Final answer:
The half-life of the radioactive isotope is approximately 2.483 days.
Step-by-step explanation:
The half-life of a radioactive isotope can be determined using the formula:
T1/2 = (ln 2) / k
Where T1/2 is the half-life, and k is the decay constant.
In this case, we are given that a 72 gm sample decays to 18 gm in 6.2 days. To find the half-life, we need to solve for k:
k = (ln(initial mass/final mass)) / time
k = (ln(72 gm/18 gm)) / 6.2 days
k = (ln(4)) / 6.2 days
Using the value of k, we can calculate the half-life:
T1/2 = (ln 2) / k
T1/2 = (ln 2) / ((ln(4)) / 6.2 days)
T1/2 ≈ 2.483 days