Question

32P is a radioactive isotope with a half-life of 14.3 days. If you currently have 30.9 g of 32P, how much 32P was present 9.00 days ago?

Answer 1

Answer – We are given, half life t ½ = 14.3 days , Nt = 30.9 g , Ni = ? time, t = 9.00 days

We know, the radioactive decay process is follow the first order

So, half life formula for first order is

Half-life , t ½ = 0.693 /k

So, decay constant , k = 0.693/ t ½

                                    = 0.693 / 14.3 days

                                    = 0.0485 days^-1

We know the formula for the first order

ln Nt/ Ni = -k *t

so, ln 30.9 g / Ni = - 0.0485 days^-1 * 9.00 days

                            = - 0.436

Taking antiln from both side

30.9 g / Ni = 0.647

So, Ni = 30.9 / 0.647

           = 47.8 g

So, 47.8 g of 32P was present 9.00 days ago.