remaining
Mass remaining = 20g × 0.0625
Mass remaining = 1.25g
Therefore, after 32 days, a 20g sample of iodine-131 would have a remaining mass of 1.25g.