After 5 days, a particular radioactive substance decays to 37% of its original amount. Find the half life of this substance.
Is this right?
Th= ln 2/ln(1/.37) x 5 days
Yes, I also got 3.48
Yes, you are correct. The half-life of a radioactive substance can be determined using the formula:
T₁/2 = (ln 2) / (ln (1/f))
where T₁/2 is the half-life of the substance and f is the fraction of the substance remaining after a certain time interval.
In this case, the substance decays to 37% of its original amount after 5 days. So, the fraction remaining (f) is 0.37.
Substituting the values into the formula:
T₁/2 = (ln 2) / (ln (1/0.37)) * 5 days
Simplifying further:
T₁/2 = (ln 2) / (ln (2.7)) * 5 days
So, the expression you provided, Th = (ln 2) / (ln (1/0.37)) * 5 days, is correct.