You are performing an experiment which uses 113Ag. 113Ag is radioactive. The rest of the equation in the description.

Question

You are performing an experiment which uses ¹¹³Ag. ¹¹³Ag is radioactive, decays by beta minus emission (β−), and has a half-life of 5.3 hours. It requires 31.8 hours to ship the material from the warehouse to your laboratory.

How many grams should you order if the experiment requires that you have 46 grams to begin the experiment.

Answer 1

There is a way to do this problem using the radioactive decay equation.

N = N₀ x e ^-λt where λ is the decay constant of the isotope, t is the elapsed time, and N and N₀ are the final and initial amounts respectively.

The decay constant can be found from λ = 0.693/t_1/2, so λ = 0.693 / 5.3 hours = 0.1308 h^-1.

Since we need 46 g for the experiment, and it takes 31.8 hours to ship it, we need to calculate N₀.

So, N₀ = N/e^{-0.1308 x 31.8} = 46 g / e^{- 0.0156} = 2949 g.

Answer 2

The half life of a substance is the amount of time until one half of it decays.

For example, if the half life of a substance is 1 year and we put 100 g in a cabinet, if we check it again in one year there will be 50 g left.

For this problem, we have to work backwards.

We divide the total amount of hours by the half life to see how many times half of the substance will decay.

31.8 / 5.3 = 6

We know it will take 6 of the substances half lives in order to get to you, so the amount of the substance will be divided in half 6 times!

We will again work backwards and multiply 46 by 2 for every hour,

46 * 2 = 92

* 2 = 184

* 2 = 368

* 2 = 736

* 2 = 1472

* 2 = 2944 g