Hi could you please help me with this? The activity of a radioactive source falls from 600 to 100 in 6 hours. What is the half-life of the isotope? I'm completely stuck :(

You can solve your problem using the equation image where N(t) is the number of atoms at a given time t, N_0 is the number of atoms at t = 0, and lambda is the decay constant.

The activity (A) can be written as image so we can multiply both factors for lambda and have the equation that will solve our problem:
image  since we know A(t), A_0 and t from the data of our problem we can find lambda.
image , image, image

Since image the half-life of our isotope is t_(1/2) = 2.32 hours.

I really hoped this helped you! Let us know if you need any more clarification on the matter of radioactive decay!

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