Answer:
Step-by-step explanation:
<u>Given:</u>
a. <u>compounded semiannually, n = 2</u>
b. <u>compounded quarterly, n = 4</u>
c. <u>compounded monthly, n = 12</u>
d. <u>compounded continuously</u>
Answer:
The approximate difference in the half-lives of the isotopes is 66 days.
Step-by-step explanation:
The decay of an isotope is represented by the following differential equation:
Where:
- Current mass of the isotope, measured in kilograms.
- Time, measured in days.
- Time constant, measured in days.
The solution of the differential equation is:
Where is the initial mass of the isotope, measure in kilograms.
Now, the time constant is cleared:
The half-life of a isotope () as a function of time constant is:
The half-life difference between isotope B and isotope A is:
If ,
and
, the difference in the half-lives of the isotopes is:
The approximate difference in the half-lives of the isotopes is 66 days.