How long will it take for a radioactive isotope with a decay constant of 0.15 (which means a half life of 4.6 days ) to decay to 5% of its original value?

(At = A0e-kt)

Question

How long will it take for a radioactive isotope with a decay constant of 0.15 (which means a half life of 4.6 days ) to decay to 5% of its original value?

(At = A0e-kt)

SmokeyBrown · Answer

Hi, and welcome to QuestionCove!

In order to find the amount of time needed for the sample to decay to 5% (or 0.05 of) its original amount, plug the values you are given into the formula and solve for t

In this case, "At" can be 0.05, "A0" can be 1, "e" is a constant (equal to about 2.718281828459045), and "k" is 0.15
Solving for "t" in this equation should give you the amount of time in seconds, which you can convert to any other unit you like