Question

Instructions Answer the questions posed in this homework. When you are finished, scan or take a picture of your work and turn the file into Canvas. Solve these growth and decay problems. Make sure you show your work. Problems 1. Magnesium-27 has a half-life of 9.45 minutes. a. What is the decay constant for Magnesium-27? b. How long until a sample of Magnesium-27 is down to 10% of its original mass? c. If you solved parts a & b of this problem using Log, solve them again using Ln. On the other hand, if you used Ln, solve them again using Log. 2. A sample of 20 grams for Beryllium-11 is observed for 512 minutes and when only 11 grams remain. a. What is the decay constant of Beryllium-11? b. What is the half-life of Beryllium-11? c. How much Beryllium-11 will remain in 2500 minutes? d. How long until there is only 1 gram of Beryllium remaining?

Answer 1

Assuming First Order Kinetice, we can write N(t)= No ek time to NCA- Amount of sample at Nor Initial amount of sample K= decay constant le N (+) = No Maha 2 At t= ty Given til - 9-45 Jo 9.45 K. - No e 2 9.45k = ) 2 = In2 =) k= 11 0.0733. 9.45 B Given Nlt)- 10 ºb o No = 10 -kt Noe No 10 Inio kt e ta In 1o =) - 31.41 minuts = ) 10= 0.07 33 Using Log 9.45 K from the equation 2- e sides we Taking log both both get log 2- 9.45k loge

1 - Ka 0.073 3 log 2 9. 45x loge both sides we (get From 10- ekt log 10= kt loge 31-41 minuty. z dog 10 kloge e k log any Given No= 20 gram At - 512, NIH) = 11 - 512K So 11= 20e - 512k 11 c c n 512k In(20) L 512 I In/20) ka 0.001167. In a In2 0:001167 594 minuts.

we need to find N (4) when - 2500 kx2500 So N(2500) 20 e -0.001167 x2500 20 e 22. 1.08 13 grams diven N(+)- Igram - 1 20 é -kt kt ekt =) a =) ta 2567 minuty. I lnzo k