What is the half-life of iodine-133?

Question

The number of disintegrations per minute (dsm) of a sample of iodine-133 is measured at 5.5 x 10² dsm. When the sample is measured 295 minutes later, the number of disintegrations has decreased to 4.7 x 10² dsm.

Answer 1

Interesting. Disintegrations per minute is usually abbreviated as dpm, not dsm, but ... whatever. That has little to do with solving the problem. For first order decay, an easy equation to use is

FR = 0.5ⁿ

FR = fraction remaining

n = number of half lives that have elapsed.

FR = 4.7x10² / 5.5x10² = 0.8545

n = ?

0.8545 = 0.5n

log 0.8545 = n log 0.5

-0.0683 = -0.301 n

n = 0.227 half lives have elapsed

Since this is equal to 295 minutes, we can easily find what 1 half life is equal to.

0.227 / 295 = 1 / x

x = 1300 min = 21.7 hours