Question

If 4.0

Answer 1

I'm assuming this is is a first order reaction, and it seems to be true. If you haven't covered order of reactions yet, this might be confusing. For 1st order reactions, the concentration versus time is the following equation: ln([A]o/[A]t)= kt. Where [A]o is the original concentration, [A]t is the concentration at a specific time, t= time, and k is the concentration's rate of decay constant. The half life equation is t=0.693/k. Since you don't have moles, the element's name, or anything like that, I'm just using the amount of atoms. The values are in ratio anyway, so they cancel out in the end to give you the units you want. And you can keep the time in years too! I advice you not to do this in class though, it messes up a lot of things. Time should be in seconds. Now for calculations!

a) the constant value:
2.3=0.693/k
k= 0.3013 sec^-1 (the units are 1/s)

b) finding the original amount of Bi:
([A]o/[A]t)= e^(kt)
(I got rid of the ln, by putting the exponential on both sides. It cancels the ln out on the left)

([A]o/[A]t)= e^(0.3013*3.7)

([A]o/[A]t)= 3.049
(since its in ratio just plug in [A]o or original amount of atoms and solve for [A]t)

(4x10^18)/3.049= 1.31*10^18 atoms