The question is incomplete, here is the complete question:
1. The radioactive source you will be working with in this lab is Cs-137. Look up the half-life of this material and report the value in units of seconds.
2. The relationship between decay constant (l) and half-life is:
![t_{1/2}=\frac{\ln 2}{k}](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%3D%5Cfrac%7B%5Cln%202%7D%7Bk%7D)
For Cs-137, what is the value of 'k' in ![s^{-1}](https://tex.z-dn.net/?f=s%5E%7B-1%7D)
<u>Answer:</u>
<u>For 1:</u> The half life for Cs-137 isotope is ![9.51\times 10^8s](https://tex.z-dn.net/?f=9.51%5Ctimes%2010%5E8s)
<u>For 2:</u> The rate constant of Cs-137 isotope is ![7.29\times 10^{-10}s^{-1}](https://tex.z-dn.net/?f=7.29%5Ctimes%2010%5E%7B-10%7Ds%5E%7B-1%7D)
<u>Explanation:</u>
Half life is defined as the time taken for half of the reaction to complete. This is also defined as the time in which the concentration of a reactant is reduced to half of its original value.
The half life for Cs-137 isotope is ![9.51\times 10^8s](https://tex.z-dn.net/?f=9.51%5Ctimes%2010%5E8s)
The relationship between decay constant (l) and half-life is: given by the equation:
![t_{1/2}=\frac{\ln 2}{k}](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%3D%5Cfrac%7B%5Cln%202%7D%7Bk%7D)
where,
= half life of Cs-137 isotope = ![9.51\times 10^8s](https://tex.z-dn.net/?f=9.51%5Ctimes%2010%5E8s)
k = rate constant
Putting values in above equation, we get:
![9.51\times 10^8s=\frac{\ln 2}{k}\\\\k=\frac{\ln 2}{9.51\times 10^8}=7.29\times 10^{-10}s^{-1}](https://tex.z-dn.net/?f=9.51%5Ctimes%2010%5E8s%3D%5Cfrac%7B%5Cln%202%7D%7Bk%7D%5C%5C%5C%5Ck%3D%5Cfrac%7B%5Cln%202%7D%7B9.51%5Ctimes%2010%5E8%7D%3D7.29%5Ctimes%2010%5E%7B-10%7Ds%5E%7B-1%7D)
Hence, the rate constant of Cs-137 isotope is ![7.29\times 10^{-10}s^{-1}](https://tex.z-dn.net/?f=7.29%5Ctimes%2010%5E%7B-10%7Ds%5E%7B-1%7D)