suppose a sample of radioactive substance weighs 34 mg. One year later, the sample weighs 23.5 mg. what is half-life of this substance? round your answer to two decimal places.

Answer 1

I will set it up for you.

m₀ = initial amount = 34 mg

t = elapsed time = 1 yr

T = half-life in years = ?

m(t) = final amount (at time t) = 23.5 mg

The relation is

m(t) = m₀ (0.5)^t/T

m(t) / m₀ = (0.5)^t/T

log[m(t) / m₀] = (t/T) log(0.5)

You have values for m(t), m₀, and t. Now solve for T and finish from here. The result will be in units of years. You can work with any base for the log.