Question

A certain radioisotope has a half-life of 10.1 days. What percentage of an initial sample of this isotope remains after 37 days?

Answer 1

GIven is:-

Half life of radioisotope = 10.1 days

Radioactive decay is exponential; that is, if N_o is the original number of particles, and N(t) is the number of particles at time t, then

Half-life   is defined as the time it takes for there to be remaining half the original number of particles; that is,

combining with the first equation, we get

by taking log both sides we get

(since ln(a/b) = ln(a) - ln(b), and ln(1) = 0). So, we see that we can relate the decay constant to the half-life

and in our case

We want the percentage of the original sample remaining after 37 days, or, in other words, we want the ratio N(37 days)/N_o.

therefore 7.90%

So, the radioisotope remains 7.90% after 37 days of decay to the initial sample.